commit 1ac322c3215b797258c85dbbdb8b8a8c764b05d2
parent 3336fd8f727d1c01a3528af06f2bf251740dbd3d
Author: Amit Dutta <amitdutta4255@gmail.com>
Date: Thu, 23 Oct 2025 12:11:14 +0530
new
Diffstat:
7 files changed, 419 insertions(+), 5 deletions(-)
diff --git a/docs/index.html b/docs/index.html
@@ -720,7 +720,7 @@ int main()
<div class="flex items-center">
<svg class="w-6 h-6 text-blue-500 mr-4 flex-shrink-0" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M3 7v10a2 2 0 002 2h14a2 2 0 002-2V9a2 2 0 00-2-2h-6l-2-2H5a2 2 0 00-2 2z"></path></svg>
<span class="font-medium text-gray-800">letusc</span>
- <span class="ml-2 text-sm text-gray-500">(48 files)</span>
+ <span class="ml-2 text-sm text-gray-500">(50 files)</span>
</div>
<div class="flex items-center space-x-4">
<a href="https://github.com/notamitgamer/bsc/tree/main/letusc" target="_blank" class="p-1 rounded-full text-gray-500 hover:bg-gray-200 hover:text-gray-800 transition-colors" onclick="event.stopPropagation()" title="View folder on GitHub">
@@ -2703,6 +2703,229 @@ int main()
<li>
<div class="flex items-center p-3 pl-8 hover:bg-gray-50 transition-colors duration-200">
<svg class="w-6 h-6 text-green-500 mr-4 flex-shrink-0" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z"></path></svg>
+ <span class="text-gray-700">luc040-logic.c</span>
+ <div class="ml-auto flex items-center space-x-4">
+ <a href="https://github.com/notamitgamer/bsc/blob/main/letusc/luc040-logic.c" target="_blank" class="p-1 rounded-full text-gray-500 hover:bg-gray-200 hover:text-gray-800 transition-colors" title="View file on GitHub">
+ <svg class="w-6 h-6" fill="currentColor" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M12 2C6.477 2 2 6.477 2 12c0 4.418 2.865 8.168 6.839 9.492.5.092.682-.217.682-.482 0-.237-.009-.868-.014-1.703-2.782.605-3.369-1.343-3.369-1.343-.454-1.158-1.11-1.466-1.11-1.466-.908-.62.069-.608.069-.608 1.003.07 1.531 1.032 1.531 1.032.892 1.53 2.341 1.088 2.91.832.092-.647.35-1.088.636-1.338-2.22-.253-4.555-1.113-4.555-4.951 0-1.093.39-1.988 1.031-2.688-.103-.253-.446-1.272.098-2.65 0 0 .84-.27 2.75 1.026A9.564 9.564 0 0112 6.844c.85.004 1.705.115 2.504.337 1.909-1.296 2.747-1.027 2.747-1.027.546 1.379.203 2.398.1 2.651.64.7 1.03 1.595 1.03 2.688 0 3.848-2.338 4.695-4.566 4.942.359.308.678.92.678 1.855 0 1.338-.012 2.419-.012 2.747 0 .268.18.58.688.482A10.001 10.001 0 0022 12c0-5.523-4.477-10-10-10z" clip-rule="evenodd"></path></svg>
+ </a>
+ <button onclick="showCode('code-letusc-luc040-logic_c', 'luc040-logic.c')" class="text-green-600 font-semibold text-sm hover:underline">View Code</button>
+ </div>
+ </div>
+ <div id="code-letusc-luc040-logic_c" class="hidden" data-github-url="https://github.com/notamitgamer/bsc/blob/main/letusc/luc040-logic.c">
+ <pre><code class="language-c">/* Ramanujan number (1729) is the smallest number that can be
+expressed as sum of cubes in two different ways - 1729 can be
+expressed as 1^3 + 12^3 and 9^3 + 10^3. Write a program to print all such
+numbers up to a reasonable limit. */
+/* Author - Amit Dutta, Date - 22th OCT, 2025 */
+/* Let Us C, Chap- 6, Page - 106, Qn No.: B(g) */
+
+// 1. INCLUDE SECTION
+#include <stdio.h> // Includes the standard input/output library, necessary for printf()
+
+// 2. CONSTANT DEFINITIONS (MACROS)
+// These define fixed values we can easily use and change later.
+#define LIMIT 100000 // The maximum number we want to search up to.
+// The maximum base value (a, b, c, or d) we need to check.
+// Since 47^3 is greater than 100,000, checking bases up to 47 covers the LIMIT.
