Merge branch 'master' into add-prime-binary-string

Author: realstealthninja

.github/workflows/awesome_workflow.yml

@@ -1,6 +1,7 @@
 name: Awesome CI Workflow
 on: [push, pull_request]
 permissions:
+  pull-requests: write
   contents: write
 
 jobs:
@@ -13,10 +14,10 @@ jobs:
           fetch-depth: 0
       - uses: actions/setup-python@v4
       - name: requirements
-        run: | 
+        run: |
           sudo apt-get -qq update
           sudo apt-get -qq install clang-tidy clang-format
-        # checks are passing with less errors when used with this version. 
+        # checks are passing with less errors when used with this version.
         # The default installs v6.0 which did not work out well in my tests
       - name: Setup Git Specs
         run: |
@@ -33,8 +34,8 @@ jobs:
           git diff --diff-filter=dr --name-only origin/master > git_diff.txt
           echo "Files changed-- `cat git_diff.txt`"
       - name: Configure for static lint checks
-        # compiling first gives clang-tidy access to all the header files and settings used to compile the programs. 
-        # This will check for macros, if any, on linux and not for Windows. But the use of portability checks should 
+        # compiling first gives clang-tidy access to all the header files and settings used to compile the programs.
+        # This will check for macros, if any, on linux and not for Windows. But the use of portability checks should
         # be able to catch any errors for other platforms.
         run: cmake -B build -S . -DCMAKE_EXPORT_COMPILE_COMMANDS=ON
       - name: Lint modified files

README.md

@@ -1,4 +1,5 @@
 # The Algorithms - C++ # {#mainpage}
+
 <!-- the suffix in the above line is required for doxygen to consider this as the index page of the generated documentation site -->
 
 [![Gitpod Ready-to-Code](https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/TheAlgorithms/C-Plus-Plus)
@@ -18,13 +19,13 @@ This repository is a collection of open-source implementation of a variety of al
 
 ## Features
 
-* The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - [C++](https://en.wikipedia.org/wiki/C%2B%2B).
-* Well documented source code with detailed explanations provide a valuable resource for educators and students alike.
-* Each source code is atomic using [STL classes](https://en.wikipedia.org/wiki/Standard_Template_Library) and _no external libraries_ are required for their compilation and execution. Thus, the fundamentals of the algorithms can be studied in much depth.
-* Source codes are [compiled and tested](https://github.com/TheAlgorithms/C-Plus-Plus/actions?query=workflow%3A%22Awesome+CI+Workflow%22) for every commit on the latest versions of three major operating systems viz., Windows, MacOS, and Ubuntu (Linux) using MSVC 19 2022, AppleClang 14.0.0, and GNU 11.3.0 respectively. 
-* Strict adherence to [C++17](https://en.wikipedia.org/wiki/C%2B%2B17) standard ensures portability of code to embedded systems as well like [ESP32](https://docs.espressif.com/projects/esp-idf/en/stable/esp32/api-guides/cplusplus.html#c-language-standard), [ARM Cortex](https://developer.arm.com/documentation/101458/2404/Standards-support/Supported-C-C---standards-in-Arm-C-C---Compiler), etc. with little to no changes.
-* Self-checks within programs ensure correct implementations with confidence.
-* Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
+- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - [C++](https://en.wikipedia.org/wiki/C%2B%2B).
+- Well documented source code with detailed explanations provide a valuable resource for educators and students alike.
+- Each source code is atomic using [STL classes](https://en.wikipedia.org/wiki/Standard_Template_Library) and _no external libraries_ are required for their compilation and execution. Thus, the fundamentals of the algorithms can be studied in much depth.
+- Source codes are [compiled and tested](https://github.com/TheAlgorithms/C-Plus-Plus/actions?query=workflow%3A%22Awesome+CI+Workflow%22) for every commit on the latest versions of three major operating systems viz., Windows, MacOS, and Ubuntu (Linux) using MSVC 19 2022, AppleClang 15.0.15, and GNU 13.3.0 respectively.
+- Strict adherence to [C++17](https://en.wikipedia.org/wiki/C%2B%2B17) standard ensures portability of code to embedded systems as well like [ESP32](https://docs.espressif.com/projects/esp-idf/en/stable/esp32/api-guides/cplusplus.html#c-language-standard), [ARM Cortex](https://developer.arm.com/documentation/101458/2404/Standards-support/Supported-C-C---standards-in-Arm-C-C---Compiler), etc. with little to no changes.
+- Self-checks within programs ensure correct implementations with confidence.
+- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
 
 ## Documentation
 

math/factorial_memoization.cpp

@@ -0,0 +1,73 @@
+/**
+ * @file
+ * @brief [Factorial](https://en.wikipedia.org/wiki/Factorial) calculation using recursion and [memoization](https://en.wikipedia.org/wiki/Memoization) 
+ * @details
+ * This program computes the factorial of a non-negative integer using recursion
+ * with memoization (top-down dynamic programming). It stores intermediate results
+ * to avoid redundant calculations for improved efficiency.
+ * 
+ * Memoization is a form of caching where the result to an expensive function call
+ * is stored and returned.
+ * Example:
+ * Input: n = 5
+ * Output: 120
+ * 
+ * Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120
+ * 
+ * The program uses a recursive function fact_recursion which caches computed 
+ * results in a memo array to avoid recalculating factorials for the same numbers.
+ *
+ * Time Complexity: O(n)
+ * Space Complexity: O(n)
+ * @author [Vedant Mukhedkar](https://github.com/git5v)
+ */
+
+#include <iostream> // for std::cout
+#include <cassert>  // For test cases
+#include <array>    // For std::array
+#include <cstdint>  // For uint64_t
+
+/// Array to store computed factorials for memoization
+std::array<uint64_t, 1000> memo{0};
+
+/**
+ * @namespace math
+ * @brief Math algorithms
+ */
+namespace math {
+
+/**
+ * @brief Computes the factorial of a non-negative integer using recursion and memoization.
+ * @param n The integer whose factorial is to be computed
+ * @returns The factorial of n
+ */
+uint64_t fact_recursion(uint64_t n) {
+    if (n == 0) return 1;        // Base case: 0! = 1
+    if (memo[n] != 0) return memo[n]; // Return already computed value
+    memo[n] = n * fact_recursion(n - 1);    // Store and return the computed value
+    return memo[n];
+}
+
+} // namespace math
+/**
+ * @brief Self-test implementations for the fact_recursion function.
+ * @returns void
+ */
+void test_fact_recursion() {
+    // Test cases for factorial computation
+    assert(math::fact_recursion(0) == 1);
+    assert(math::fact_recursion(1) == 1);
+    assert(math::fact_recursion(5) == 120);
+    assert(math::fact_recursion(10) == 3628800);
+    std::cout << "All test cases passed!\n";
+}
+
+/**
+ * @brief Main function to run test cases and interact with the user.
+ * @returns 0 on program success
+ */
+int main() {
+    // Run test cases
+    test_fact_recursion();
+    return 0;
+}