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---

 <u><h1 align="center">INDEX</h1></u>
 
 | Serial No. | Problem Statement                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | Page No. | Teacher's Signature |
 | ---------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------- | ------------------- |
 | 1          | Write a program to implement a Diagonal Matrix, a Lower Triangular Matrix, an Upper Triangular Matrix, and a Symmetric Matrix using a one-dimensional array.                                                                                                                                                                                                                                                                                                                                                                                              | 2        |                     |
 | 2          | Write a program to search an element from a list. Give user the option to perform Linear or Binary search.                                                                                                                                                                                                                                                                                                                                                                                                                                                | 9        |                     |
 | 3          | WAP to sort a list of elements. Give user the option to perform sorting using Insertion sort, Bubble sort or Selection sort.                                                                                                                                                                                                                                                                                                                                                                                                                              | 15       |                     |
 | 4          | Implement Linked List. Include functions for insertion, deletion and search of a number, reverse the list and concatenate two linked lists (include a function and also overload operator +).                                                                                                                                                                                                                                                                                                                                                             | 21       |                     |
 | 5          | Implement Doubly Linked List. Include functions for insertion, deletion and search of a number, reverse the list.                                                                                                                                                                                                                                                                                                                                                                                                                                         | 31       |                     |
 | 6          | Implement Circular Linked List. Include functions for insertion, deletion and search of a number, reverse the list.                                                                                                                                                                                                                                                                                                                                                                                                                                       | 40       |                     |
 | 7          | Perform Stack operations using Linked List implementation.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 50       |                     |
 | 8          | Perform Stack operations using Array implementation.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | 55       |                     |
 | 9          | Perform Queue operations using Array.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 59       |                     |
 | 10         | Perform Circular Queue operations using Array.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | 64       |                     |
 | 11         | Perform Queue operations using Linked List.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               | 69       |                     |
 | 12         | Create and perform different operations on Double-ended Queues using Linked List implementation.                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 73       |                     |
 | 13         | WAP to scan a polynomial using linked list and add two polynomials.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | 79       |                     |
 | 14         | WAP to calculate factorial and to compute the factors of a given no. (i) using recursion, (ii) using iteration.                                                                                                                                                                                                                                                                                                                                                                                                                                           | 85       |                     |
 | 15         | WAP to display Fibonacci series (i) using recursion, (ii) using iteration.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 89       |                     |
 | 16         | WAP to create a Binary Search Tree and include following operations in tree: i. Insertion (Recursive and Iterative Implementation) ii. Deletion by copying iii. Deletion by Merging iv. Search a no. in BST v. Display its preorder, postorder and inorder traversals Recursively vi. Display its preorder, postorder and inorder traversals Iteratively vii. Display its level-by-level traversals viii. Count the non-leaf nodes and leaf nodes ix. Display height of tree x. Create a mirror image of tree xi. Check whether two BSTs are equal or not | 92       |                     |
 | 17         | WAP to convert the Sparse Matrix into non-zero form and vice-versa.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | 110      |                     |
 | 18         | WAP to reverse the order of the elements in the stack using additional stack.                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 116      |                     |
 | 19         | WAP to reverse the order of the elements in the stack using additional Queue.                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 120      |                     |
 ///
 ## Assignment 1
 
 ### Problem Statement: 
 Write a program to implement a Diagonal Matrix, a Lower Triangular Matrix, an Upper Triangular Matrix, and a Symmetric Matrix using a one-dimensional array.
 
 ### Problem Definition: 
 Matrix memory optimization means storing special matrices efficiently by avoiding storage of predictable zero or duplicate elements, using compact 1D array instead of full 2D array.
 - **Diagonal Matrix:** Only diagonal elements `(i == j)` are non-zero. Stored using the formula `arr[i]`.
 - **Lower Triangular Matrix:** All elements above the main diagonal are zero. Non-zero elements mapped using `i*(i+1)/2 + j`.
 - **Upper Triangular Matrix:** All elements below the main diagonal are zero. Non-zero elements mapped using `n*i - i*(i-1)/2 + (j-i)`.
 - **Symmetric Matrix:** Matrix equal to its transpose `(A[i][j] = A[j][i])`. Only the lower triangular half is stored, using `i*(i+1)/2 + j`.
 
 ### Algorithm: 
 **Diagonal Matrix:** 
 ```
 procedure setDiagonal(arr, i, j, x)
 begin
 	if(i == j)
 		arr[i] <- x;
 	end if
 end procedure
 
 procedure getDiagonal(arr, i, j)
 begin
 	if(i == j)
 		return arr[i];
 	else
 		return 0;
 	end if
 end procedure
 ```
 
 **Lower Triangular Matrix:**
 ```
 procedure setLower(arr, i, j, x)
 begin
 	if(i >= j)
 		arr[i*(i+1)/2+j] <- x;
 	end if
 end procedure
   
 procedure getLower(arr, i, j)
 begin
 	if(i >= j)
 		return arr[i*(i+1)/2+j];
 	else
 		return 0;
 	end if
 end procedure
 ```  
 
 **Upper Triangular Matrix:**
 ```
 Procedure setUpper(arr, n, i, j, x)
 begin
 	if(i <= j)
 		arr[n*i-i*(i-1)/2+(j-i)] <- x;
 	end if
 end procedure
 
 Procedure getUpper(arr, n, i, j)
 begin
 	if(i <= j)
 		return arr[n*i-i*(i-1)/2+(j-i)];
 	else
 		return 0;
 	end if
 end procedure
 ```
 
 **Symmetric Matrix:**
 ```
 Procedure setSymmetric(arr, i, j, x)
 begin
 	if(i >= j)
 		arr[i*(i+1)/2+j] <- x;
 	else
 		arr[j*(j+1)/2+i] <- x;
 	end if
 end procedure
 
 Procedure getSymmetric(arr, i, j)
 begin
 	if(i >= j)
 		return arr[i*(i+1)/2+j];
 	else
 		return arr[j*(j+1)/2+i];
 	end if
 end procedure
 ```
 
 ///
 ### Source Code: 
 ```
 #include <iostream>
 
 using namespace std;
 
 class Matrix
 {
 private:
   int n, *arr;
 
 public:
   Matrix(int size)
   {
     n = size;
     arr = new int[n * (n + 1) / 2];
   }
 
   void setDiagonal(int i, int j, int x)
   {
     if (i == j)
       arr[i] = x;
   }
   void setLowerTri(int i, int j, int x)
   {
     if (i >= j)
       arr[i * (i + 1) / 2 + j] = x;
   }
   void setUpperTri(int i, int j, int x)
   {
     if (i <= j)
       arr[n * i - (i * (i - 1) / 2) + (j - i)] = x;
   }
   void setSymmetric(int i, int j, int x)
   {
     (i >= j) ? arr[i * (i + 1) / 2 + j] = x : arr[j * (j + 1) / 2 + i] = x;
   }
 
   int getDiagonal(int i, int j)
   {
     return (i == j) ? arr[i] : 0;
   }
   int getLowerTri(int i, int j)
   {
     return (i >= j) ? arr[i * (i + 1) / 2 + j] : 0;
   }
   int getUpperTri(int i, int j)
   {
     return (i <= j) ? arr[n * i - i * (i - 1) / 2 + (j - i)] : 0;
   }
   int getSymmetric(int i, int j)
   {
     return (i >= j) ? arr[i * (i + 1) / 2 + j] : arr[j * (j + 1) / 2 + i];
   }
 
   void display(int type)
   {
     cout << endl
          << "Matrix:" << endl;
     for (int i = 0; i < n; i++)
     {
       for (int j = 0; j < n; j++)
       {
         if (type == 1)
           cout << getDiagonal(i, j) << " ";
         else if (type == 2)
           cout << getLowerTri(i, j) << " ";
         else if (type == 3)
           cout << getUpperTri(i, j) << " ";
         else if (type == 4)
           cout << getSymmetric(i, j) << " ";
       }
       cout << endl;
     }
   }
 
   ~Matrix()
   {
     delete[] arr;
   }
 };
 
 int main()
 {
   int n, choice, x;
   cout << "Enter the order of the matrix : ";
   cin >> n;
   Matrix M(n);
 
   cout << "\n1. Diagonal Matrix.";
   cout << "\n2. Lower Triangular Matrix.";
   cout << "\n3. Upper Triangular Matrix.";
   cout << "\n4. Symmetric Matrix.";
   cout << "\nEnter your choice : ";
   cin >> choice;
 
   switch (choice)
   {
   case 1:
     cout << "\nEnter the diagonal elements : ";
     for (int i = 0; i < n; i++)
     {
       cin >> x;
       M.setDiagonal(i, i, x);
     }
     M.display(1);
     break;
 
   case 2:
     cout << "\nEnter the elements : ";
     for (int i = 0; i < n; i++)
     {
       for (int j = 0; j <= i; j++)
       {
         cin >> x;
         M.setLowerTri(i, j, x);
       }
     }
     M.display(2);
     break;
 
   case 3:
     cout << "\nEnter the elements : ";
     for (int i = 0; i < n; i++)
     {
       for (int j = i; j < n; j++)
       {
         cin >> x;
         M.setUpperTri(i, j, x);
       }
     }
     M.display(3);
     break;
 
   case 4:
     cout << "\nEnter the elements : ";
     for (int i = 0; i < n; i++)
     {
       for (int j = 0; j <= i; j++)
       {
         cin >> x;
         M.setSymmetric(i, j, x);
       }
     }
     M.display(4);
     break;
 
   default:
     cout << "Invalid Choice.";
   }
   return 0;
 }
 ```
 
 ### Output: 
 ![[Pasted image 20260922092253.png|431]]
 
 ![[Pasted image 20260922092306.png|431]]
 
 ### Discussion: 
 This program demonstrates how memory can be saved when working with special types of matrices — **Diagonal**, **Lower Triangular**, **Upper Triangular**, and **Symmetric** — by storing only their essential elements in a single dynamically allocated 1D array, rather than a full 2D array.
 
 A **Matrix** class is used to bundle together the storage (the array) and the logic needed to interpret it correctly for each matrix type.
   
 Two private members drive the class:
 
 - **arr** - a dynamically allocated integer pointer that holds the compact array of stored values.
 - **n** - the order (size) of the square matrix.
 
 When a **Matrix** object is created, the constructor computes the array size as **n*(n+1)/2** and allocates it on the heap using **new**.
 
 The class's functionality is built around these key methods:
 
 - **setDiagonal()**, **setLowerTri()**, **setUpperTri()** and **setSymmetric()** – Each of these accepts a row index, column index, and a value, then applies a matrix-specific formula to determine exactly where that value should be placed in the 1D array.
 - **getDiagonal()**, **getLowerTri()**, **getUpperTri()** and **getSymmetric()** – These reconstruct values for any **(i, j)** position by locating them in the array (using ternary conditions), returning 0 for positions that were never stored, and — in the Symmetric case — reflecting values across the diagonal when needed.
 - **display()** – Using two nested loops, this method walks through every position of the conceptual n×n matrix and prints the corresponding value, effectively rebuilding the full matrix view from the compact array.
 
 Finally, the destructor **~Matrix()** ensures proper cleanup by releasing the dynamically allocated array with **delete[]** once the object goes out of scope, preventing memory leaks.
 
 ///
 ## Assignment 2
 ### Problem Statement:
 Write a program to search an element from a list of elements using Linear Search and Binary Search techniques.
 
 ### Problem Definition:
 Searching is the process of finding whether a particular element is present in a given collection of elements, and if present, locating its position.
 
 - **Linear Search:** Examines each element of the list sequentially, one by one, starting from the first, until the desired element is found or the list ends. It works on both sorted and unsorted lists but has a time complexity of `O(n)`.
 - **Binary Search:** Works only on a sorted list. It repeatedly divides the search interval in half — comparing the key with the middle element and eliminating the half of the list where the key cannot exist — giving a time complexity of `O(log n)`.
 
 ### Algorithm:
 **Linear Search:**
 ```
 procedure linearSearch(arr, n, key)
 begin
 	for i ← 0 to n - 1 do
 		if(arr[i] = key)
 			return i;
 		end if
 	end for
 	return -1;
 end procedure
 ```
 