+#define MAX_BASE_VAL 47
+
+// 3. MAIN FUNCTION
+int main()
+{
+ // 4. VARIABLE DECLARATION
+
+ // sum1 and sum2 store the results of a^3 + b^3 and c^3 + d^3.
+ // We use 'long long' because cubes (like 47^3) are large and can exceed
+ // the capacity of a standard 'int', preventing errors.
+ long long sum1, sum2;
+
+ int count = 0; // Counter to keep track of how many Ramanujan numbers we find.
+
+ // This flag is used to optimize the search. If we find the second way (c^3 + d^3)
+ // to make sum1, we set this to 1 and immediately stop the inner loops.
+ int found_match;
+
+ // Print introductory message to the user.
+ printf("Ramanujan Number Finder (a^3 + b^3 = c^3 + d^3)\n");
+ printf("Searching up to %d (Max base value is %d)\n", LIMIT, MAX_BASE_VAL);
+ printf("---------------------------------------------------\n");
+
+ // 5. OUTER LOOPS: Establishing the FIRST SUM (a^3 + b^3 = sum1)
+
+ // Loop for 'a' (the smaller base of the first pair)
+ for (int a = 1; a <= MAX_BASE_VAL; a++)
+ {
+
+ // Loop for 'b' (the larger base of the first pair)
+ // We start 'b' at 'a + 1' to enforce the rule a < b.
+ // This prevents us from checking redundant pairs like (1, 12) and (12, 1).
+ for (int b = a + 1; b <= MAX_BASE_VAL; b++)
+ {
+
+ // Calculate the first sum: sum1 = a^3 + b^3
+ // (long long) is a cast to ensure the math is done using the 'long long' type.
+ sum1 = (long long)a * a * a + (long long)b * b * b;
+
+ // Optimization 1: Check if the sum exceeds the global limit.
+ if (sum1 > LIMIT)
+ {
+ // Since 'b' is increasing, any further increase will also be over the limit.
+ // We stop the 'b' loop and move to the next 'a'.
+ break;
+ }
+
+ // Reset the flag for every new sum1.
+ // We start searching for a second way for this new 'sum1', so we reset the flag to 0.
+ found_match = 0;
+
+ // 6. INNER LOOPS: Searching for the SECOND SUM (c^3 + d^3 = sum2)
+
+ // Loop for 'c' (the smaller base of the second pair)
+ // We start 'c' at 'a + 1' to enforce the rule a < c.
+ // This ensures the two pairs {(a, b) and (c, d)} are truly distinct (e.g., 1729 = 1^3 + 12^3 and 9^3 + 10^3).
+ for (int c = a + 1; c <= MAX_BASE_VAL; c++)
+ {
+
+ // Optimization 2: Check the flag to exit the 'c' loop early.
+ if (found_match)
+ {
+ // If we already found the second way (c, d) in a previous iteration of 'c', stop searching and move to the next (a, b) pair.
+ break;
+ }
+
+ // Loop for 'd' (the larger base of the second pair)
+ // We start 'd' at 'c + 1' to enforce c < d.
+ for (int d = c + 1; d <= MAX_BASE_VAL; d++)
+ {
+
+ // Calculate the second sum: sum2 = c^3 + d^3
+ sum2 = (long long)c * c * c + (long long)d * d * d;
+
+ // Optimization 3: Check if the second sum has passed the first sum.
+ if (sum2 > sum1)
+ {
+ // Since 'd' is increasing, any further increase will also be greater than sum1.
+ // We stop the 'd' loop and move to the next 'c'.
+ break;
+ }
+
+ // 7. CONDITION CHECK: Have we found a Ramanujan number?
+ // Check if the two sums are equal.
+ if (sum1 == sum2)
+ {
+ count++; // Increment the counter
+
+ // Print the result in the required format.
+ printf("[%d] %lld = %d^3 + %d^3 = %d^3 + %d^3\n",
+ count, sum1, a, b, c, d);
+
+ // Set the flag to 1, confirming we found the second way.
+ found_match = 1;
+
+ // Stop the 'd' loop immediately, as we found the required second pair.
+ break;
+ }
+ }
+ // If found_match was set to 1, the 'break' in the d loop will execute,
+ // then the 'if (found_match) break;' in the c loop will execute,
+ // and the program will move to the next (a, b) pair.
+ }
+ }
+ }
+
+ // 8. CONCLUSION
+ printf("---------------------------------------------------\n");
+ printf("Search complete. Found %d Ramanujan-type numbers.\n", count);
+
+ return 0; // Standard way to indicate successful program execution.
