mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-02-03 18:46:50 +08:00
78 lines
2.0 KiB
C++
78 lines
2.0 KiB
C++
/**
|
|
* @file
|
|
* @brief Algorithm to find largest x such that p^x divides n! (factorial) using
|
|
* Legendre's Formula.
|
|
* @details Given an integer n and a prime number p, the task is to find the
|
|
* largest x such that p^x (p raised to power x) divides n! (factorial). This
|
|
* will be done using Legendre's formula: x = [n/(p^1)] + [n/(p^2)] + [n/(p^3)]
|
|
* + \ldots + 1
|
|
* @see more on
|
|
* https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n
|
|
* @author [uday6670](https://github.com/uday6670)
|
|
*/
|
|
|
|
#include <cassert> /// for assert
|
|
#include <cstdint> /// for integral typedefs
|
|
#include <iostream> /// for std::cin and std::cout
|
|
/**
|
|
* @namespace math
|
|
* @brief Mathematical algorithms
|
|
*/
|
|
namespace math {
|
|
|
|
/**
|
|
* @brief Function to calculate largest power
|
|
* @param n number
|
|
* @param p prime number
|
|
* @returns largest power
|
|
*/
|
|
uint64_t largestPower(uint32_t n, const uint16_t& p) {
|
|
// Initialize result
|
|
int x = 0;
|
|
|
|
// Calculate result
|
|
while (n) {
|
|
n /= p;
|
|
x += n;
|
|
}
|
|
return x;
|
|
}
|
|
|
|
} // namespace math
|
|
|
|
/**
|
|
* @brief Function for testing largestPower function.
|
|
* test cases and assert statement.
|
|
* @returns `void`
|
|
*/
|
|
static void test() {
|
|
uint8_t test_case_1 = math::largestPower(5, 2);
|
|
assert(test_case_1 == 3);
|
|
std::cout << "Test 1 Passed!" << std::endl;
|
|
|
|
uint16_t test_case_2 = math::largestPower(10, 3);
|
|
assert(test_case_2 == 4);
|
|
std::cout << "Test 2 Passed!" << std::endl;
|
|
|
|
uint32_t test_case_3 = math::largestPower(25, 5);
|
|
assert(test_case_3 == 6);
|
|
std::cout << "Test 3 Passed!" << std::endl;
|
|
|
|
uint32_t test_case_4 = math::largestPower(27, 2);
|
|
assert(test_case_4 == 23);
|
|
std::cout << "Test 4 Passed!" << std::endl;
|
|
|
|
uint16_t test_case_5 = math::largestPower(7, 3);
|
|
assert(test_case_5 == 2);
|
|
std::cout << "Test 5 Passed!" << std::endl;
|
|
}
|
|
|
|
/**
|
|
* @brief Main function
|
|
* @returns 0 on exit
|
|
*/
|
|
int main() {
|
|
test(); // execute the tests
|
|
return 0;
|
|
}
|