 **Binary Search:**
 ```
 procedure binarySearch(arr, n, key)
 begin
 	call insertionSort(arr, n);
 	left ← 0;
 	right ← n - 1;
 	while(left <= right) do
 		mid ← left + (right - left) / 2;
 		if(arr[mid] = key)
 			return mid;
 		else if(arr[mid] < key)
 			left ← mid + 1;
 		else
 			right ← mid - 1;
 		end if
 	end while
 	return -1;
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 #include <iomanip>
 using namespace std;
 
 typedef struct MenuItem {
     int id;
     const char* name;
 } menu;
 
 class SearchList {
 private:
     int *arr;
     int n;
 
     void insertionSort() {
         for (int i = 1; i < n; i++) {
             int key = arr[i];
             int j = i - 1;
             while (j >= 0 && arr[j] > key) {
                 arr[j + 1] = arr[j];
                 j--;
             }
             arr[j + 1] = key;
         }
     }
 
 public:
     SearchList(int size) {
         n = size;
         arr = new int[n];
     }
 
     void inputElements() {
         cout << "\nEnter " << n << " elements: ";
         for (int i = 0; i < n; i++) {
             cin >> arr[i];
         }
     }
 
     int linearSearch(int key) {
         for (int i = 0; i < n; i++) {
             if (arr[i] == key) {
                 return i;
             }
         }
         return -1;
     }
 
     int binarySearch(int key) {
         
         insertionSort();
         cout << "\n(Array automatically sorted for Binary Search)";
         display();
 
         int left = 0;
         int right = n - 1;
 
         while (left <= right) {
             int mid = left + (right - left) / 2;
 
             if (arr[mid] == key) {
                 return mid;
             } else if (arr[mid] < key) {
                 left = mid + 1;
             } else {
                 right = mid - 1;
             }
         }
         return -1;
     }
 
     void display() {
         cout << "\nCurrent List: ";
         for (int i = 0; i < n; i++) {
             cout << arr[i] << " ";
         }
         cout << endl;
     }
 
     void printMenu() {
         menu items[] = {
             {1, "Linear Search"}, {2, "Binary Search"},
             {0, "Display List"},  {-1, "Exit"}
         };
 
         cout << "\n## Choose Search Method --\n--------------------------------------------\n";
         for (int i = 0; i < 4; i++) {
             cout << items[i].id << ". " << left << setw(20) << items[i].name;
             if (i % 2 == 1) cout << "\n";
         }
     }
 
     ~SearchList() {
         delete[] arr;
     }
 };
 
 int main() {
     int n, choice, key;
     cout << "Enter the size of the list: ";
     cin >> n;
 
     if (n <= 0) {
         cout << "Invalid list size!\n";
         return 0;
     }
 
     SearchList list(n);
     list.inputElements();
 
     while (true) {
         list.printMenu();
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: {
                 cout << "\nEnter element to search: ";
                 cin >> key;
                 int index = list.linearSearch(key);
                 if (index != -1)
                     cout << "\nElement " << key << " found at index " << index << ".\n";
                 else
                     cout << "\nElement " << key << " not found in the list.\n";
                 break;
             }
             case 2: {
                 cout << "\nEnter element to search: ";
                 cin >> key;
                 int index = list.binarySearch(key);
                 if (index != -1)
                     cout << "\nElement " << key << " found at index " << index << " in sorted array.\n";
                 else
                     cout << "\nElement " << key << " not found in the list.\n";
                 break;
             }
             case 0:
                 list.display();
                 break;
             case -1:
                 cout << "\nExiting program.....\nMemory cleared!\nExit 0\n";
                 return 0;
             default:
                 cout << "\nEntered wrong choice. Try again.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260922133534.png|400]]
 
 ![[Pasted image 20260922133550.png|402]]
 
 ### Discussion:
 This program demonstrates two fundamental searching techniques — **Linear Search** and **Binary Search** — wrapped inside a **SearchList** class that manages a dynamically allocated array of integers.
 
 Two private members support the class:
 
 - **arr** – a dynamically allocated integer pointer holding the list of elements.
 - **n** – the total number of elements in the list.
 
 A helper method, **insertionSort()**, is kept private since it is only meant to be used internally to prepare the array before a binary search is performed.
 
 The class exposes the following key methods:
 
 - **inputElements()** – Reads `n` integers from the user into the array.
 - **linearSearch()** – Iterates through the array sequentially, comparing each element with the key, and returns the index where a match is found, or `-1` if the key doesn't exist in the list.
 - **binarySearch()** – First sorts the array using **insertionSort()**, since binary search only works correctly on sorted data, then uses two pointers, **left** and **right**, to repeatedly narrow down the search range by comparing the key against the middle element until it is found or the range is exhausted.
 - **display()** – Prints all current elements of the list.
 - **printMenu()** – Uses a globally defined `MenuItem` struct (aliased as `menu`) to store menu options as `{id, name}` pairs in a local array, then loops through and prints them in a formatted two-column layout using `setw()`.
 
 The **main()** function drives the program using an infinite loop with a `switch` statement, allowing the user to repeatedly choose between performing a linear search, a binary search, displaying the list, or exiting the program. Since binary search requires sorted data, the program automatically sorts and displays the array before performing that operation, keeping the underlying array consistent for future operations.
 
 Finally, the destructor **~SearchList()** releases the dynamically allocated array using **delete[]** when the object is destroyed, avoiding memory leaks.
 
 ///
 ## Assignment 3
 ### Problem Statement:
 Write a program to sort a list of elements. Give the user the option to perform sorting using Insertion Sort, Bubble Sort, or Selection Sort.
 
 ### Problem Definition:
 Sorting is the process of arranging elements of a list in a particular order (ascending/descending).
 
 - **Insertion Sort:** Builds the sorted list one element at a time by picking an element and inserting it into its correct position among the already-sorted part. Time complexity `O(n²)`.
 - **Bubble Sort:** Repeatedly compares adjacent elements and swaps them if out of order, pushing the largest element to the end each pass. Time complexity `O(n²)`.
 - **Selection Sort:** Repeatedly finds the minimum element from the unsorted part and places it at the beginning. Time complexity `O(n²)`.
 
 ### Algorithm:
 **Insertion Sort:**
 ```
 procedure insertionSort(arr, n)
 begin
 	for i ← 1 to n - 1 do
 		key ← arr[i];
 		j ← i - 1;
 		while(j >= 0 and arr[j] > key) do
 			arr[j + 1] ← arr[j];
 			j ← j - 1;
 		end while
 		arr[j + 1] ← key;
 	end for
 end procedure
 ```
 
 **Bubble Sort:**
 ```
 procedure bubbleSort(arr, n)
 begin
 	for i ← 0 to n - 2 do
 		swapped ← false;
 		for j ← 0 to n - i - 2 do
 			if(arr[j] > arr[j + 1])
 				swap(arr[j], arr[j + 1]);
 				swapped ← true;
 			end if
 		end for
 		if(swapped = false)
 			break;
 		end if
 	end for
 end procedure
 ```
 
 **Selection Sort:**
 ```
 procedure selectionSort(arr, n)
 begin
 	for i ← 0 to n - 2 do
 		minIdx ← i;
 		for j ← i + 1 to n - 1 do
 			if(arr[j] < arr[minIdx])
 				minIdx ← j;
 			end if
 		end for
 		if(minIdx ≠ i)
 			swap(arr[i], arr[minIdx]);
 		end if
 	end for
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 #include <iomanip>
 using namespace std;
 
 typedef struct MenuItem {
     int id;
     const char* name;
 } menu;
 
 class SortList {
 private:
     int *arr;
     int *tempArr;
     int n;
 
     void swapElements(int &a, int &b) {
         int temp = a;
         a = b;
         b = temp;
     }
 
     void reset() {
         for (int i = 0; i < n; i++) tempArr[i] = arr[i];
     }
 
 public:
     SortList(int size) {
         n = size;
         arr = new int[n];
         tempArr = new int[n];
     }
 
     void inputElements() {
         cout << "\nEnter " << n << " elements: ";
         for (int i = 0; i < n; i++) {
             cin >> arr[i];
             tempArr[i] = arr[i];
         }
     }
 
     void insertionSort() {
         reset();
         for (int i = 1; i < n; i++) {
             int key = tempArr[i];
             int j = i - 1;
             while (j >= 0 && tempArr[j] > key) {
                 tempArr[j + 1] = tempArr[j];
                 j--;
             }
             tempArr[j + 1] = key;
         }
         display();
     }
 
     void bubbleSort() {
         reset();
         for (int i = 0; i < n - 1; i++) {
             bool swapped = false;
             for (int j = 0; j < n - i - 1; j++) {
                 if (tempArr[j] > tempArr[j + 1]) {
                     swapElements(tempArr[j], tempArr[j + 1]);
                     swapped = true;
                 }
             }
             if (!swapped) break;
         }
         display();
     }
 
     void selectionSort() {
         reset();
         for (int i = 0; i < n - 1; i++) {
             int minIdx = i;
             for (int j = i + 1; j < n; j++) {
                 if (tempArr[j] < tempArr[minIdx]) minIdx = j;
             }
             if (minIdx != i) swapElements(tempArr[i], tempArr[minIdx]);
         }
         display();
     }
 
     void display() {
         cout << "Sorted Array: ";
         for (int i = 0; i < n; i++) cout << tempArr[i] << " ";
         cout << endl;
     }
 
     void displayOriginal() {
         cout << "\nOriginal List: ";
         for (int i = 0; i < n; i++) cout << arr[i] << " ";
         cout << endl;
     }
 
     void printMenu() {
         menu items[] = {
             {1, "Insertion Sort"}, {2, "Bubble Sort"},
             {3, "Selection Sort"}, {0, "Display Original"},
             {-1, "Exit"}
         };
         for (int i = 0; i < 5; i++) {
             cout << items[i].id << ". " << items[i].name << "\n";
         }
     }
 
     ~SortList() {
         delete[] arr;
         delete[] tempArr;
     }
 };
 
 int main() {
     int n, choice;
     cout << "Enter number of elements: ";
     cin >> n;
     if (n <= 0) {
         cout << "Invalid size!\n";
         return 0;
     }
 
     SortList sorter(n);
     sorter.inputElements();
 
     while (true) {
         sorter.printMenu();
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: sorter.insertionSort(); break;
             case 2: sorter.bubbleSort(); break;
             case 3: sorter.selectionSort(); break;
             case 0: sorter.displayOriginal(); break;
             case -1:
                 cout << "\nExiting program.....\nMemory cleared!\nExit 0\n";
                 return 0;
             default:
                 cout << "\nEntered wrong choice. Try again.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260922133021.png|522]]
 <p align="right">Continue to next page...</p>
 ///
 ![[Pasted image 20260922102559.png|521]]
 ### Discussion:
 - **insertionSort()** copies `arr` into `tempArr` via `reset()`, then repeatedly takes an element (`key`) and shifts larger elements in the sorted left portion rightward until it finds the correct spot to insert the key.
 - **bubbleSort()** makes repeated passes, swapping adjacent out-of-order elements; a `swapped` flag lets it exit early once a pass makes no swaps, avoiding unnecessary iterations on an already-sorted array.
 - **selectionSort()** finds the index of the minimum element in the unsorted portion (`minIdx`) on each pass and swaps it into place at the front, growing the sorted portion by one each time.
 
 All three operate on `tempArr`, a working copy of the original `arr`, so the original input remains unaffected and can be displayed separately via `displayOriginal()`.
 
 ///
 ## Assignment 4
 ### Problem Statement:
 Implement a Singly Linked List. Include functions for insertion, deletion and search of a number, reverse the list, and concatenate two linked lists (include a function and also overload the `+` operator).
 
 ### Problem Definition:
 A **Linked List** is a linear data structure where elements (nodes) are connected using pointers, with each node storing data and a reference to the next node.
 
 - **Insertion/Deletion:** Adding or removing a node at the beginning, end, or a given position by adjusting pointer links.
 - **Search:** Traversing the list sequentially to find the position of a given value.
 - **Reverse:** Reversing the direction of the `next` pointers so the list traverses in the opposite order.
 - **Concatenation:** Joining two lists, done both via a function and an overloaded `+` operator. The function links the last node of the first list to the head of the second (modifying the first list), while `operator+` builds a brand-new list by copying the nodes of both lists.
 
 ### Algorithm:
 **Insertion at Beginning:**
 ```
 procedure insertAtBegin(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← head;
 	head ← newNode;
 end procedure
 ```
 
 **Insertion at End:**
 ```
 procedure insertAtEnd(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← NULL;
 	if(head = NULL)
 		head ← newNode;
 	else
 		temp ← head;
 		while(temp.next ≠ NULL) do
 			temp ← temp.next;
 		end while
 		temp.next ← newNode;
 	end if
 end procedure
 ```
 
 ///
 **Insertion at Position:**
 ```
 procedure insertAtPos(head, pos, val)
 begin
 	if(pos < 1)
 		print "Invalid Position";
 		return;
 	end if
 	if(pos = 1)
 		call insertAtBegin(head, val);
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 2 do
 		if(temp = NULL)
 			break;
 		end if
 		temp ← temp.next;
 	end for
 	if(temp = NULL)
 		print "Out of range";
 		return;
 	end if
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← temp.next;
 	temp.next ← newNode;
 end procedure
 ```
 
 **Deletion at Beginning:**
 ```
 procedure deleteAtBegin(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	temp ← head;
 	head ← head.next;
 	free temp;
 end procedure
 ```
 
 **Deletion at End:**
 ```
 procedure deleteAtEnd(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	if(head.next = NULL)
 		free head;
 		head ← NULL;
 		return;
 	end if
 	temp ← head;
 	while(temp.next.next ≠ NULL) do
 		temp ← temp.next;
 	end while
 	free temp.next;
 	temp.next ← NULL;
 end procedure
 ```
 
 **Deletion at Position:**
 ```
 procedure deleteAtPos(head, pos)
 begin
 	if(head = NULL or pos < 1)
 		print "Unable to process";
 		return;
 	end if
 	if(pos = 1)
 		call deleteAtBegin(head);
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 2 do
 		if(temp = NULL)
 			break;
 		end if
 		temp ← temp.next;
 	end for
 	if(temp = NULL or temp.next = NULL)
 		print "Out of range";
 		return;
 	end if
 	delNode ← temp.next;
 	temp.next ← delNode.next;
 	free delNode;
 end procedure
 ```
 
 **Search:**
 ```
 procedure search(head, key)
 begin
 	temp ← head;
 	pos ← 1;
 	while(temp ≠ NULL) do
 		if(temp.data = key)
 			return pos;
 		end if
 		temp ← temp.next;
 		pos ← pos + 1;
 	end while
 	return -1;
 end procedure
 ```
 
 **Reverse:**
 ```
 procedure reverse(head)
 begin
 	prev ← NULL;
 	curr ← head;
 	nxt ← NULL;
 	while(curr ≠ NULL) do
 		nxt ← curr.next;
 		curr.next ← prev;
 		prev ← curr;
 		curr ← nxt;
 	end while
 	head ← prev;
 end procedure
 ```
 
 **Concatenate:**
 ```
 procedure concatenate(head1, head2)
 begin
 	if(head1 = NULL)
 		head1 ← head2;
 		head2 ← NULL;
 		return;
 	end if
 	temp ← head1;
 	while(temp.next ≠ NULL) do
 		temp ← temp.next;
 	end while
 	temp.next ← head2;
 	head2 ← NULL;
 end procedure
 ```
 