+}
+</code></pre>
+ </div>
+ </li>
+
+ <li>
+ <div class="flex items-center p-3 pl-8 hover:bg-gray-50 transition-colors duration-200">
+ <svg class="w-6 h-6 text-green-500 mr-4 flex-shrink-0" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z"></path></svg>
+ <span class="text-gray-700">luc040.c</span>
+ <div class="ml-auto flex items-center space-x-4">
+ <a href="https://github.com/notamitgamer/bsc/blob/main/letusc/luc040.c" target="_blank" class="p-1 rounded-full text-gray-500 hover:bg-gray-200 hover:text-gray-800 transition-colors" title="View file on GitHub">
+ <svg class="w-6 h-6" fill="currentColor" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M12 2C6.477 2 2 6.477 2 12c0 4.418 2.865 8.168 6.839 9.492.5.092.682-.217.682-.482 0-.237-.009-.868-.014-1.703-2.782.605-3.369-1.343-3.369-1.343-.454-1.158-1.11-1.466-1.11-1.466-.908-.62.069-.608.069-.608 1.003.07 1.531 1.032 1.531 1.032.892 1.53 2.341 1.088 2.91.832.092-.647.35-1.088.636-1.338-2.22-.253-4.555-1.113-4.555-4.951 0-1.093.39-1.988 1.031-2.688-.103-.253-.446-1.272.098-2.65 0 0 .84-.27 2.75 1.026A9.564 9.564 0 0112 6.844c.85.004 1.705.115 2.504.337 1.909-1.296 2.747-1.027 2.747-1.027.546 1.379.203 2.398.1 2.651.64.7 1.03 1.595 1.03 2.688 0 3.848-2.338 4.695-4.566 4.942.359.308.678.92.678 1.855 0 1.338-.012 2.419-.012 2.747 0 .268.18.58.688.482A10.001 10.001 0 0022 12c0-5.523-4.477-10-10-10z" clip-rule="evenodd"></path></svg>
+ </a>
+ <button onclick="showCode('code-letusc-luc040_c', 'luc040.c')" class="text-green-600 font-semibold text-sm hover:underline">View Code</button>
+ </div>
+ </div>
+ <div id="code-letusc-luc040_c" class="hidden" data-github-url="https://github.com/notamitgamer/bsc/blob/main/letusc/luc040.c">
+ <pre><code class="language-c">/* Ramanujan number (1729) is the smallest number that can be
+expressed as sum of cubes in two different ways - 1729 can be
+expressed as 1^3 + 12^3 and 9^3 + 10^3. Write a program to print all such
+numbers up to a reasonable limit. */
+/* Author - Amit Dutta, Date - 22th OCT, 2025 */
+/* Let Us C, Chap- 6, Page - 106, Qn No.: B(g) */
+
+#include <stdio.h>
+
+#define limit 100000
+#define max_base 47
+
+int main()
+{
+
+ long long sum1, sum2;
+ int count = 0;
+
+ printf("Ramanujan numbers : \n");
+
+ int found_match;
+
+ for (int a = 1; a <= max_base; a++)
+ {
+ for (int b = a + 1; b <= max_base; b++)
+ {
+ sum1 = (long long)a * a * a + (long long)b * b * b;
+ if (sum1 > limit)
+ {
+ break;
+ }
+
+ found_match = 0;
+
+ for (int c = a + 1; c <= max_base; c++)
+ {
+ if (found_match)
+ {
+ break;
+ }
+ for (int d = c + 1; d <= max_base; d++)
+ {
+ sum2 = (long long)c * c * c + (long long)d * d * d;
+ if (sum2 > sum1)
+ {
+ break;
+ }
+ if (sum1 == sum2)
+ {
+ count++;
+ printf("(%d.) %lld = %d^3 + %d^3 = %d^3 + %d^3\n", count, sum1, a, b, c, d);
+
+ found_match = 1;
+ break;
+ }
+ }
+ }
+ }
+ }
+
+ printf("-------------------------------\n");
+ printf("Search complete.");
+
+ return 0;
+}</code></pre>
+ </div>
+ </li>
+
+ <li>
+ <div class="flex items-center p-3 pl-8 hover:bg-gray-50 transition-colors duration-200">
+ <svg class="w-6 h-6 text-green-500 mr-4 flex-shrink-0" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z"></path></svg>
<span class="text-gray-700">lucproblem001.c</span>
<div class="ml-auto flex items-center space-x-4">
<a href="https://github.com/notamitgamer/bsc/blob/main/letusc/lucproblem001.c" target="_blank" class="p-1 rounded-full text-gray-500 hover:bg-gray-200 hover:text-gray-800 transition-colors" title="View file on GitHub">
diff --git a/letusc/luc037.c b/letusc/luc037.c
@@ -2,7 +2,7 @@
(x-1)/x + 1/2 ((x-1)/x)^2 + 1/2 ((x-1)/x)^3 + 1/2 ((x-1)/x)^4 + ...
