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* Create check_even_odd.cpp Implementation to Check if a number is Even or Odd using Bitwise Operator * Update check_even_odd.cpp * Create factorial_top_down_dp.cpp * Delete dynamic_programming/factorial_top_down_dp.cpp Deleted the one file as there was 2 files in the commit * Create factorial_top_down_dp.cpp * Delete bit_manipulation/check_even_odd.cpp * Update dynamic_programming/factorial_top_down_dp.cpp Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * Update dynamic_programming/factorial_top_down_dp.cpp Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * Update dynamic_programming/factorial_top_down_dp.cpp Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * Update factorial_top_down_dp.cpp modified * Update factorial_top_down_dp.cpp added __uint128_t for handling fixed-width integer types * Create memoised_factorial.cpp * Rename memoised_factorial.cpp to factorial_memoization.cpp * Update factorial_memoization.cpp * Delete dynamic_programming/factorial_top_down_dp.cpp deleted the file from dp folder * Update math/factorial_memoization.cpp Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * Update factorial_memoization.cpp added cstdint header and switched to uint64 Thanks * fix: wrap factorial functions under math namespace * chore: add scope specifier in test cases * doc: add documentation to headers * doc: add defintion of memoisation as well as rewrite brief --------- Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>
74 lines
2.2 KiB
C++
74 lines
2.2 KiB
C++
/**
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* @file
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* @brief [Factorial](https://en.wikipedia.org/wiki/Factorial) calculation using recursion and [memoization](https://en.wikipedia.org/wiki/Memoization)
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* @details
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* This program computes the factorial of a non-negative integer using recursion
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* with memoization (top-down dynamic programming). It stores intermediate results
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* to avoid redundant calculations for improved efficiency.
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*
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* Memoization is a form of caching where the result to an expensive function call
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* is stored and returned.
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* Example:
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* Input: n = 5
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* Output: 120
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*
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* Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120
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*
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* The program uses a recursive function fact_recursion which caches computed
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* results in a memo array to avoid recalculating factorials for the same numbers.
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*
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* Time Complexity: O(n)
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* Space Complexity: O(n)
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* @author [Vedant Mukhedkar](https://github.com/git5v)
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*/
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#include <iostream> // for std::cout
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#include <cassert> // For test cases
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#include <array> // For std::array
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#include <cstdint> // For uint64_t
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/// Array to store computed factorials for memoization
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std::array<uint64_t, 1000> memo{0};
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/**
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* @namespace math
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* @brief Math algorithms
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*/
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namespace math {
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/**
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* @brief Computes the factorial of a non-negative integer using recursion and memoization.
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* @param n The integer whose factorial is to be computed
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* @returns The factorial of n
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*/
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uint64_t fact_recursion(uint64_t n) {
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if (n == 0) return 1; // Base case: 0! = 1
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if (memo[n] != 0) return memo[n]; // Return already computed value
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memo[n] = n * fact_recursion(n - 1); // Store and return the computed value
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return memo[n];
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}
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} // namespace math
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/**
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* @brief Self-test implementations for the fact_recursion function.
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* @returns void
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*/
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void test_fact_recursion() {
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// Test cases for factorial computation
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assert(math::fact_recursion(0) == 1);
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assert(math::fact_recursion(1) == 1);
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assert(math::fact_recursion(5) == 120);
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assert(math::fact_recursion(10) == 3628800);
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std::cout << "All test cases passed!\n";
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}
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/**
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* @brief Main function to run test cases and interact with the user.
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* @returns 0 on program success
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*/
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int main() {
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// Run test cases
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test_fact_recursion();
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return 0;
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}
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