 **Operator + (Concatenate into a New List):**
 ```
 procedure operator+(list1, list2)
 begin
 	result ← empty list;
 	temp ← list1.head;
 	while(temp ≠ NULL) do
 		call insertAtEnd(result, temp.data);
 		temp ← temp.next;
 	end while
 	temp ← list2.head;
 	while(temp ≠ NULL) do
 		call insertAtEnd(result, temp.data);
 		temp ← temp.next;
 	end while
 	return result;
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 typedef struct nodeType {
     int data;
     nodeType *next = nullptr;
 } node;
 
 class SinglyLinkedList {
 private:
     node *head;
 
 public:
     SinglyLinkedList() { head = nullptr; }
 
     SinglyLinkedList(const SinglyLinkedList &other) {
         head = nullptr;
         node *temp = other.head;
         while (temp != nullptr) {
             insertAtEnd(temp->data);
             temp = temp->next;
         }
     }
 
     void insertAtBegin(int val) {
         node *newNode = new node;
         newNode->data = val;
         newNode->next = head;
         head = newNode;
     }
 
     void insertAtEnd(int val) {
         node *newNode = new node;
         newNode->data = val;
         newNode->next = nullptr;
         if (head == nullptr) {
             head = newNode;
         } else {
             node *temp = head;
             while (temp->next != nullptr) temp = temp->next;
             temp->next = newNode;
         }
     }
 
     void insertAtPos(int pos, int val) {
         if (pos < 1) { cout << "Invalid Position!\n"; return; }
         if (pos == 1) { insertAtBegin(val); return; }
         node *temp = head;
         for (int i = 1; i < pos - 1 && temp != nullptr; i++) temp = temp->next;
         if (temp == nullptr) { cout << "Out of range!\n"; return; }
         node *newNode = new node;
         newNode->data = val;
         newNode->next = temp->next;
         temp->next = newNode;
     }
 
     void deleteAtBegin() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         node *temp = head;
         head = head->next;
         delete temp;
     }
 
     void deleteAtEnd() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         if (head->next == nullptr) { delete head; head = nullptr; return; }
         node *temp = head;
         while (temp->next->next != nullptr) temp = temp->next;
         delete temp->next;
         temp->next = nullptr;
     }
 
     void deleteAtPos(int pos) {
         if (head == nullptr || pos < 1) { cout << "Unable to process!\n"; return; }
         if (pos == 1) { deleteAtBegin(); return; }
         node *temp = head;
         for (int i = 1; i < pos - 1 && temp != nullptr; i++) temp = temp->next;
         if (temp == nullptr || temp->next == nullptr) { cout << "Out of range!\n"; return; }
         node *delNode = temp->next;
         temp->next = delNode->next;
         delete delNode;
     }
 
     int search(int key) {
         node *temp = head;
         int pos = 1;
         while (temp != nullptr) {
             if (temp->data == key) return pos;
             temp = temp->next;
             pos++;
         }
         return -1;
     }
 
     void reverse() {
         node *prev = nullptr, *curr = head, *nxt = nullptr;
         while (curr != nullptr) {
             nxt = curr->next;
             curr->next = prev;
             prev = curr;
             curr = nxt;
         }
         head = prev;
     }
 
     void concatenate(SinglyLinkedList &other) {
         if (head == nullptr) { head = other.head; other.head = nullptr; return; }
         node *temp = head;
         while (temp->next != nullptr) temp = temp->next;
         temp->next = other.head;
         other.head = nullptr;
     }
 
     SinglyLinkedList operator+(const SinglyLinkedList &other) const {
         SinglyLinkedList result;
         node *temp = head;
         while (temp != nullptr) { result.insertAtEnd(temp->data); temp = temp->next; }
         temp = other.head;
         while (temp != nullptr) { result.insertAtEnd(temp->data); temp = temp->next; }
         return result;
     }
 
     void display() const {
         node *temp = head;
         cout << "List: ";
         while (temp != nullptr) { cout << temp->data << " -> "; temp = temp->next; }
         cout << "nullptr\n";
     }
 
     void printMenu() {
         cout << "1.insertAtBegin 2.insertAtEnd 3.insertAtPos 4.deleteAtBegin 5.deleteAtEnd \n"
              << "6.deleteAtPos 7.search 8.reverse 9.concatenate 10.operator+ 0.Display -1.Exit\n";
     }
 
     ~SinglyLinkedList() {
         node *temp;
         while (head != nullptr) { temp = head; head = head->next; delete temp; }
     }
 };
 
 int main() {
     SinglyLinkedList list1;
     int choice, val, pos;
 
     while (true) {
         list1.printMenu();
         cout << "Enter your choice: ";
         cin >> choice;
         switch (choice) {
             case 1: cout << "Enter value: "; cin >> val; list1.insertAtBegin(val); break;
             case 2: cout << "Enter value: "; cin >> val; list1.insertAtEnd(val); break;
             case 3:
                 cout << "Enter position: "; cin >> pos;
                 cout << "Enter value: "; cin >> val;
                 list1.insertAtPos(pos, val);
                 break;
             case 4: list1.deleteAtBegin(); break;
             case 5: list1.deleteAtEnd(); break;
             case 6: cout << "Enter position: "; cin >> pos; list1.deleteAtPos(pos); break;
             case 7: {
                 cout << "Enter value to search: "; cin >> val;
                 int res = list1.search(val);
                 if (res != -1) cout << "Found at position " << res << ".\n";
                 else cout << "Not found.\n";
                 break;
             }
             case 8: list1.reverse(); break;
             case 9: {
                 SinglyLinkedList list2;
                 int m, tempVal;
                 cout << "Enter number of elements in second list: "; cin >> m;
                 for (int i = 0; i < m; i++) { cin >> tempVal; list2.insertAtEnd(tempVal); }
                 list1.concatenate(list2);
                 break;
             }
             case 10: {
                 SinglyLinkedList list2;
                 int m, tempVal;
                 cout << "Enter number of elements in second list: "; cin >> m;
                 for (int i = 0; i < m; i++) { cin >> tempVal; list2.insertAtEnd(tempVal); }
                 SinglyLinkedList combined = list1 + list2;
                 combined.display();
                 break;
             }
             case 0: list1.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice. Try again.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260922135426.png|623]]
 <p align="right" >Continue to next page...</p>
 ///
 ![[Pasted image 20260922135454.png|561]]
 ### Discussion:
 - **insertAtBegin/insertAtEnd/insertAtPos** create a new node and link it into the chain — at the head, by traversing to the last node, or by traversing to the node just before the target position.
 - **deleteAtBegin/deleteAtEnd/deleteAtPos** unlink a node by redirecting the previous node's `next` pointer around it before freeing it, with edge cases handled for an empty list or a single-node list.
 - **search()** traverses the list sequentially, comparing each node's data with the key, returning its 1-based position or `-1`.
 - **reverse()** rebuilds the list by walking through it once, flipping each node's `next` pointer to point backward using three tracking pointers (`prev`, `curr`, `nxt`).
 - **concatenate()** links the last node of the calling list directly to the head of the other list, modifying the calling list in place.
 - **operator+** builds an entirely new list by copying all nodes from both lists in sequence, leaving both original lists unmodified.
 ///
 ## Assignment 5
 ### Problem Statement:
 Implement a Doubly Linked List. Include functions for insertion, deletion and search of a number, and reverse the list.
 
 ### Problem Definition:
 A **Doubly Linked List** is a linear data structure where each node stores data along with two pointers — `prev` and `next` — pointing to the previous and next nodes, allowing traversal in both directions.
 
 - **Insertion/Deletion:** Adding or removing a node at the beginning, end, or a given position by updating both `prev` and `next` links.
 - **Search:** Traversing the list sequentially to find the position of a given value.
 - **Reverse:** Swapping the `prev` and `next` pointers of every node so the list's direction is flipped.
 
 ### Algorithm:
 **Insertion at Beginning:**
 ```
 procedure insAtBegin(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.prev ← NULL;
 	newNode.next ← head;
 	if(head ≠ NULL)
 		head.prev ← newNode;
 	end if
 	head ← newNode;
 end procedure
 ```
 
 **Insertion at End:**
 ```
 procedure insAtEnd(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← NULL;
 	if(head = NULL)
 		newNode.prev ← NULL;
 		head ← newNode;
 	else
 		temp ← head;
 		while(temp.next ≠ NULL) do
 			temp ← temp.next;
 		end while
 		temp.next ← newNode;
 		newNode.prev ← temp;
 	end if
 end procedure
 ```
 
 **Insertion at Position:**
 ```
 procedure insAtPos(head, pos, val)
 begin
 	if(pos < 1)
 		print "Invalid Position";
 		return;
 	end if
 	if(pos = 1)
 		call insAtBegin(head, val);
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 2 do
 		if(temp = NULL)
 			break;
 		end if
 		temp ← temp.next;
 	end for
 	if(temp = NULL)
 		print "Out of range";
 		return;
 	end if
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← temp.next;
 	newNode.prev ← temp;
 	if(temp.next ≠ NULL)
 		temp.next.prev ← newNode;
 	end if
 	temp.next ← newNode;
 end procedure
 ```
 
 **Deletion at Beginning:**
 ```
 procedure delAtBegin(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	temp ← head;
 	head ← head.next;
 	if(head ≠ NULL)
 		head.prev ← NULL;
 	end if
 	free temp;
 end procedure
 ```
 
 **Deletion at End:**
 ```
 procedure delAtEnd(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	if(head.next = NULL)
 		free head;
 		head ← NULL;
 		return;
 	end if
 	temp ← head;
 	while(temp.next ≠ NULL) do
 		temp ← temp.next;
 	end while
 	temp.prev.next ← NULL;
 	free temp;
 end procedure
 ```
 
 **Deletion at Position:**
 ```
 procedure delAtPos(head, pos)
 begin
 	if(head = NULL or pos < 1)
 		print "Unable to process";
 		return;
 	end if
 	if(pos = 1)
 		call delAtBegin(head);
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 1 do
 		if(temp = NULL)
 			break;
 		end if
 		temp ← temp.next;
 	end for
 	if(temp = NULL)
 		print "Out of range";
 		return;
 	end if
 	if(temp.next ≠ NULL)
 		temp.next.prev ← temp.prev;
 	end if
 	if(temp.prev ≠ NULL)
 		temp.prev.next ← temp.next;
 	end if
 	free temp;
 end procedure
 ```
 
 **Search:**
 ```
 procedure search(head, key)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	temp ← head;
 	pos ← 1;
 	while(temp ≠ NULL) do
 		if(temp.data = key)
 			print "Found at position: ", pos;
 			return;
 		end if
 		temp ← temp.next;
 		pos ← pos + 1;
 	end while
 	print "Element not found";
 end procedure
 ```
 
 **Reverse:**
 ```
 procedure reverse(head)
 begin
 	if(head = NULL or head.next = NULL)
 		return;
 	end if
 	curr ← head;
 	temp ← NULL;
 	while(curr ≠ NULL) do
 		temp ← curr.prev;
 		curr.prev ← curr.next;
 		curr.next ← temp;
 		curr ← curr.prev;
 	end while
 	if(temp ≠ NULL)
 		head ← temp.prev;
 	end if
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 typedef struct nodeType {
     int data;
     nodeType *prev = nullptr;
     nodeType *next = nullptr;
 } node;
 
 class DoublyLinkedList {
 private:
     node *head;
 
 public:
     DoublyLinkedList() { head = nullptr; }
 
     void insAtBegin() {
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->prev = nullptr;
         newNode->next = head;
         if (head != nullptr) head->prev = newNode;
         head = newNode;
     }
 
     void insAtEnd() {
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->next = nullptr;
         if (head == nullptr) {
             newNode->prev = nullptr;
             head = newNode;
         } else {
             node *temp = head;
             while (temp->next != nullptr) temp = temp->next;
             temp->next = newNode;
             newNode->prev = temp;
         }
     }
 
     void insAtPos() {
         int pos;
         cout << "Enter the position: ";
         cin >> pos;
         if (pos < 1) { cout << "Invalid Position!\n"; return; }
         if (pos == 1) { insAtBegin(); return; }
         node *temp = head;
         for (int i = 1; i < pos - 1 && temp != nullptr; i++) temp = temp->next;
         if (temp == nullptr) { cout << "Out of range!\n"; return; }
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->next = temp->next;
         newNode->prev = temp;
         if (temp->next != nullptr) temp->next->prev = newNode;
         temp->next = newNode;
     }
 
     void delAtBegin() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         node *temp = head;
         head = head->next;
         if (head != nullptr) head->prev = nullptr;
         delete temp;
     }
 
     void delAtEnd() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         if (head->next == nullptr) { delete head; head = nullptr; return; }
         node *temp = head;
         while (temp->next != nullptr) temp = temp->next;
         temp->prev->next = nullptr;
         delete temp;
     }
 
     void delAtPos() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         int pos;
         cout << "Enter the position: ";
         cin >> pos;
         if (pos < 1) { cout << "Invalid Position!\n"; return; }
         if (pos == 1) { delAtBegin(); return; }
         node *temp = head;
         for (int i = 1; i < pos && temp != nullptr; i++) temp = temp->next;
         if (temp == nullptr) { cout << "Out of range!\n"; return; }
         if (temp->next != nullptr) temp->next->prev = temp->prev;
         if (temp->prev != nullptr) temp->prev->next = temp->next;
         delete temp;
     }
 
     void search() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         int key, pos = 1;
         cout << "Enter the element to search: ";
         cin >> key;
         node *temp = head;
         while (temp != nullptr) {
             if (temp->data == key) { cout << "Found at position: " << pos << "\n"; return; }
             temp = temp->next;
             pos++;
         }
         cout << "Element not found.\n";
     }
 
     void reverse() {
         if (head == nullptr || head->next == nullptr) return;
         node *curr = head, *temp = nullptr;
         while (curr != nullptr) {
             temp = curr->prev;
             curr->prev = curr->next;
             curr->next = temp;
             curr = curr->prev;
         }
         if (temp != nullptr) head = temp->prev;
     }
 
     void display() {
         node *temp = head;
         cout << "List: nullptr  ";
         while (temp != nullptr) { cout << temp->data << "  "; temp = temp->next; }
         cout << "nullptr\n";
     }
 
     void printMenu() {
         cout << "1.insertAtBegin 2.insertAtEnd 3.insertAtPos 4.deleteAtBegin 5.deleteAtEnd \n"
              << "6.deleteAtPos 7.search 8.reverse 0.Display -1.Exit\n";
     }
 
     ~DoublyLinkedList() {
         node *temp;
         while (head != nullptr) { temp = head; head = head->next; delete temp; }
     }
 };
 
 int main() {
     DoublyLinkedList list;
     int choice;
 