If x is input through the keyboard, write a program to calculate the
sum of the first seven terms of this series. */
-/* Author - Amit Dutta, Date - 21th OCT, 2025 */
+/* Author - Amit Dutta, Date - 21st OCT, 2025 */
/* Let Us C, Chap- 6, Page - 106, Qn No.: B(d) */
#include <stdio.h>
diff --git a/letusc/luc038.c b/letusc/luc038.c
@@ -1,6 +1,6 @@
/* Write a program to generate all Pythagorean Triplets with slide
length less than or equal to 30. */
-/* Author - Amit Dutta, Date - 21th OCT, 2025 */
+/* Author - Amit Dutta, Date - 21st OCT, 2025 */
/* Let Us C, Chap- 6, Page - 106, Qn No.: B(e) */
#include <stdio.h>
diff --git a/letusc/luc039.c b/letusc/luc039.c
@@ -2,7 +2,7 @@
steadily at the rate of 10% per year for last 10 years. Write a
program to determine the population at the end of each year in the
last decade. */
-/* Author - Amit Dutta, Date - 21th OCT, 2025 */
+/* Author - Amit Dutta, Date - 21st OCT, 2025 */
/* Let Us C, Chap- 6, Page - 106, Qn No.: B(f) */
#include <stdio.h>
diff --git a/letusc/luc040-logic.c b/letusc/luc040-logic.c
@@ -0,0 +1,127 @@
+/* Ramanujan number (1729) is the smallest number that can be
+expressed as sum of cubes in two different ways - 1729 can be
+expressed as 1^3 + 12^3 and 9^3 + 10^3. Write a program to print all such
+numbers up to a reasonable limit. */
+/* Author - Amit Dutta, Date - 22nd - 23rd OCT, 2025 */
+/* Let Us C, Chap- 6, Page - 106, Qn No.: B(g) */
+
+// 1. INCLUDE SECTION
+#include <stdio.h> // Includes the standard input/output library, necessary for printf()
+
+// 2. CONSTANT DEFINITIONS (MACROS)
+// These define fixed values we can easily use and change later.
+#define LIMIT 100000 // The maximum number we want to search up to.
+// The maximum base value (a, b, c, or d) we need to check.
+// Since 47^3 is greater than 100,000, checking bases up to 47 covers the LIMIT.
+#define MAX_BASE_VAL 47
+
+// 3. MAIN FUNCTION
+int main()
+{
+ // 4. VARIABLE DECLARATION
+
+ // sum1 and sum2 store the results of a^3 + b^3 and c^3 + d^3.
+ // We use 'long long' because cubes (like 47^3) are large and can exceed
+ // the capacity of a standard 'int', preventing errors.
+ long long sum1, sum2;
+
+ int count = 0; // Counter to keep track of how many Ramanujan numbers we find.
+
+ // This flag is used to optimize the search. If we find the second way (c^3 + d^3)
+ // to make sum1, we set this to 1 and immediately stop the inner loops.
+ int found_match;
+
+ // Print introductory message to the user.
+ printf("Ramanujan Number Finder (a^3 + b^3 = c^3 + d^3)\n");
+ printf("Searching up to %d (Max base value is %d)\n", LIMIT, MAX_BASE_VAL);
+ printf("---------------------------------------------------\n");
+
+ // 5. OUTER LOOPS: Establishing the FIRST SUM (a^3 + b^3 = sum1)
+
+ // Loop for 'a' (the smaller base of the first pair)
+ for (int a = 1; a <= MAX_BASE_VAL; a++)
+ {
+
+ // Loop for 'b' (the larger base of the first pair)
+ // We start 'b' at 'a + 1' to enforce the rule a < b.
+ // This prevents us from checking redundant pairs like (1, 12) and (12, 1).
+ for (int b = a + 1; b <= MAX_BASE_VAL; b++)
+ {
+
+ // Calculate the first sum: sum1 = a^3 + b^3
+ // (long long) is a cast to ensure the math is done using the 'long long' type.
+ sum1 = (long long)a * a * a + (long long)b * b * b;
+
+ // Optimization 1: Check if the sum exceeds the global limit.
+ if (sum1 > LIMIT)
+ {
+ // Since 'b' is increasing, any further increase will also be over the limit.
+ // We stop the 'b' loop and move to the next 'a'.
+ break;
+ }
+
+ // Reset the flag for every new sum1.
+ // We start searching for a second way for this new 'sum1', so we reset the flag to 0.
