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* Quality of life FIX: initlized sum to 1 instead of adding it before return CHORE: cleaned documentation aswell as adding new documentation, namespace math added * Update math/check_amicable_pair.cpp Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * Update math/check_amicable_pair.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update math/check_amicable_pair.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update math/check_amicable_pair.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * clang-format and clang-tidy fixes forbc87fea5* clang-format and clang-tidy fixes for0a19d1ad--------- Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> Co-authored-by: David Leal <halfpacho@gmail.com> Co-authored-by: github-actions[bot] <github-actions@users.noreply.github.com>
85 lines
2.4 KiB
C++
85 lines
2.4 KiB
C++
/**
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* @file
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* @brief A C++ Program to check whether a pair of numbers is an [amicable
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* pair](https://en.wikipedia.org/wiki/Amicable_numbers) or not.
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*
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* @details
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* An Amicable Pair is two positive integers such that the sum of the proper
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* divisor for each number is equal to the other number.
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*
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* @note Remember that a proper divisor is any positive whole number that
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* divides into a selected number, apart from the selected number itself, and
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* returns a positive integer. for example 1, 2 and 5 are all proper divisors
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* of 10.
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*
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* @author [iamnambiar](https://github.com/iamnambiar)
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*/
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#include <cassert> /// for assert
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#include <iostream> /// for IO operations
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/**
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* @brief Mathematical algorithms
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* @namespace
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*/
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namespace math {
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/**
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* @brief Function to calculate the sum of all the proper divisor
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* of an integer.
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* @param num selected number.
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* @return Sum of the proper divisor of the number.
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*/
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int sum_of_divisor(int num) {
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// Variable to store the sum of all proper divisors.
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int sum = 1;
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// Below loop condition helps to reduce Time complexity by a factor of
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// square root of the number.
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for (int div = 2; div * div <= num; ++div) {
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// Check 'div' is divisor of 'num'.
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if (num % div == 0) {
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// If both divisor are same, add once to 'sum'
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if (div == (num / div)) {
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sum += div;
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} else {
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// If both divisor are not the same, add both to 'sum'.
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sum += (div + (num / div));
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}
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}
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}
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return sum;
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}
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/**
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* @brief Function to check whether the pair is amicable or not.
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* @param x First number.
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* @param y Second number.
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* @return `true` if the pair is amicable
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* @return `false` if the pair is not amicable
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*/
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bool are_amicable(int x, int y) {
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return (sum_of_divisor(x) == y) && (sum_of_divisor(y) == x);
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}
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} // namespace math
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/**
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* @brief Self-test implementations
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* @returns void
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*/
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static void tests() {
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assert(math::are_amicable(220, 284) == true);
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assert(math::are_amicable(6368, 6232) == true);
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assert(math::are_amicable(458, 232) == false);
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assert(math::are_amicable(17296, 18416) == true);
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assert(math::are_amicable(18416, 17296) == true);
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std::cout << "All tests have successfully passed!" << std::endl;
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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tests(); // perform self-tests implementations
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return 0;
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}
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