     while (true) {
         list.printMenu();
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: list.insAtBegin(); break;
             case 2: list.insAtEnd(); break;
             case 3: list.insAtPos(); break;
             case 4: list.delAtBegin(); break;
             case 5: list.delAtEnd(); break;
             case 6: list.delAtPos(); break;
             case 7: list.search(); break;
             case 8: list.reverse(); break;
             case 0: list.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice. Try again.\n";
         }
     }
 }
 ```
 
 ///
 ### Output:
 ![[Pasted image 20260922142353.png|466]]
 
 ### Discussion:
 - **insAtBegin/insAtEnd/insAtPos** create a new node and link it into the chain by updating both the `next` pointer of the preceding node and the `prev` pointer of the following node, unlike a singly linked list which only needs one direction updated.
 - **delAtBegin/delAtEnd/delAtPos** unlink a node by connecting its neighboring nodes directly to each other via their `prev` and `next` pointers before freeing it, handling edge cases for an empty or single-node list.
 - **search()** traverses the list sequentially from `head`, comparing each node's data with the key, and reports the 1-based position if found.
 - **reverse()** walks through the entire list once, swapping each node's `prev` and `next` pointers, then updates `head` to what was previously the last node — reversing the traversal direction in place without allocating new nodes.
 ///
 ## Assignment 6
 ### Problem Statement:
 Implement a Circular Linked List. Include functions for insertion, deletion and search of a number, and reverse the list.
 
 ### Problem Definition:
 A **Circular Linked List** is a linear structure where the last node's `next` points back to the head instead of `NULL`, forming a loop. Insertion/deletion require tracking the last node to preserve the loop; traversal loops must use `do-while`-style checks (`temp != head` after moving) to avoid infinite loops.
 
 ### Algorithm:
 **Insertion at Beginning:**
 ```
 procedure insertAtBegin(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	if(head = NULL)
 		head ← newNode;
 		newNode.next ← head;
 	else
 		temp ← head;
 		while(temp.next ≠ head) do
 			temp ← temp.next;
 		end while
 		newNode.next ← head;
 		temp.next ← newNode;
 		head ← newNode;
 	end if
 end procedure
 ```
 
 **Insertion at End:**
 ```
 procedure insertAtEnd(head, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	if(head = NULL)
 		head ← newNode;
 		newNode.next ← head;
 	else
 		temp ← head;
 		while(temp.next ≠ head) do
 			temp ← temp.next;
 		end while
 		temp.next ← newNode;
 		newNode.next ← head;
 	end if
 end procedure
 ```
 
 **Insertion at Position:**
 ```
 procedure insertAtPos(head, pos, val)
 begin
 	if(pos < 1)
 		print "Invalid Position";
 		return;
 	end if
 	if(pos = 1)
 		call insertAtBegin(head, val);
 		return;
 	end if
 	if(head = NULL)
 		print "Out of range";
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 2 do
 		temp ← temp.next;
 		if(temp = head)
 			print "Out of range";
 			return;
 		end if
 	end for
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← temp.next;
 	temp.next ← newNode;
 end procedure
 ```
 
 **Deletion at Beginning:**
 ```
 procedure deleteAtBegin(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	if(head.next = head)
 		free head;
 		head ← NULL;
 		return;
 	end if
 	temp ← head;
 	last ← head;
 	while(last.next ≠ head) do
 		last ← last.next;
 	end while
 	head ← head.next;
 	last.next ← head;
 	free temp;
 end procedure
 ```
 
 **Deletion at End:**
 ```
 procedure deleteAtEnd(head)
 begin
 	if(head = NULL)
 		print "List is empty";
 		return;
 	end if
 	if(head.next = head)
 		free head;
 		head ← NULL;
 		return;
 	end if
 	temp ← head;
 	while(temp.next.next ≠ head) do
 		temp ← temp.next;
 	end while
 	delNode ← temp.next;
 	temp.next ← head;
 	free delNode;
 end procedure
 ```
 
 **Deletion at Position:**
 ```
 procedure deleteAtPos(head, pos)
 begin
 	if(head = NULL or pos < 1)
 		print "Unable to process";
 		return;
 	end if
 	if(pos = 1)
 		call deleteAtBegin(head);
 		return;
 	end if
 	temp ← head;
 	for i ← 1 to pos - 2 do
 		temp ← temp.next;
 		if(temp = head)
 			print "Out of range";
 			return;
 		end if
 	end for
 	if(temp.next = head)
 		print "Out of range";
 		return;
 	end if
 	delNode ← temp.next;
 	temp.next ← delNode.next;
 	free delNode;
 end procedure
 ```
 
 **Search:**
 ```
 procedure search(head, key)
 begin
 	if(head = NULL)
 		return -1;
 	end if
 	temp ← head;
 	pos ← 1;
 	repeat
 		if(temp.data = key)
 			return pos;
 		end if
 		temp ← temp.next;
 		pos ← pos + 1;
 	until temp = head;
 	return -1;
 end procedure
 ```
 
 **Reverse:**
 ```
 procedure reverse(head)
 begin
 	if(head = NULL or head.next = head)
 		return;
 	end if
 	prev ← NULL;
 	curr ← head;
 	nxt ← NULL;
 	oldHead ← head;
 	repeat
 		nxt ← curr.next;
 		curr.next ← prev;
 		prev ← curr;
 		curr ← nxt;
 	until curr = head;
 	oldHead.next ← prev;
 	head ← prev;
 end procedure
 ```
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 struct node {
     int data;
     node *next = nullptr;
 };
 
 class CircularLinkedList {
 private:
     node *head = nullptr;
 
 public:
     void insertAtBegin(int val) {
         node *newNode = new node{val};
         if (head == nullptr) { head = newNode; newNode->next = head; return; }
         node *temp = head;
         while (temp->next != head) temp = temp->next;
         newNode->next = head;
         temp->next = newNode;
         head = newNode;
     }
 
     void insertAtEnd(int val) {
         node *newNode = new node{val};
         if (head == nullptr) { head = newNode; newNode->next = head; return; }
         node *temp = head;
         while (temp->next != head) temp = temp->next;
         temp->next = newNode;
         newNode->next = head;
     }
 
     void insertAtPos(int pos, int val) {
         if (pos < 1) { cout << "Invalid Position!\n"; return; }
         if (pos == 1) { insertAtBegin(val); return; }
         if (head == nullptr) { cout << "Out of range!\n"; return; }
         node *temp = head;
         for (int i = 1; i < pos - 1; i++) {
             temp = temp->next;
             if (temp == head) { cout << "Out of range!\n"; return; }
         }
         node *newNode = new node{val};
         newNode->next = temp->next;
         temp->next = newNode;
     }
 
     void deleteAtBegin() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         if (head->next == head) { delete head; head = nullptr; return; }
         node *temp = head, *last = head;
         while (last->next != head) last = last->next;
         head = head->next;
         last->next = head;
         delete temp;
     }
 
     void deleteAtEnd() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         if (head->next == head) { delete head; head = nullptr; return; }
         node *temp = head;
         while (temp->next->next != head) temp = temp->next;
         node *delNode = temp->next;
         temp->next = head;
         delete delNode;
     }
 
     void deleteAtPos(int pos) {
         if (head == nullptr || pos < 1) { cout << "Unable to process!\n"; return; }
         if (pos == 1) { deleteAtBegin(); return; }
         node *temp = head;
         for (int i = 1; i < pos - 1; i++) {
             temp = temp->next;
             if (temp == head) { cout << "Out of range!\n"; return; }
         }
         if (temp->next == head) { cout << "Out of range!\n"; return; }
         node *delNode = temp->next;
         temp->next = delNode->next;
         delete delNode;
     }
 
     int search(int key) {
         if (head == nullptr) return -1;
         node *temp = head;
         int pos = 1;
         do {
             if (temp->data == key) return pos;
             temp = temp->next;
             pos++;
         } while (temp != head);
         return -1;
     }
 
     void reverse() {
         if (head == nullptr || head->next == head) return;
         node *prev = nullptr, *curr = head, *nxt = nullptr, *oldHead = head;
         do {
             nxt = curr->next;
             curr->next = prev;
             prev = curr;
             curr = nxt;
         } while (curr != head);
         oldHead->next = prev;
         head = prev;
     }
 
     void display() {
         if (head == nullptr) { cout << "List is empty!\n"; return; }
         node *temp = head;
         cout << "List: ";
         do { cout << temp->data << " -> "; temp = temp->next; } while (temp != head);
         cout << "(head)\n";
     }
 
     void printMenu() {
         cout << "1.insertAtBegin 2.insertAtEnd 3.insertAtPos 4.deleteAtBegin 5.deleteAtEnd \n"
              << "6.deleteAtPos 7.search 8.reverse 0.Display -1.Exit\n";
     }
 
     ~CircularLinkedList() {
         if (head == nullptr) return;
         node *temp = head->next;
         while (temp != head) { node *next = temp->next; delete temp; temp = next; }
         delete head;
     }
 };
 
 int main() {
     CircularLinkedList list;
     int choice, val, pos;
 
     while (true) {
         list.printMenu();
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: cout << "Enter value: "; cin >> val; list.insertAtBegin(val); break;
             case 2: cout << "Enter value: "; cin >> val; list.insertAtEnd(val); break;
             case 3:
                 cout << "Enter position: "; cin >> pos;
                 cout << "Enter value: "; cin >> val;
                 list.insertAtPos(pos, val);
                 break;
             case 4: list.deleteAtBegin(); break;
             case 5: list.deleteAtEnd(); break;
             case 6: cout << "Enter position: "; cin >> pos; list.deleteAtPos(pos); break;
             case 7: {
                 cout << "Enter value to search: "; cin >> val;
                 int res = list.search(val);
                 if (res != -1) cout << "Found at position " << res << ".\n";
                 else cout << "Not found.\n";
                 break;
             }
             case 8: list.reverse(); break;
             case 0: list.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice. Try again.\n";
         }
     }
 }
 ```
 
 ///
 ### Output:
 ![[Pasted image 20260923185808.png]]
 ![[Pasted image 20260923185824.png]]
 ///
 ### Discussion:
 
 - **insertAtBegin/insertAtEnd/insertAtPos** create a new node and link it in, always ensuring the last node's `next` still points to the (possibly updated) `head` to preserve the circle.
 - **deleteAtBegin/deleteAtEnd/deleteAtPos** unlink a node by finding its neighbors and relinking around it, with the last node's `next` updated to the new head where relevant.
 - **search()** traverses using a `do-while` loop (since `head` itself must be checked first) and stops once it loops back to `head`.
 - **reverse()** performs a standard 3-pointer reversal (`prev`, `curr`, `nxt`) but loops until `curr` returns to the original `head`, then fixes the old head's `next` to close the circle with the new head.
 
 ///
 ## Assignment 7
 ### Problem Statement:
 Perform Stack operations using Linked List implementation.
 ### Problem Definition:
 A **Stack** is a linear data structure that follows LIFO (Last In First Out) order. In a linked list implementation, each element is stored as a **node** containing data and a pointer to the next node, with the **top** pointer always referring to the most recently inserted node.
 
 - **Push:** Insert a new node at the top.
 - **Pop:** Remove the node from the top.
 - **Peek:** View the top element without removing it.
 ### Algorithm:
 **Check Empty:**
 ```
 procedure isEmpty(top)
 begin
 	if(top = NULL)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Push Operation:**
 ```
 procedure push(top, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← top;
 	top ← newNode;
 end procedure
 ```
 
 **Pop Operation:**
 ```
 procedure pop(top)
 begin
 	if(isEmpty(top))
 		print "Stack Underflow";
 		return;
 	end if
 	temp ← top;
 	val ← temp.data;
 	top ← top.next;
 	free temp;
 	return val;
 end procedure
 ```
   
 **Peek Operation:**
 ```
 procedure peek(top)
 begin
 	if(isEmpty(top))
 		print "Stack is empty";
 		return;
 	end if
 	return top.data;
 end procedure
 ```
   
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 struct node
 {
     int data;
     node *next;
 };
 
 class Stack
 {
 private:
     node *top;
 
 public:
     Stack() { top = nullptr; }
 
     bool isEmpty() { return (top == nullptr); }
 
     void push(int val)
     {
         node *newNode = new node;
         newNode->data = val;
         newNode->next = top;
         top = newNode;
     }
 
     int pop()
     {
         if (isEmpty())
         {
             cout << "Stack Underflow!\n";
             return -1;
         }
         node *temp = top;
         int val = temp->data;
         top = top->next;
         delete temp;
         return val;
     }
 
     int peek()
     {
         if (isEmpty())
         {
             cout << "Stack is empty!\n";
             return -1;
         }
         return top->data;
     }
 
     void display()
     {
         if (isEmpty())
         {
             cout << "Stack is empty!\n";
             return;
         }
         node *temp = top;
         while (temp != nullptr)
         {
             cout << temp->data << " ";
             temp = temp->next;
         }
         cout << endl;
     }
 
     ~Stack()
     {
         node *temp;
         while (top != nullptr)
         {
             temp = top;
             top = top->next;
             delete temp;
         }
     }
 };
 
 int main()
 {
     Stack s;
     int choice, val;
 
     while (true)
     {
         cout << "1.push 2.pop 3.peek 4.isEmpty 0.Display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice)
         {
         case 1:
             cout << "Enter value: ";
             cin >> val;
             s.push(val);
             break;
 
         case 2:
         {
             int v = s.pop();
             if (v != -1)
                 cout << "Popped value: " << v << endl;
             break;
         }
 
         case 3:
         {
             int v = s.peek();
             if (v != -1)
                 cout << "Top element: " << v << endl;
             break;
         }
 
         case 4:
             cout << (s.isEmpty() ? "Empty\n" : "Not empty\n");
             break;
 
         case 0:
             s.display();
             break;
 
         case -1:
             cout << "Exiting...\n";
             return 0;
 
         default:
             cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:  
 ![[Pasted image 20260923191234.png]]
 
 ### Discussion:
 - **push()** creates a new node, links it to the current top, and updates `top` to point to this new node.
 - **pop()** checks for underflow, then removes the node pointed to by `top`, updates `top` to the next node, and returns the removed value.
 - **peek()** returns the data stored at `top` without modifying the stack.
 
 ///
 ## Assignment 8
 ### Problem Statement:
 Perform Stack operations using Array implementation.
 ### Problem Definition:
 A **Stack** is a linear data structure that follows LIFO (Last In First Out) order. Elements are added and removed only from one end, called the **top**.
 - **Push:** Insert an element at the top.
 - **Pop:** Remove the element from the top.
 - **Peek:** View the top element without removing it.
 ### Algorithm:
 **Check Full:**
 ```
 procedure isFull(top, capacity)
 begin
 	if(top = capacity - 1)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Check Empty:**
 ```
 procedure isEmpty(top)
 begin
 	if(top = -1)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Push Operation:**
 ```
 procedure push(arr, top, capacity, val)
 begin
 	if(isFull(top, capacity))
 		print "Stack Overflow";
 		return;
 	end if
 	top ← top + 1;
 	arr[top] ← val;
 end procedure
 ```
 
 **Pop Operation:**
 ```
 procedure pop(arr, top)
 begin
 	if(isEmpty(top))
 		print "Stack Underflow";
 		return;
 	end if
 	val ← arr[top];
 	top ← top - 1;
 	return val;
 end procedure
 ```
 
 **Peek Operation:**
 ```
 procedure peek(arr, top)
 begin
 	if(isEmpty(top))
 		print "Stack is empty";
 		return;
 	end if
 	return arr[top];
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class Stack {
 private:
     int *arr;
     int top;
     int capacity;
 
 public:
     Stack(int size) {
         capacity = size;
         arr = new int[capacity];
         top = -1;
     }
 
     bool isFull() { return (top == capacity - 1); }
     bool isEmpty() { return (top == -1); }
 
     void push() {
         if (isFull()) { cout << "Stack Overflow!\n"; return; }
         int val;
         cout << "Enter the value: ";
         cin >> val;
         arr[++top] = val;
     }
 
     void pop() {
         if (isEmpty()) { cout << "Stack Underflow!\n"; return; }
         int val = arr[top--];
         cout << "Popped value: " << val << endl;
     }
 
     void peek() {
         if (isEmpty()) { cout << "Stack is empty!\n"; return; }
         cout << "Top element: " << arr[top] << endl;
     }
 
     void display() {
         if (isEmpty()) { cout << "Stack is empty!\n"; return; }
         for (int i = top; i >= 0; i--) cout << arr[i] << " ";
         cout << endl;
     }
 
     ~Stack() { delete[] arr; }
 };
 
 int main() {
     int size, choice;
     cout << "Enter stack capacity: ";
     cin >> size;
     if (size <= 0) { cout << "Invalid size!\n"; return 0; }
 
     Stack s(size);
     while (true) {
         cout << "1.push 2.pop 3.peek 4.isFull 5.isEmpty 0.Display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: s.push(); break;
             case 2: s.pop(); break;
             case 3: s.peek(); break;
             case 4: cout << (s.isFull() ? "Full\n" : "Not full\n"); break;
             case 5: cout << (s.isEmpty() ? "Empty\n" : "Not empty\n"); break;
             case 0: s.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923191813.png]]
 
 ### Discussion:
 - **push()** checks for overflow, then increments `top` and stores the value at `arr[top]`.
 - **pop()** checks for underflow, then returns `arr[top]` and decrements `top`, effectively removing it logically without clearing memory.
 - **peek()** returns `arr[top]` without modifying `top`, allowing the caller to inspect the top element.
 
 ///
 ## Assignment 9
 ### Problem Statement:
 Perform Queue operations using Array.
 ### Problem Definition:
 A **Queue** is a linear data structure that follows FIFO (First In First Out) order. Elements are inserted from the **rear** and removed from the **front**.
 - **Enqueue:** Insert an element at the rear.
 - **Dequeue:** Remove an element from the front.
 - **Peek:** View the front element without removing it.
 ### Algorithm:
 **Check Full:**
 ```
 procedure isFull(rear, capacity)
 begin
 	if(rear = capacity - 1)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Check Empty:**
 ```
 procedure isEmpty(front, rear)
 begin
 	if(front = -1 or front > rear)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Enqueue Operation:**
 ```
 procedure enqueue(arr, front, rear, capacity, val)
 begin
 	if(isFull(rear, capacity))
 		print "Queue Overflow";
 		return;
 	end if
 	if(front = -1)
 		front ← 0;
 	end if
 	rear ← rear + 1;
 	arr[rear] ← val;
 end procedure
 ```
 
 **Dequeue Operation:**
 ```
 procedure dequeue(arr, front, rear)
 begin
 	if(isEmpty(front, rear))
 		print "Queue Underflow";
 		return;
 	end if
 	val ← arr[front];
 	front ← front + 1;
 	if(front > rear)
 		front ← -1;
 		rear ← -1;
 	end if
 	return val;
 end procedure
 ```
 