+ found_match = 0;
+
+ // 6. INNER LOOPS: Searching for the SECOND SUM (c^3 + d^3 = sum2)
+
+ // Loop for 'c' (the smaller base of the second pair)
+ // We start 'c' at 'a + 1' to enforce the rule a < c.
+ // This ensures the two pairs {(a, b) and (c, d)} are truly distinct (e.g., 1729 = 1^3 + 12^3 and 9^3 + 10^3).
+ for (int c = a + 1; c <= MAX_BASE_VAL; c++)
+ {
+
+ // Optimization 2: Check the flag to exit the 'c' loop early.
+ if (found_match)
+ {
+ // If we already found the second way (c, d) in a previous iteration of 'c', stop searching and move to the next (a, b) pair.
+ break;
+ }
+
+ // Loop for 'd' (the larger base of the second pair)
+ // We start 'd' at 'c + 1' to enforce c < d.
+ for (int d = c + 1; d <= MAX_BASE_VAL; d++)
+ {
+
+ // Calculate the second sum: sum2 = c^3 + d^3
+ sum2 = (long long)c * c * c + (long long)d * d * d;
+
+ // Optimization 3: Check if the second sum has passed the first sum.
+ if (sum2 > sum1)
+ {
+ // Since 'd' is increasing, any further increase will also be greater than sum1.
+ // We stop the 'd' loop and move to the next 'c'.
+ break;
+ }
+
+ // 7. CONDITION CHECK: Have we found a Ramanujan number?
+ // Check if the two sums are equal.
+ if (sum1 == sum2)
+ {
+ count++; // Increment the counter
+
+ // Print the result in the required format.
+ printf("[%d] %lld = %d^3 + %d^3 = %d^3 + %d^3\n",
+ count, sum1, a, b, c, d);
+
+ // Set the flag to 1, confirming we found the second way.
+ found_match = 1;
+
+ // Stop the 'd' loop immediately, as we found the required second pair.
+ break;
+ }
+ }
+ // If found_match was set to 1, the 'break' in the d loop will execute,
+ // then the 'if (found_match) break;' in the c loop will execute,
+ // and the program will move to the next (a, b) pair.
+ }
+ }
+ }
+
+ // 8. CONCLUSION
+ printf("---------------------------------------------------\n");
+ printf("Search complete. Found %d Ramanujan-type numbers.\n", count);
+
+ return 0; // Standard way to indicate successful program execution.
+}
diff --git a/letusc/luc040.c b/letusc/luc040.c
@@ -2,5 +2,64 @@
expressed as sum of cubes in two different ways - 1729 can be
expressed as 1^3 + 12^3 and 9^3 + 10^3. Write a program to print all such
numbers up to a reasonable limit. */
-/* Author - Amit Dutta, Date - 22th OCT, 2025 */
+/* Author - Amit Dutta, Date - 22nd - 23rd OCT, 2025 */
/* Let Us C, Chap- 6, Page - 106, Qn No.: B(g) */
+
+#include <stdio.h>
+
+#define limit 100000
+#define max_base 47
+
+int main()
+{
+
+ long long sum1, sum2;
+ int count = 0;
+
+ printf("Ramanujan numbers : \n");
+
+ int found_match;
+
+ for (int a = 1; a <= max_base; a++)
+ {
+ for (int b = a + 1; b <= max_base; b++)
+ {
+ sum1 = (long long)a * a * a + (long long)b * b * b;
+ if (sum1 > limit)
+ {
+ break;
+ }
+
+ found_match = 0;
+
+ for (int c = a + 1; c <= max_base; c++)
+ {
+ if (found_match)
+ {
+ break;
+ }
+ for (int d = c + 1; d <= max_base; d++)
+ {
+ sum2 = (long long)c * c * c + (long long)d * d * d;
+ if (sum2 > sum1)
+ {
+ break;
+ }
+ if (sum1 == sum2)
+ {
+ count++;
+ printf("(%d.) %lld = %d^3 + %d^3 = %d^3 + %d^3\n", count, sum1, a, b, c, d);
+
+ found_match = 1;
+ break;
+ }
+ }
+ }
+ }
+ }
+
+ printf("-------------------------------\n");
+ printf("Search complete.");
+
+ return 0;
+}+
\ No newline at end of file
diff --git a/letusc/luc041.c b/letusc/luc041.c
@@ -0,0 +1,3 @@
+/* Write */
+/* Author - Amit Dutta, Date - 23rd OCT, 2025 */
+/* Let Us C, Chap- 6, Page - 106, Qn No.: B(h) */+
\ No newline at end of file