 **Peek Operation:**
 ```
 procedure peek(arr, front, rear)
 begin
 	if(isEmpty(front, rear))
 		print "Queue is empty";
 		return;
 	end if
 	return arr[front];
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class Queue {
 private:
     int *arr;
     int front, rear, capacity;
 
 public:
     Queue(int size) {
         capacity = size;
         arr = new int[capacity];
         front = -1;
         rear = -1;
     }
 
     bool isFull() { return (rear == capacity - 1); }
     bool isEmpty() { return (front == -1 || front > rear); }
 
     void enqueue() {
         if (isFull()) { cout << "Queue Overflow!\n"; return; }
         int val;
         cout << "Enter the value: ";
         cin >> val;
         if (front == -1) front = 0;
         arr[++rear] = val;
     }
 
     void dequeue() {
         if (isEmpty()) { cout << "Queue Underflow!\n"; return; }
         int val = arr[front++];
         if (front > rear) { front = -1; rear = -1; }
         cout << "Dequeued value: " << val << endl;
     }
 
     void peek() {
         if (isEmpty()) { cout << "Queue is empty!\n"; return; }
         cout << "Front element: " << arr[front] << endl;
     }
 
     void display() {
         if (isEmpty()) { cout << "Queue is empty!\n"; return; }
         for (int i = front; i <= rear; i++) cout << arr[i] << " ";
         cout << endl;
     }
 
     ~Queue() { delete[] arr; }
 };
 
 int main() {
     int size, choice;
     cout << "Enter queue capacity: ";
     cin >> size;
     if (size <= 0) { cout << "Invalid size!\n"; return 0; }
 
     Queue q(size);
     while (true) {
         cout << "1.enqueue 2.dequeue 3.peek 4.isFull 5.isEmpty 0.Display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: q.enqueue(); break;
             case 2: q.dequeue(); break;
             case 3: q.peek(); break;
             case 4: cout << (q.isFull() ? "Full\n" : "Not full\n"); break;
             case 5: cout << (q.isEmpty() ? "Empty\n" : "Not empty\n"); break;
             case 0: q.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923192135.png|476]]
 
 ///
 ### Discussion:
 - **enqueue()** checks for overflow, initializes `front` to 0 on the first insertion, then places the value at `arr[++rear]`.
 - **dequeue()** checks for underflow, returns `arr[front]`, increments `front`, and resets both `front` and `rear` to `-1` once the queue empties — since this linear queue does not reuse freed front slots.
 - **peek()** returns `arr[front]` without modifying either pointer.
 
 ///
 ## Assignment 10
 ### Problem Statement:
 Perform Circular Queue operations using Array.
 ### Problem Definition:
 A **Circular Queue** is a queue implemented using a fixed-size array where the rear wraps around to the front once it reaches the end, using modulo arithmetic. This allows reuse of freed slots, unlike a linear queue.
 ### Algorithm:
 **Check Empty:**
 ```
 procedure isEmpty(front)
 begin
 	if(front = -1)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Check Full:**
 ```
 procedure isFull(front, rear, size)
 begin
 	if((rear + 1) mod size = front)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Enqueue Operation:**
 ```
 procedure enqueue(queue, front, rear, size, val)
 begin
 	if(isFull(front, rear, size))
 		print "Queue is Full";
 		return;
 	end if
 	if(isEmpty(front))
 		front ← 0;
 		rear ← 0;
 	else
 		rear ← (rear + 1) mod size;
 	end if
 	queue[rear] ← val;
 end procedure
 ```
 
 **Dequeue Operation:**
 ```
 procedure dequeue(queue, front, rear, size)
 begin
 	if(isEmpty(front))
 		print "Queue is Empty";
 		return;
 	end if
 	val ← queue[front];
 	if(front = rear)
 		front ← -1;
 		rear ← -1;
 	else
 		front ← (front + 1) mod size;
 	end if
 	return val;
 end procedure
 ```
 
 **Peek Operation:**
 ```
 procedure peek(queue, front)
 begin
 	if(isEmpty(front))
 		print "Queue is Empty";
 		return;
 	end if
 	return queue[front];
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class CircularQueue {
 private:
     int *queue;
     int front, rear, size;
 
 public:
     CircularQueue(int n) {
         size = n;
         queue = new int[size];
         front = -1;
         rear = -1;
     }
 
     bool isEmpty() { return front == -1; }
     bool isFull() { return (rear + 1) % size == front; }
 
     void enqueue(int val) {
         if (isFull()) { cout << "Queue is Full!\n"; return; }
         if (isEmpty()) { front = 0; rear = 0; }
         else rear = (rear + 1) % size;
         queue[rear] = val;
     }
 
     void dequeue() {
         if (isEmpty()) { cout << "Queue is Empty!\n"; return; }
         int val = queue[front];
         if (front == rear) { front = -1; rear = -1; }
         else front = (front + 1) % size;
         cout << "Removed: " << val << endl;
     }
 
     void peek() {
         if (isEmpty()) { cout << "Queue is Empty!\n"; return; }
         cout << "Front element: " << queue[front] << endl;
     }
 
     void display() {
         if (isEmpty()) { cout << "Queue is Empty!\n"; return; }
         int i = front;
         while (true) {
             cout << queue[i] << " ";
             if (i == rear) break;
             i = (i + 1) % size;
         }
         cout << endl;
     }
 
     ~CircularQueue() { delete[] queue; }
 };
 
 int main() {
     int n, choice, val;
     cout << "Enter queue size: ";
     cin >> n;
     if (n <= 0) { cout << "Invalid size!\n"; return 0; }
 
     CircularQueue q(n);
     while (true) {
         cout << "1.enqueue 2.dequeue 3.peek 4.isEmpty 5.isFull 6.Display 0.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: cout << "Enter value: "; cin >> val; q.enqueue(val); break;
             case 2: q.dequeue(); break;
             case 3: q.peek(); break;
             case 4: cout << (q.isEmpty() ? "Empty\n" : "Not empty\n"); break;
             case 5: cout << (q.isFull() ? "Full\n" : "Not full\n"); break;
             case 6: q.display(); break;
             case 0: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923192435.png|483]]
 ///
 ### Discussion:
 - **enqueue()** checks fullness using `(rear + 1) % size == front`, sets `front`/`rear` to `0` on the first insertion, otherwise advances `rear` circularly with modulo before storing the value.
 - **dequeue()** returns `queue[front]`, and either resets both pointers to `-1` (if it was the last element) or advances `front` circularly, allowing wrapped-around slots to be reused.
 - **peek()** simply returns `queue[front]` without altering any pointer.
 
 ///
 ## Assignment 11
 ### Problem Statement:
 Perform Queue operations using Linked List.
 ### Problem Definition:
 A **Queue** implemented via a linked list uses two pointers, `front` and `rear`, to track the first and last nodes, allowing enqueue and dequeue in `O(1)` without a fixed capacity.
 ### Algorithm:
 **Check Empty:**
 ```
 procedure isEmpty(front)
 begin
 	if(front = NULL)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Enqueue Operation:**
 ```
 procedure enqueue(front, rear, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← NULL;
 	if(isEmpty(front))
 		front ← newNode;
 		rear ← newNode;
 	else
 		rear.next ← newNode;
 		rear ← newNode;
 	end if
 end procedure
 ```
 
 **Dequeue Operation:**
 ```
 procedure dequeue(front, rear)
 begin
 	if(isEmpty(front))
 		print "Queue Underflow";
 		return;
 	end if
 	temp ← front;
 	val ← temp.data;
 	front ← front.next;
 	if(front = NULL)
 		rear ← NULL;
 	end if
 	free temp;
 	return val;
 end procedure
 ```
 
 **Peek Operation:**
 ```
 procedure peek(front)
 begin
 	if(isEmpty(front))
 		print "Queue is empty";
 		return;
 	end if
 	return front.data;
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 struct node {
     int data;
     node *next = nullptr;
 };
 
 class Queue {
 private:
     node *front, *rear;
 
 public:
     Queue() { front = nullptr; rear = nullptr; }
     bool isEmpty() { return (front == nullptr); }
 
     void enqueue() {
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->next = nullptr;
         if (isEmpty()) front = rear = newNode;
         else { rear->next = newNode; rear = newNode; }
     }
 
     void dequeue() {
         if (isEmpty()) { cout << "Queue Underflow!\n"; return; }
         node *temp = front;
         int val = temp->data;
         front = front->next;
         if (front == nullptr) rear = nullptr;
         delete temp;
         cout << "Dequeued: " << val << endl;
     }
 
     void peek() {
         if (isEmpty()) { cout << "Queue is empty!\n"; return; }
         cout << "Front element: " << front->data << endl;
     }
 
     void display() {
         if (isEmpty()) { cout << "Queue is empty!\n"; return; }
         node *temp = front;
         while (temp != nullptr) { cout << temp->data << " "; temp = temp->next; }
         cout << endl;
     }
 
     ~Queue() {
         node *temp;
         while (front != nullptr) { temp = front; front = front->next; delete temp; }
     }
 };
 
 int main() {
     Queue q;
     int choice;
 
     while (true) {
         cout << "1.enqueue 2.dequeue 3.peek 4.isEmpty 0.Display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: q.enqueue(); break;
             case 2: q.dequeue(); break;
             case 3: q.peek(); break;
             case 4: cout << (q.isEmpty() ? "Empty\n" : "Not empty\n"); break;
             case 0: q.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923192749.png]]
 
 ### Discussion:
 - **enqueue()** creates a new node and links it after `rear`, updating `rear` to point to it; if the queue was empty, both `front` and `rear` are set to the new node.
 - **dequeue()** removes the node at `front`, advancing `front` to the next node, and resets `rear` to `NULL` if the list becomes empty.
 - **peek()** returns `front->data` without modifying the queue.
 
 ///
 ## Assignment 12
 ### Problem Statement:
 Create and perform different operations on Double-ended Queues (Deque) using Linked List implementation.
 ### Problem Definition:
 A **Deque (Double-Ended Queue)** allows insertion and deletion from both ends — front and rear. It is implemented here using a doubly linked list, so both `prev` and `next` pointers are updated during insert/delete at either end.
 ### Algorithm:
 **Check Empty:**
 ```
 procedure isEmpty(front)
 begin
 	if(front = NULL)
 		return true;
 	else
 		return false;
 	end if
 end procedure
 ```
 
 **Insert at Front:**
 ```
 procedure insertFront(front, rear, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.prev ← NULL;
 	newNode.next ← front;
 	if(isEmpty(front))
 		front ← newNode;
 		rear ← newNode;
 	else
 		front.prev ← newNode;
 		front ← newNode;
 	end if
 end procedure
 ```
 
 **Insert at Rear:**
 ```
 procedure insertRear(front, rear, val)
 begin
 	newNode ← create new node;
 	newNode.data ← val;
 	newNode.next ← NULL;
 	newNode.prev ← rear;
 	if(isEmpty(front))
 		front ← newNode;
 		rear ← newNode;
 	else
 		rear.next ← newNode;
 		rear ← newNode;
 	end if
 end procedure
 ```
 
 **Delete from Front:**
 ```
 procedure deleteFront(front, rear)
 begin
 	if(isEmpty(front))
 		print "Deque Underflow";
 		return;
 	end if
 	temp ← front;
 	val ← temp.data;
 	front ← front.next;
 	if(front = NULL)
 		rear ← NULL;
 	else
 		front.prev ← NULL;
 	end if
 	free temp;
 	return val;
 end procedure
 ```
 
 **Delete from Rear:**
 ```
 procedure deleteRear(front, rear)
 begin
 	if(isEmpty(front))
 		print "Deque Underflow";
 		return;
 	end if
 	temp ← rear;
 	val ← temp.data;
 	rear ← rear.prev;
 	if(rear = NULL)
 		front ← NULL;
 	else
 		rear.next ← NULL;
 	end if
 	free temp;
 	return val;
 end procedure
 ```
 
 **Get Front / Get Rear:**
 ```
 procedure getFront(front)
 begin
 	if(isEmpty(front))
 		print "Deque is empty";
 		return;
 	end if
 	return front.data;
 end procedure
 
 procedure getRear(rear)
 begin
 	if(rear = NULL)
 		print "Deque is empty";
 		return;
 	end if
 	return rear.data;
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 struct node {
     int data;
     node *prev = nullptr;
     node *next = nullptr;
 };
 
 class Deque {
 private:
     node *front, *rear;
 
 public:
     Deque() { front = nullptr; rear = nullptr; }
     bool isEmpty() { return (front == nullptr); }
 
     void insertFront() {
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->prev = nullptr;
         newNode->next = front;
         if (isEmpty()) front = rear = newNode;
         else { front->prev = newNode; front = newNode; }
     }
 
     void insertRear() {
         node *newNode = new node;
         cout << "Enter the value: ";
         cin >> newNode->data;
         newNode->next = nullptr;
         newNode->prev = rear;
         if (isEmpty()) front = rear = newNode;
         else { rear->next = newNode; rear = newNode; }
     }
 
     void deleteFront() {
         if (isEmpty()) { cout << "Deque Underflow!\n"; return; }
         node *temp = front;
         int val = temp->data;
         front = front->next;
         if (front == nullptr) rear = nullptr;
         else front->prev = nullptr;
         delete temp;
         cout << "Deleted from front: " << val << endl;
     }
 
     void deleteRear() {
         if (isEmpty()) { cout << "Deque Underflow!\n"; return; }
         node *temp = rear;
         int val = temp->data;
         rear = rear->prev;
         if (rear == nullptr) front = nullptr;
         else rear->next = nullptr;
         delete temp;
         cout << "Deleted from rear: " << val << endl;
     }
 
     void getFront() {
         if (isEmpty()) { cout << "Deque is empty!\n"; return; }
         cout << "Front element: " << front->data << endl;
     }
 
     void getRear() {
         if (isEmpty()) { cout << "Deque is empty!\n"; return; }
         cout << "Rear element: " << rear->data << endl;
     }
 
     void display() {
         if (isEmpty()) { cout << "Deque is empty!\n"; return; }
         node *temp = front;
         while (temp != nullptr) { cout << temp->data << " "; temp = temp->next; }
         cout << endl;
     }
 
     ~Deque() {
         node *temp;
         while (front != nullptr) { temp = front; front = front->next; delete temp; }
     }
 };
 
 int main() {
     Deque dq;
     int choice;
 
     while (true) {
         cout << "1.insertFront 2.insertRear 3.deleteFront 4.deleteRear\n"
              << "5.getFront 6.getRear 7.isEmpty 0.Display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: dq.insertFront(); break;
             case 2: dq.insertRear(); break;
             case 3: dq.deleteFront(); break;
             case 4: dq.deleteRear(); break;
             case 5: dq.getFront(); break;
             case 6: dq.getRear(); break;
             case 7: cout << (dq.isEmpty() ? "Empty\n" : "Not empty\n"); break;
             case 0: dq.display(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260923193206.png]]
 ### Discussion:
 - **insertFront()/insertRear()** create a new node and link it at the respective end, updating both `prev` and `next` pointers of neighboring nodes to maintain the doubly linked structure.
 - **deleteFront()/deleteRear()** remove the node at the respective end by advancing `front` or `rear` to the adjacent node and clearing the freed node's neighbor pointer, with `front`/`rear` both reset to `NULL` if the deque becomes empty.
 - **getFront()/getRear()** simply return `front->data` or `rear->data` without modifying the deque.
 
 ///
 ## Assignment 13
 ### Problem Statement:
 Write a program to scan a polynomial using a linked list and add two polynomials.
 ### Problem Definition:
 A **Polynomial** can be represented as a linked list of terms, where each node stores a `coeff` (coefficient) and `exp` (exponent), sorted in decreasing order of exponent.
 - **insertTerm:** Inserts a term into the list in the correct sorted position, merging with an existing term of the same exponent.
 - **Addition:** Two polynomials are added by traversing both lists simultaneously, comparing exponents, and combining coefficients of matching terms.
 ### Algorithm:
 **Insert Term in Sorted Order:**
 ```
 procedure insertTerm(head, coeff, exp)
 begin
 	if(coeff = 0)
 		return;
 	end if
 	newNode ← create new node;
 	newNode.coeff ← coeff;
 	newNode.exp ← exp;
 	newNode.next ← NULL;
 	if(head = NULL or exp > head.exp)
 		newNode.next ← head;
 		head ← newNode;
 		return;
 	end if
 	if(head.exp = exp)
 		head.coeff ← head.coeff + coeff;
 		free newNode;
 		if(head.coeff = 0)
 			temp ← head;
 			head ← head.next;
 			free temp;
 		end if
 		return;
 	end if
 	temp ← head;
 	while(temp.next ≠ NULL and temp.next.exp > exp) do
 		temp ← temp.next;
 	end while
 	if(temp.next ≠ NULL and temp.next.exp = exp)
 		temp.next.coeff ← temp.next.coeff + coeff;
 		free newNode;
 		if(temp.next.coeff = 0)
 			delNode ← temp.next;
 			temp.next ← delNode.next;
 			free delNode;
 		end if
 	else
 		newNode.next ← temp.next;
 		temp.next ← newNode;
 	end if
 end procedure
 ```
 
 **Scan Polynomial:**
 ```
 procedure scanPolynomial(head)
 begin
 	read n;
 	for i ← 1 to n do
 		read coeff, exp;
 		call insertTerm(head, coeff, exp);
 	end for
 end procedure
 ```
 
 **Add Polynomials:**
 ```
 procedure addPolynomials(head1, head2, resultHead)
 begin
 	p ← head1;
 	q ← head2;
 	while(p ≠ NULL and q ≠ NULL) do
 		if(p.exp = q.exp)
 			sum ← p.coeff + q.coeff;
 			if(sum ≠ 0)
 				call insertTerm(resultHead, sum, p.exp);
 			end if
 			p ← p.next;
 			q ← q.next;
 		else if(p.exp > q.exp)
 			call insertTerm(resultHead, p.coeff, p.exp);
 			p ← p.next;
 		else
 			call insertTerm(resultHead, q.coeff, q.exp);
 			q ← q.next;
 		end if
 	end while
 	while(p ≠ NULL) do
 		call insertTerm(resultHead, p.coeff, p.exp);
 		p ← p.next;
 	end while
 	while(q ≠ NULL) do
 		call insertTerm(resultHead, q.coeff, q.exp);
 		q ← q.next;
 	end while
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 #include <cmath>
 using namespace std;
 
 struct node {
     int coeff, exp;
     node *next = nullptr;
 };
 
 class Polynomial {
 private:
     node *head;
 
     void clear() {
         node *temp;
         while (head != nullptr) {
             temp = head;
             head = head->next;
             delete temp;
         }
     }
 
     void copyFrom(const Polynomial &other) {
         if (other.head == nullptr) {
             head = nullptr;
             return;
         }
         head = new node{other.head->coeff, other.head->exp, nullptr};
         node *current = head;
         node *otherCurrent = other.head->next;
         while (otherCurrent != nullptr) {
             current->next = new node{otherCurrent->coeff, otherCurrent->exp, nullptr};
             current = current->next;
             otherCurrent = otherCurrent->next;
         }
     }
 
 public:
     Polynomial() { head = nullptr; }
 
     Polynomial(const Polynomial &other) {
         copyFrom(other);
     }
 
     Polynomial& operator=(const Polynomial &other) {
         if (this != &other) {
             clear();
             copyFrom(other);
         }
         return *this;
     }
 
     ~Polynomial() {
         clear();
     }
 
     void insertTerm(int coeff, int exp) {
         if (coeff == 0) return;
         node *newNode = new node{coeff, exp, nullptr};
 
         if (head == nullptr || exp > head->exp) {
             newNode->next = head;
             head = newNode;
             return;
         }
         if (head->exp == exp) {
             head->coeff += coeff;
             delete newNode;
             if (head->coeff == 0) {
                 node* temp = head;
                 head = head->next;
                 delete temp;
             }
             return;
         }
         node *temp = head;
         while (temp->next != nullptr && temp->next->exp > exp) temp = temp->next;
         if (temp->next != nullptr && temp->next->exp == exp) {
             temp->next->coeff += coeff;
             delete newNode;
             if (temp->next->coeff == 0) {
                 node* toDelete = temp->next;
                 temp->next = temp->next->next;
                 delete toDelete;
             }
         } else {
             newNode->next = temp->next;
             temp->next = newNode;
         }
     }
 
     void inputPolynomial() {
         int n, coeff, exp;
         cout << "Enter number of terms: ";
         cin >> n;
         for (int i = 0; i < n; i++) {
             cout << "Coefficient: "; cin >> coeff;
             cout << "Exponent: "; cin >> exp;
             insertTerm(coeff, exp);
         }
     }
 
     Polynomial add(const Polynomial &other) const {
         Polynomial result;
         node *p = head, *q = other.head;
         while (p != nullptr && q != nullptr) {
             if (p->exp == q->exp) {
                 int sum = p->coeff + q->coeff;
                 if (sum != 0) result.insertTerm(sum, p->exp);
                 p = p->next; q = q->next;
             } else if (p->exp > q->exp) {
                 result.insertTerm(p->coeff, p->exp);
                 p = p->next;
             } else {
                 result.insertTerm(q->coeff, q->exp);
                 q = q->next;
             }
         }
         while (p != nullptr) { result.insertTerm(p->coeff, p->exp); p = p->next; }
         while (q != nullptr) { result.insertTerm(q->coeff, q->exp); q = q->next; }
         return result;
     }
 
     void display() const {
         if (head == nullptr) { cout << "0\n"; return; }
         node *temp = head;
         bool first = true;
         while (temp != nullptr) {
             if (!first && temp->coeff > 0) cout << " + ";
             else if (!first && temp->coeff < 0) cout << " - ";
             else if (temp->coeff < 0) cout << "-";
             int c = abs(temp->coeff);
             if (temp->exp == 0) cout << c;
             else if (temp->exp == 1) cout << (c == 1 ? "x" : to_string(c) + "x");
             else cout << (c == 1 ? "x^" + to_string(temp->exp) : to_string(c) + "x^" + to_string(temp->exp));
             first = false;
             temp = temp->next;
         }
         cout << endl;
     }
 };
 
 int main() {
     Polynomial p1, p2, result;
     cout << "--- First Polynomial ---\n";
     p1.inputPolynomial();
     cout << "--- Second Polynomial ---\n";
     p2.inputPolynomial();
 
     cout << "First: "; p1.display();
     cout << "Second: "; p2.display();
 
     result = p1.add(p2);
     cout << "Sum: "; result.display();
     return 0;
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923194003.png]]
 
 ### Discussion:
 - **insertTerm()** inserts a term into the correct sorted-by-exponent position, merging its coefficient into an existing node if a term with the same exponent already exists, and discarding it entirely if the resulting coefficient is zero.
 - **inputPolynomial()** reads the number of terms, then takes each coefficient and exponent from the user and passes them to `insertTerm()`, so the list is always kept sorted by exponent.
 - **add()** walks both polynomial lists in parallel, comparing exponents at each step: matching exponents have their coefficients summed, while the term with the higher exponent is copied over as-is, until one list is exhausted and the rest of the other is appended — producing a new sorted result polynomial.
 
 ///
 ## Assignment 14
 ### Problem Statement:
 Write a program to calculate factorial and to compute the factors of a given number using (i) recursion and (ii) iteration.
 ### Problem Definition:
 - **Factorial (n!):** Product of all positive integers up to `n`. Recursive definition: `n! = n * (n-1)!`, with base case `0! = 1! = 1`.
 - **Factors:** Numbers that divide `n` exactly (remainder 0). Can be found either by recursively checking divisors from 1 to `n`, or with a simple iterative loop.
 ### Algorithm:
 **Factorial using Recursion:**
 ```
 procedure factorialRecursive(n)
 begin
 	if(n <= 1)
 		return 1;
 	else
 		return n * factorialRecursive(n - 1);
 	end if
 end procedure
 ```
 
 **Factorial using Iteration:**
 ```
 procedure factorialIterative(n)
 begin
 	fact ← 1;
 	for i ← 2 to n do
 		fact ← fact * i;
 	end for
 	return fact;
 end procedure
 ```
 
 **Factors using Recursion:**
 ```
 procedure factorsRecursive(n, divisor)
 begin
 	if(divisor > n)
 		return;
 	end if
 	if(n mod divisor = 0)
 		print divisor + " ";
 	end if
 	call factorsRecursive(n, divisor + 1);
 end procedure
 ```
 
 **Factors using Iteration:**
 ```
 procedure factorsIterative(n)
 begin
 	for i ← 1 to n do
 		if(n mod i = 0)
 			print i + " ";
 		end if
 	end for
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class MathOperations {
 private:
     int num;
 
     long long factorialRecursive(int n) {
         if (n <= 1) return 1;
         return n * factorialRecursive(n - 1);
     }
 
     void factorsRecursive(int n, int divisor) {
         if (divisor > n) return;
         if (n % divisor == 0) cout << divisor << " ";
         factorsRecursive(n, divisor + 1);
     }
 
 public:
     MathOperations(int n) { num = n; }
 
     void calculateFactorialRecursive() {
         if (num < 0) { cout << "Not defined for negative numbers.\n"; return; }
         cout << "Factorial (Recursive): " << factorialRecursive(num) << endl;
     }
 
     void calculateFactorialIterative() {
         if (num < 0) { cout << "Not defined for negative numbers.\n"; return; }
         long long fact = 1;
         for (int i = 2; i <= num; i++) fact *= i;
         cout << "Factorial (Iterative): " << fact << endl;
     }
 
     void computeFactorsRecursive() {
         if (num <= 0) { cout << "Factors need a positive integer.\n"; return; }
         cout << "Factors (Recursive): ";
         factorsRecursive(num, 1);
         cout << endl;
     }
 
     void computeFactorsIterative() {
         if (num <= 0) { cout << "Factors need a positive integer.\n"; return; }
         cout << "Factors (Iterative): ";
         for (int i = 1; i <= num; i++) if (num % i == 0) cout << i << " ";
         cout << endl;
     }
 };
 
 int main() {
     int n, choice;
     cout << "Enter a number: ";
     cin >> n;
     MathOperations op(n);
 
     while (true) {
         cout << "1.Factorial(Recursive) 2.Factorial(Iterative) "
              << "3.Factors(Recursive) 4.Factors(Iterative) 0.Change Number -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: op.calculateFactorialRecursive(); break;
             case 2: op.calculateFactorialIterative(); break;
             case 3: op.computeFactorsRecursive(); break;
             case 4: op.computeFactorsIterative(); break;
             case 0: cout << "Enter new number: "; cin >> n; op = MathOperations(n); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260923195210.png]]
 
 ### Discussion:
 - **factorialRecursive()** breaks the problem down as `n * factorial(n-1)`, terminating at the base case `n <= 1`, building up the result through the call stack as it unwinds.
 - **factorialIterative()** achieves the same result with a simple loop multiplying `fact` by each integer from 2 to `n`, avoiding recursive call overhead.
 - **factorsRecursive()** checks divisibility for the current `divisor` and recurses with `divisor + 1` until it exceeds `n`, printing each valid divisor along the way.
 - **factorsIterative()** performs the same check using a single `for` loop from 1 to `n`.
 
 ///
 ## Assignment 15
 ### Problem Statement:
 Write a program to display the Fibonacci series using (i) recursion and (ii) iteration.
 ### Problem Definition:
 The **Fibonacci series** is a sequence where each term is the sum of the two preceding ones (`0, 1, 1, 2, 3, 5, ...`), defined recursively as `F(n) = F(n-1) + F(n-2)` with base cases `F(0) = 0` and `F(1) = 1`.
 ### Algorithm:
 **Fibonacci Term using Recursion:**
 ```
 procedure fibRecursive(k)
 begin
 	if(k <= 0)
 		return 0;
 	end if
 	if(k = 1)
 		return 1;
 	end if
 	return fibRecursive(k - 1) + fibRecursive(k - 2);
 end procedure
 ```
 
 **Fibonacci Series using Iteration:**
 ```
 procedure fibIterative(n)
 begin
 	if(n <= 0)
 		return;
 	end if
 	first ← 0;
 	second ← 1;
 	for i ← 0 to n - 1 do
 		if(i = 0)
 			print first + " ";
 		else if(i = 1)
 			print second + " ";
 		else
 			nextTerm ← first + second;
 			print nextTerm + " ";
 			first ← second;
 			second ← nextTerm;
 		end if
 	end for
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class Fibonacci {
 private:
     int n;
 
     int fibRecursive(int k) {
         if (k <= 0) return 0;
         if (k == 1) return 1;
         return fibRecursive(k - 1) + fibRecursive(k - 2);
     }
 
 public:
     Fibonacci(int count) { n = count; }
 
     void displayRecursive() {
         cout << "Fibonacci (Recursive): ";
         for (int i = 0; i < n; i++) cout << fibRecursive(i) << " ";
         cout << endl;
     }
 
     void displayIterative() {
         cout << "Fibonacci (Iterative): ";
         if (n <= 0) { cout << endl; return; }
         int first = 0, second = 1;
         for (int i = 0; i < n; i++) {
             if (i == 0) cout << first << " ";
             else if (i == 1) cout << second << " ";
             else {
                 int nextTerm = first + second;
                 cout << nextTerm << " ";
                 first = second;
                 second = nextTerm;
             }
         }
         cout << endl;
     }
 };
 
 int main() {
     int n, choice;
     cout << "Enter number of terms: ";
     cin >> n;
     if (n < 0) { cout << "Invalid number of terms!\n"; return 0; }
 
     Fibonacci fib(n);
     while (true) {
         cout << "1.Recursive 2.Iterative -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: fib.displayRecursive(); break;
             case 2: fib.displayIterative(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923195554.png|484]]
 
 ### Discussion:
 - **fibRecursive()** computes the k-th term by recursively summing the two preceding terms, with base cases returning `0` and `1` for `k <= 0` and `k = 1` respectively — called once per term for the recursive display.
 - **displayIterative()** builds the series in a single pass using two tracking variables, `first` and `second`, updating them each iteration to hold the last two computed terms, avoiding the exponential recomputation of the recursive approach.
 
 ///
 ## Assignment 16
 ### Problem Statement:
 WAP to create a Binary Search Tree and include following operations in tree:
 i. Insertion (Recursive and Iterative Implementation) 
 ii. Deletion by copying 
 iii. Deletion by Merging 
 iv. Search a no. in BST 
 v. Display its preorder, postorder and inorder traversals Recursively 
 vi. Display its preorder, postorder and inorder traversals Iteratively 
 vii. Display its level-by-level traversals 
 viii. Count the non-leaf nodes and leaf nodes 
 ix. Display height of tree 
 x. Create a mirror image of tree 
 xi. Check whether two BSTs are equal or not
 ### Problem Definition:
 A **Binary Search Tree (BST)** is a binary tree in which every node's left subtree contains only values smaller than the node, and the right subtree contains only values larger. Key operations include **insertion**, **deletion** (by copying the inorder predecessor or by merging subtrees), **search**, and **traversals** (preorder, inorder, postorder, level order) to visit all nodes in different orders.
 ### Algorithm:
 **Recursive Insertion:**
 ```
 procedure insertRecursive(root, val)
 begin
 	if(root = NULL)
 		newNode ← create new node with val;
 		return newNode;
 	end if
 	if(val < root.data)
 		root.left ← insertRecursive(root.left, val);
 	else if(val > root.data)
 		root.right ← insertRecursive(root.right, val);
 	else
 		print "Duplicate value ignored";
 	end if
 	return root;
 end procedure
 ```
 
 **Iterative Insertion:**
 ```
 procedure insertIterative(root, val)
 begin
 	newNode ← create new node with val;
 	if(root = NULL)
 		root ← newNode;
 		return;
 	end if
 	current ← root;
 	parent ← NULL;
 	while(current ≠ NULL) do
 		parent ← current;
 		if(val < current.data)
 			current ← current.left;
 		else if(val > current.data)
 			current ← current.right;
 		else
 			print "Duplicate value ignored";
 			free newNode;
 			return;
 		end if
 	end while
 	if(val < parent.data)
 		parent.left ← newNode;
 	else
 		parent.right ← newNode;
 	end if
 end procedure
 ```
 
 **Search:**
 ```
 procedure search(root, key)
 begin
 	current ← root;
 	while(current ≠ NULL) do
 		if(current.data = key)
 			return true;
 		else if(key < current.data)
 			current ← current.left;
 		else
 			current ← current.right;
 		end if
 	end while
 	return false;
 end procedure
 ```
 
 **Deletion by Copying:**
 ```
 procedure deleteByCopying(root, key)
 begin
 	if(root = NULL)
 		return NULL;
 	end if
 	if(key < root.data)
 		root.left ← deleteByCopying(root.left, key);
 	else if(key > root.data)
 		root.right ← deleteByCopying(root.right, key);
 	else
 		if(root.left = NULL)
 			temp ← root.right;
 			free root;
 			return temp;
 		else if(root.right = NULL)
 			temp ← root.left;
 			free root;
 			return temp;
 		end if
 		pred ← root.left;
 		while(pred.right ≠ NULL) do
 			pred ← pred.right;
 		end while
 		root.data ← pred.data;
 		root.left ← deleteByCopying(root.left, pred.data);
 	end if
 	return root;
 end procedure
 ```
 
 **Deletion by Merging:**
 ```
 procedure deleteByMerging(root, key)
 begin
 	if(root = NULL)
 		return NULL;
 	end if
 	if(key < root.data)
 		root.left ← deleteByMerging(root.left, key);
 		return root;
 	else if(key > root.data)
 		root.right ← deleteByMerging(root.right, key);
 		return root;
 	end if
 	if(root.left = NULL)
 		temp ← root.right;
 		free root;
 		return temp;
 	else if(root.right = NULL)
 		temp ← root.left;
 		free root;
 		return temp;
 	end if
 	successor ← root.right;
 	while(successor.left ≠ NULL) do
 		successor ← successor.left;
 	end while
 	successor.left ← root.left;
 	temp ← root.right;
 	free root;
 	return temp;
 end procedure
 ```
 
 **Preorder Traversal (Recursive):**
 ```
 procedure preorderRecursive(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	print root.data + " ";
 	call preorderRecursive(root.left);
 	call preorderRecursive(root.right);
 end procedure
 ```
 
 **Inorder Traversal (Recursive):**
 ```
 procedure inorderRecursive(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	call inorderRecursive(root.left);
 	print root.data + " ";
 	call inorderRecursive(root.right);
 end procedure
 ```
 
 **Postorder Traversal (Recursive):**
 ```
 procedure postorderRecursive(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	call postorderRecursive(root.left);
 	call postorderRecursive(root.right);
 	print root.data + " ";
 end procedure
 ```
 ///
 **Preorder Traversal (Iterative):**
 ```
 procedure preorderIterative(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	initialize stack S;
 	push(S, root);
 	while(not isEmpty(S)) do
 		current ← pop(S);
 		print current.data + " ";
 		if(current.right ≠ NULL)
 			push(S, current.right);
 		end if
 		if(current.left ≠ NULL)
 			push(S, current.left);
 		end if
 	end while
 end procedure
 ```
 
 **Inorder Traversal (Iterative):**
 ```
 procedure inorderIterative(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	initialize stack S;
 	current ← root;
 	while(current ≠ NULL or not isEmpty(S)) do
 		while(current ≠ NULL) do
 			push(S, current);
 			current ← current.left;
 		end while
 		current ← pop(S);
 		print current.data + " ";
 		current ← current.right;
 	end while
 end procedure
 ```
 
 **Postorder Traversal (Iterative):**
 ```
 procedure postorderIterative(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	initialize stacks S1, S2;
 	push(S1, root);
 	while(not isEmpty(S1)) do
 		current ← pop(S1);
 		push(S2, current);
 		if(current.left ≠ NULL)
 			push(S1, current.left);
 		end if
 		if(current.right ≠ NULL)
 			push(S1, current.right);
 		end if
 	end while
 	while(not isEmpty(S2)) do
 		current ← pop(S2);
 		print current.data + " ";
 	end while
 end procedure
 ```
 
 **Level Order Traversal:**
 ```
 procedure levelOrder(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	initialize queue Q;
 	enqueue(Q, root);
 	while(not isEmpty(Q)) do
 		current ← dequeue(Q);
 		print current.data + " ";
 		if(current.left ≠ NULL)
 			enqueue(Q, current.left);
 		end if
 		if(current.right ≠ NULL)
 			enqueue(Q, current.right);
 		end if
 	end while
 end procedure
 ```
 
 **Count Leaf Nodes:**
 ```
 procedure countLeaf(root)
 begin
 	if(root = NULL)
 		return 0;
 	end if
 	if(root.left = NULL and root.right = NULL)
 		return 1;
 	end if
 	return countLeaf(root.left) + countLeaf(root.right);
 end procedure
 ```
 
 **Count Non-Leaf Nodes:**
 ```
 procedure countNonLeaf(root)
 begin
 	if(root = NULL or (root.left = NULL and root.right = NULL))
 		return 0;
 	end if
 	return 1 + countNonLeaf(root.left) + countNonLeaf(root.right);
 end procedure
 ```
 
 **Calculate Height:**
 ```
 procedure height(root)
 begin
 	if(root = NULL)
 		return -1;
 	end if
 	leftHeight ← height(root.left);
 	rightHeight ← height(root.right);
 	return 1 + max(leftHeight, rightHeight);
 end procedure
 ```
 
 **Mirror Image:**
 ```
 procedure mirror(root)
 begin
 	if(root = NULL)
 		return;
 	end if
 	temp ← root.left;
 	root.left ← root.right;
 	root.right ← temp;
 	call mirror(root.left);
 	call mirror(root.right);
 end procedure
 ```
 
 **Check Trees Equal:**
 ```
 procedure areEqual(root1, root2)
 begin
 	if(root1 = NULL and root2 = NULL)
 		return true;
 	end if
 	if(root1 = NULL or root2 = NULL)
 		return false;
 	end if
 	if(root1.data ≠ root2.data)
 		return false;
 	end if
 	return areEqual(root1.left, root2.left) and areEqual(root1.right, root2.right);
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 #include <stack>
 #include <queue>
 #include <algorithm>
 
 using namespace std;
 
 struct node {
     int data;
     node *left;
     node *right;
 
     node(int val) {
         data = val;
         left = nullptr;
         right = nullptr;
     }
 };
 
 class BST {
 private:
     node *root;
 
     node* insertRecursive(node *current, int val, bool &inserted) {
         if (current == nullptr) {
             inserted = true;
             return new node(val);
         }
         if (val < current->data) current->left = insertRecursive(current->left, val, inserted);
         else if (val > current->data) current->right = insertRecursive(current->right, val, inserted);
         else { cout << "Duplicate value ignored.\n"; inserted = false; }
         return current;
     }
 
     void preorderRecursive(node *current) {
         if (current == nullptr) return;
         cout << current->data << " ";
         preorderRecursive(current->left);
         preorderRecursive(current->right);
     }
 
     void inorderRecursive(node *current) {
         if (current == nullptr) return;
         inorderRecursive(current->left);
         cout << current->data << " ";
         inorderRecursive(current->right);
     }
 
     void postorderRecursive(node *current) {
         if (current == nullptr) return;
         postorderRecursive(current->left);
         postorderRecursive(current->right);
         cout << current->data << " ";
     }
 
     node* deleteByCopying(node *current, int key) {
         if (current == nullptr) return nullptr;
         if (key < current->data) {
             current->left = deleteByCopying(current->left, key);
         } else if (key > current->data) {
             current->right = deleteByCopying(current->right, key);
         } else {
             if (current->left == nullptr) { node *temp = current->right; delete current; return temp; }
             if (current->right == nullptr) { node *temp = current->left; delete current; return temp; }
             node *pred = current->left;
             while (pred->right != nullptr) pred = pred->right;
             current->data = pred->data;
             current->left = deleteByCopying(current->left, pred->data);
         }
         return current;
     }
 
     node* deleteByMerging(node *current, int key) {
         if (current == nullptr) return nullptr;
         if (key < current->data) { current->left = deleteByMerging(current->left, key); return current; }
         if (key > current->data) { current->right = deleteByMerging(current->right, key); return current; }
         if (current->left == nullptr) { node *temp = current->right; delete current; return temp; }
         if (current->right == nullptr) { node *temp = current->left; delete current; return temp; }
         node *successor = current->right;
         while (successor->left != nullptr) successor = successor->left;
         successor->left = current->left;
         node *temp = current->right;
         delete current;
         return temp;
     }
 
     int countLeaf(node *current) {
         if (current == nullptr) return 0;
         if (current->left == nullptr && current->right == nullptr) return 1;
         return countLeaf(current->left) + countLeaf(current->right);
     }
 
     int countNonLeaf(node *current) {
         if (current == nullptr) return 0;
         if (current->left == nullptr && current->right == nullptr) return 0;
         return 1 + countNonLeaf(current->left) + countNonLeaf(current->right);
     }
 
     int height(node *current) {
         if (current == nullptr) return -1;
         return 1 + max(height(current->left), height(current->right));
     }
 
     void mirror(node *current) {
         if (current == nullptr) return;
         node *temp = current->left;
         current->left = current->right;
         current->right = temp;
         mirror(current->left);
         mirror(current->right);
     }
 
     bool areEqual(node *root1, node *root2) {
         if (root1 == nullptr && root2 == nullptr) return true;
         if (root1 == nullptr || root2 == nullptr) return false;
         if (root1->data != root2->data) return false;
         return areEqual(root1->left, root2->left) && areEqual(root1->right, root2->right);
     }
 
     void destroy(node *current) {
         if (current == nullptr) return;
         destroy(current->left);
         destroy(current->right);
         delete current;
     }
 
 public:
     BST() { root = nullptr; }
 
     void insertRecursive(int val) {
         bool inserted = false;
         root = insertRecursive(root, val, inserted);
     }
 
     void insertIterative(int val) {
         node *newNode = new node(val);
         if (root == nullptr) { root = newNode; return; }
         node *current = root;
         node *parent = nullptr;
         while (current != nullptr) {
             parent = current;
             if (val < current->data) current = current->left;
             else if (val > current->data) current = current->right;
             else { cout << "Duplicate value ignored.\n"; delete newNode; return; }
         }
         if (val < parent->data) parent->left = newNode;
         else parent->right = newNode;
     }
 
     void deleteCopying(int key) {
         if (!search(key)) { cout << "Element not found in BST.\n"; return; }
         root = deleteByCopying(root, key);
     }
 
     void deleteMerging(int key) {
         if (!search(key)) { cout << "Element not found in BST.\n"; return; }
         root = deleteByMerging(root, key);
     }
 
     bool search(int key) {
         node *current = root;
         while (current != nullptr) {
             if (current->data == key) return true;
             current = (key < current->data) ? current->left : current->right;
         }
         return false;
     }
 
     void preorderRecursive() { preorderRecursive(root); cout << endl; }
     void inorderRecursive() { inorderRecursive(root); cout << endl; }
     void postorderRecursive() { postorderRecursive(root); cout << endl; }
 
     void preorderIterative() {
         if (root == nullptr) return;
         stack<node*> s;
         s.push(root);
         while (!s.empty()) {
             node *current = s.top(); s.pop();
             cout << current->data << " ";
             if (current->right != nullptr) s.push(current->right);
             if (current->left != nullptr) s.push(current->left);
         }
         cout << endl;
     }
 
     void inorderIterative() {
         stack<node*> s;
         node *current = root;
         while (current != nullptr || !s.empty()) {
             while (current != nullptr) { s.push(current); current = current->left; }
             current = s.top(); s.pop();
             cout << current->data << " ";
             current = current->right;
         }
         cout << endl;
     }
 
     void postorderIterative() {
         if (root == nullptr) return;
         stack<node*> s1, s2;
         s1.push(root);
         while (!s1.empty()) {
             node *current = s1.top(); s1.pop();
             s2.push(current);
             if (current->left != nullptr) s1.push(current->left);
             if (current->right != nullptr) s1.push(current->right);
         }
         while (!s2.empty()) { cout << s2.top()->data << " "; s2.pop(); }
         cout << endl;
     }
 
     void levelOrder() {
         if (root == nullptr) return;
         queue<node*> q;
         q.push(root);
         while (!q.empty()) {
             node *current = q.front(); q.pop();
             cout << current->data << " ";
             if (current->left != nullptr) q.push(current->left);
             if (current->right != nullptr) q.push(current->right);
         }
         cout << endl;
     }
 
     void countNodes() {
         cout << "Leaf Nodes: " << countLeaf(root) << endl;
         cout << "Non-Leaf Nodes: " << countNonLeaf(root) << endl;
     }
 
     void displayHeight() { cout << "Height of Tree: " << height(root) << endl; }
 
     void createMirror() { mirror(root); }
 
     bool isEqual(BST &other) { return areEqual(root, other.root); }
 
     ~BST() { destroy(root); }
 };
 
 int main() {
     BST tree;
     int choice, value;
 
     while (true) {
         cout << "1.InsertRec 2.InsertIter 3.DeleteCopy 4.DeleteMerge 5.Search\n";
         cout << "6.PreorderRec 7.InorderRec 8.PostorderRec 9.PreorderIter 10.InorderIter\n";
         cout << "11.PostorderIter 12.LevelOrder 13.CountNodes 14.Height 15.Mirror 16.CheckEqual 0.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: cout << "Enter value: "; cin >> value; tree.insertRecursive(value); break;
             case 2: cout << "Enter value: "; cin >> value; tree.insertIterative(value); break;
             case 3: cout << "Enter value to delete: "; cin >> value; tree.deleteCopying(value); break;
             case 4: cout << "Enter value to delete: "; cin >> value; tree.deleteMerging(value); break;
             case 5:
                 cout << "Enter value to search: "; cin >> value;
                 cout << (tree.search(value) ? "Found\n" : "Not found\n");
                 break;
             case 6: tree.preorderRecursive(); break;
             case 7: tree.inorderRecursive(); break;
             case 8: tree.postorderRecursive(); break;
             case 9: tree.preorderIterative(); break;
             case 10: tree.inorderIterative(); break;
             case 11: tree.postorderIterative(); break;
             case 12: tree.levelOrder(); break;
             case 13: tree.countNodes(); break;
             case 14: tree.displayHeight(); break;
             case 15: tree.createMirror(); break;
             case 16: {
                 BST tree2;
                 int n;
                 cout << "Enter number of nodes for second BST: "; cin >> n;
                 for (int i = 0; i < n; i++) { cin >> value; tree2.insertIterative(value); }
                 cout << (tree.isEqual(tree2) ? "Both BSTs are equal.\n" : "BSTs are not equal.\n");
                 break;
             }
             case 0: return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260923202214.png|691]]
 <p align="right">Continue to next page...</p>
 ///
 ![[Pasted image 20260923202219.png|694]]
 <p align="right">Continue to next page...</p>
 ///
 ![[Pasted image 20260923202226.png|697]]
 ///
 ### Discussion:
 - **insertRecursive()** recursively finds the correct NULL position by comparing with each node's data and attaches the new node there.
 - **insertIterative()** walks down the tree using a `current`/`parent` pointer pair until it finds the correct empty spot, then links the new node.
 - **search()** iteratively compares the key against each node's data, moving left or right until found or the tree is exhausted.
 - **deleteByCopying()** locates the node, then replaces its data with the inorder predecessor's data and recursively deletes that predecessor.
 - **deleteByMerging()** locates the node and, if it has two children, attaches its left subtree under the leftmost node of its right subtree, then removes the node.
 - **preorderRecursive() / inorderRecursive() / postorderRecursive()** visit root-left-right, left-root-right, and left-right-root respectively using recursive calls.
 - **preorderIterative()** uses a stack, pushing right then left children so left is processed first.
 - **inorderIterative()** pushes left children onto a stack until NULL, then pops, prints, and moves right.
 - **postorderIterative()** uses two stacks: the first collects nodes in a modified preorder, the second reverses that order for postorder output.
 - **levelOrder()** uses a queue to visit nodes breadth-first, enqueuing children as each node is dequeued.
 - **countLeaf() / countNonLeaf()** recursively count nodes with no children versus nodes with at least one child.
 - **height()** recursively computes `1 + max(leftHeight, rightHeight)`, with an empty tree returning -1.
 - **mirror()** recursively swaps the left and right children of every node.
 - **areEqual()** recursively compares two trees node by node, checking both structure and data.
 
 ///
 ## Assignment 17
 ### Problem Statement:
 WAP to convert the Sparse Matrix into non-zero form and vice-versa.
 ### Problem Definition:
 A **Sparse Matrix** is a matrix in which most elements are zero. Storing it in standard 2D form wastes memory, so it is instead represented in **3-tuple (triplet) form**, storing only the row, column, and value of each non-zero element, along with the matrix's total rows, columns, and non-zero count in the first row.
 ### Algorithm:
 **Convert Standard 2D Matrix to 3-Tuple Representation:**
 ```
 procedure convertToTriplet(matrix, rows, cols)
 begin
 	count ← 0;
 	for i ← 0 to rows - 1 do
 		for j ← 0 to cols - 1 do
 			if(matrix[i][j] ≠ 0)
 				count ← count + 1;
 			end if
 		end for
 	end for
 
 	allocate triplet of size (count + 1) x 3;
 	triplet[0][0] ← rows;
 	triplet[0][1] ← cols;
 	triplet[0][2] ← count;
 
 	k ← 1;
 	for i ← 0 to rows - 1 do
 		for j ← 0 to cols - 1 do
 			if(matrix[i][j] ≠ 0)
 				triplet[k][0] ← i;
 				triplet[k][1] ← j;
 				triplet[k][2] ← matrix[i][j];
 				k ← k + 1;
 			end if
 		end for
 	end for
 end procedure
 ```
 
 **Convert 3-Tuple Representation to Standard 2D Matrix:**
 ```
 procedure convertToStandard(triplet)
 begin
 	rows ← triplet[0][0];
 	cols ← triplet[0][1];
 	count ← triplet[0][2];
 
 	allocate matrix of size rows x cols;
 	for i ← 0 to rows - 1 do
 		for j ← 0 to cols - 1 do
 			matrix[i][j] ← 0;
 		end for
 	end for
 
 	for i ← 1 to count do
 		r ← triplet[i][0];
 		c ← triplet[i][1];
 		val ← triplet[i][2];
 		if(r >= 0 and r < rows and c >= 0 and c < cols)
 			matrix[r][c] ← val;
 		end if
 	end for
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class SparseMatrix {
 private:
     int rows;
     int cols;
     int **standardMatrix;
     int **triplet;
     int nonZeroCount;
 
     void allocateStandard(int r, int c) {
         rows = r;
         cols = c;
         standardMatrix = new int*[rows];
         for (int i = 0; i < rows; i++) {
             standardMatrix[i] = new int[cols];
             for (int j = 0; j < cols; j++) standardMatrix[i][j] = 0;
         }
     }
 
     void freeStandard() {
         if (standardMatrix != nullptr) {
             for (int i = 0; i < rows; i++) delete[] standardMatrix[i];
             delete[] standardMatrix;
             standardMatrix = nullptr;
         }
     }
 
     void freeTriplet() {
         if (triplet != nullptr) {
             for (int i = 0; i <= nonZeroCount; i++) delete[] triplet[i];
             delete[] triplet;
             triplet = nullptr;
         }
     }
 
 public:
     SparseMatrix() {
         rows = 0; cols = 0; nonZeroCount = 0;
         standardMatrix = nullptr;
         triplet = nullptr;
     }
 
     void inputStandardMatrix() {
         freeStandard();
         freeTriplet();
         cout << "Enter number of rows: "; cin >> rows;
         cout << "Enter number of columns: "; cin >> cols;
         if (rows <= 0 || cols <= 0) { cout << "Invalid matrix dimensions!\n"; rows = cols = 0; return; }
         allocateStandard(rows, cols);
         cout << "Enter matrix elements (" << rows << " x " << cols << "):\n";
         for (int i = 0; i < rows; i++)
             for (int j = 0; j < cols; j++) cin >> standardMatrix[i][j];
     }
 
     void convertToTriplet() {
         if (standardMatrix == nullptr) { cout << "No standard matrix available!\n"; return; }
         freeTriplet();
         nonZeroCount = 0;
         for (int i = 0; i < rows; i++)
             for (int j = 0; j < cols; j++)
                 if (standardMatrix[i][j] != 0) nonZeroCount++;
 
         triplet = new int*[nonZeroCount + 1];
         for (int i = 0; i <= nonZeroCount; i++) triplet[i] = new int[3];
 
         triplet[0][0] = rows;
         triplet[0][1] = cols;
         triplet[0][2] = nonZeroCount;
 
         int k = 1;
         for (int i = 0; i < rows; i++)
             for (int j = 0; j < cols; j++)
                 if (standardMatrix[i][j] != 0) {
                     triplet[k][0] = i;
                     triplet[k][1] = j;
                     triplet[k][2] = standardMatrix[i][j];
                     k++;
                 }
     }
 
     void inputTripletForm() {
         freeStandard();
         freeTriplet();
         int r, c, count;
         cout << "Enter total rows: "; cin >> r;
         cout << "Enter total columns: "; cin >> c;
         cout << "Enter number of non-zero elements: "; cin >> count;
         if (r <= 0 || c <= 0 || count < 0 || count > r * c) { cout << "Invalid input parameters!\n"; return; }
 
         rows = r; cols = c; nonZeroCount = count;
         triplet = new int*[nonZeroCount + 1];
         for (int i = 0; i <= nonZeroCount; i++) triplet[i] = new int[3];
 
         triplet[0][0] = rows;
         triplet[0][1] = cols;
         triplet[0][2] = nonZeroCount;
 
         cout << "Enter (row, col, value) for each non-zero element:\n";
         for (int i = 1; i <= nonZeroCount; i++) cin >> triplet[i][0] >> triplet[i][1] >> triplet[i][2];
     }
 
     void convertToStandard() {
         if (triplet == nullptr) { cout << "No 3-tuple representation found!\n"; return; }
         freeStandard();
         rows = triplet[0][0];
         cols = triplet[0][1];
         nonZeroCount = triplet[0][2];
         allocateStandard(rows, cols);
 
         for (int i = 1; i <= nonZeroCount; i++) {
             int r = triplet[i][0];
             int c = triplet[i][1];
             int val = triplet[i][2];
             if (r >= 0 && r < rows && c >= 0 && c < cols) standardMatrix[r][c] = val;
         }
     }
 
     void displayStandard() {
         if (standardMatrix == nullptr) { cout << "Standard matrix is empty!\n"; return; }
         for (int i = 0; i < rows; i++) {
             for (int j = 0; j < cols; j++) cout << standardMatrix[i][j] << " ";
             cout << endl;
         }
     }
 
     void displayTriplet() {
         if (triplet == nullptr) { cout << "3-Tuple representation is empty!\n"; return; }
         for (int i = 0; i <= nonZeroCount; i++)
             cout << triplet[i][0] << " " << triplet[i][1] << " " << triplet[i][2] << endl;
     }
 
     ~SparseMatrix() {
         freeStandard();
         freeTriplet();
     }
 };
 
 int main() {
     SparseMatrix sm;
     int choice;
 
     while (true) {
         cout << "1.InputMatrix 2.ToTriplet 3.DisplayTriplet \n4.InputTriplet 5.ToStandard 6.DisplayMatrix -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1: sm.inputStandardMatrix(); break;
             case 2: sm.convertToTriplet(); break;
             case 3: sm.displayTriplet(); break;
             case 4: sm.inputTripletForm(); break;
             case 5: sm.convertToStandard(); break;
             case 6: sm.displayStandard(); break;
             case -1: cout << "Exiting...\n"; return 0;
             default: cout << "Wrong choice.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260923203309.png|384]]
 ![[Pasted image 20260923203343.png|380]]
 ### Discussion:
 - **convertToTriplet()** scans the 2D matrix to count non-zero elements, allocates a triplet array of that size, and fills it with the row, column, and value of each non-zero entry, with row 0 storing the matrix dimensions and non-zero count.
 - **convertToStandard()** reads the dimensions and count from row 0 of the triplet array, allocates a zero-filled 2D matrix, and places each stored value at its recorded row and column.
 
 ///
 ## Assignment 18
 ### Problem Statement:
 WAP to reverse the order of the elements in the stack using additional stack.
 ### Problem Definition:
 Reversing a **Stack** means making the bottom element the new top and vice versa. This can be achieved using two **auxiliary stacks**: elements are popped off the original stack and pushed twice across two helper stacks, which reverses the order twice and restores the elements to the original stack in reversed order.
 
 ### Algorithm:
 **Reverse Stack Using Additional Stacks:**
 ```
 procedure reverseUsingAdditionalStacks(S, capacity)
 begin
 	if(isEmpty(S))
 		print "Stack is empty! Nothing to reverse.";
 		return;
 	end if
 
 	initialize stack S1 of capacity;
 	initialize stack S2 of capacity;
 
 	while(not isEmpty(S)) do
 		val ← pop(S);
 		push(S1, val);
 	end while
 
 	while(not isEmpty(S1)) do
 		val ← pop(S1);
 		push(S2, val);
 	end while
 
 	while(not isEmpty(S2)) do
 		val ← pop(S2);
 		push(S, val);
 	end while
 end procedure
 ```
 
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class Stack {
 private:
     int *arr;
     int top;
     int capacity;
 
 public:
     Stack(int size) {
         capacity = size;
         arr = new int[capacity];
         top = -1;
     }
 
     Stack(const Stack&) = delete;
     Stack& operator=(const Stack&) = delete;
 
     bool isFull() const { return (top == capacity - 1); }
     bool isEmpty() const { return (top == -1); }
 
     void push(int val) {
         if (isFull()) { cout << "Stack Overflow!\n"; return; }
         arr[++top] = val;
     }
 
     int pop() {
         if (isEmpty()) { cout << "Stack Underflow!\n"; return -1; }
         return arr[top--];
     }
 
     void display() const {
         if (isEmpty()) { cout << "Stack is empty!\n"; return; }
         for (int i = top; i >= 0; i--) cout << arr[i] << " ";
         cout << endl;
     }
 
     void reverseUsingAdditionalStacks() {
         if (isEmpty()) { cout << "Stack is empty! Nothing to reverse.\n"; return; }
 
         Stack s1(capacity);
         Stack s2(capacity);
 
         while (!isEmpty()) s1.push(pop());
         while (!s1.isEmpty()) s2.push(s1.pop());
         while (!s2.isEmpty()) push(s2.pop());
     }
 
     ~Stack() { delete[] arr; }
 };
 
 int main() {
     int size, choice, val;
     cout << "Enter the capacity of the stack: ";
     cin >> size;
     if (size <= 0) { cout << "Invalid stack size!\n"; return 0; }
 
     Stack s(size);
 
     while (true) {
         cout << "1.push 2.pop 3.reverse 0.display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1:
                 cout << "Enter value: ";
                 cin >> val;
                 s.push(val);
                 break;
             case 2: {
                 int v = s.pop();
                 if (v != -1) cout << "Popped element: " << v << endl;
                 break;
             }
             case 3:
                 s.reverseUsingAdditionalStacks();
                 cout << "Stack reversed.\n"; // Added feedback
                 break;
             case 0:
                 s.display();
                 break;
             case -1:
                 cout << "Exiting...\n";
                 return 0;
             default:
                 cout << "Wrong choice.\n";
         }
     }
 }
 ```
 ///
 ### Output:
 ![[Pasted image 20260923205641.png]]
 
 ### Discussion:
 - **reverseUsingAdditionalStacks()** empties the original stack into `s1` (reversing the order once), then transfers `s1` into `s2` (reversing it again), then pushes `s2`'s elements back into the original stack, leaving it in reversed order.
 
 ///
 ## Assignment 19
 ### Problem Statement:
 WAP to reverse the order of the elements in the stack using additional Queue.
 ### Problem Definition:
 Reversing a **Stack** using an auxiliary **Queue** exploits the FIFO order of a queue: elements popped off the stack (in top-to-bottom order) are enqueued, and dequeuing them back (in the same order they were enqueued) and pushing them onto the stack reverses the original arrangement.
 ### Algorithm:
 **Reverse Stack Using Additional Queue:**
 ```
 procedure reverseUsingQueue(S, capacity)
 begin
 	if(isEmpty(S))
 		print "Stack is empty! Nothing to reverse.";
 		return;
 	end if
 
 	initialize queue Q of capacity;
 
 	while(not isEmpty(S)) do
 		val ← pop(S);
 		enqueue(Q, val);
 	end while
 
 	while(not isEmpty(Q)) do
 		val ← dequeue(Q);
 		push(S, val);
 	end while
 end procedure
 ```
 ### Source Code:
 ```
 #include <iostream>
 using namespace std;
 
 class Queue {
 private:
     int *arr;
     int front;
     int rear;
     int capacity;
 
 public:
     Queue(int size) {
         capacity = size;
         arr = new int[capacity];
         front = -1;
         rear = -1;
     }
 
     bool isEmpty() { return (front == -1 || front > rear); }
     bool isFull() { return (rear == capacity - 1); }
 
     void enqueue(int val) {
         if (isFull()) return;
         if (front == -1) front = 0;
         arr[++rear] = val;
     }
 
     int dequeue() {
         if (isEmpty()) return -1;
         int val = arr[front++];
         if (front > rear) { front = -1; rear = -1; }
         return val;
     }
 
     ~Queue() { delete[] arr; }
 };
 
 class Stack {
 private:
     int *arr;
     int top;
     int capacity;
 
 public:
     Stack(int size) {
         capacity = size;
         arr = new int[capacity];
         top = -1;
     }
 
     bool isFull() { return (top == capacity - 1); }
     bool isEmpty() { return (top == -1); }
 
     void push(int val) {
         if (isFull()) { cout << "Stack Overflow!\n"; return; }
         arr[++top] = val;
     }
 
     int pop() {
         if (isEmpty()) { cout << "Stack Underflow!\n"; return -1; }
         return arr[top--];
     }
 
     void display() {
         if (isEmpty()) { cout << "Stack is empty!\n"; return; }
         for (int i = top; i >= 0; i--) cout << arr[i] << " ";
         cout << endl;
     }
 
     void reverseUsingQueue() {
         if (isEmpty()) { cout << "Stack is empty! Nothing to reverse.\n"; return; }
 
         Queue q(capacity);
         while (!isEmpty()) q.enqueue(pop());
         while (!q.isEmpty()) push(q.dequeue());
     }
 
     ~Stack() { delete[] arr; }
 };
 
 int main() {
     int size, choice, val;
     cout << "Enter the capacity of the stack: ";
     cin >> size;
     if (size <= 0) { cout << "Invalid stack size!\n"; return 0; }
 
     Stack s(size);
 
     while (true) {
         cout << "1.push 2.pop 3.reverse 0.display -1.Exit\n";
         cout << "Enter your choice: ";
         cin >> choice;
 
         switch (choice) {
             case 1:
                 cout << "Enter value: ";
                 cin >> val;
                 s.push(val);
                 break;
             case 2: {
                 int v = s.pop();
                 if (v != -1) cout << "Popped element: " << v << endl;
                 break;
             }
             case 3:
                 s.reverseUsingQueue();
                 break;
             case 0:
                 s.display();
                 break;
             case -1:
                 cout << "Exiting...\n";
                 return 0;
             default:
                 cout << "Wrong choice.\n";
         }
     }
 }
 ```
 
 ### Output:
 ![[Pasted image 20260923205948.png|422]]
 ### Discussion:
 - **reverseUsingQueue()** dequeues elements from the stack and enqueues them into a queue in top-to-bottom order, then dequeues them from the queue (same order) and pushes them back onto the stack, producing the reversed arrangement.