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feat: Add ncr mod p code (#1325)

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* feat: Add ncr mod p code (#1323)

* Update math/ncr_modulo_p.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Added all functions inside a class + added more asserts

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for f6df24a5

* Replace int64_t to uint64_t + add namespace + detailed documentation

* clang-format and clang-tidy fixes for e09a0579

* Add extra namespace + add const& in function arguments

* clang-format and clang-tidy fixes for 8111f881

* Update ncr_modulo_p.cpp

* clang-format and clang-tidy fixes for 2ad2f721

* Update math/ncr_modulo_p.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/ncr_modulo_p.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/ncr_modulo_p.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 5b69ba5c

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for a8401d4b

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
This commit is contained in:
Kaustubh Damania
2020-11-22 23:05:01 +05:30
committed by GitHub
parent c8ce6f404c
commit 67e26cfbae
19 changed files with 1068 additions and 854 deletions
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math/lcm_sum.cpp
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@@ -1,67 +1,67 @@
/**
* @file
* @brief An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\f$
* @details An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\f$ where \f$\mathrm{LCM}(i,n)\f$
* denotes the Least Common Multiple of the integers i and n. For n greater than or equal to 1.
* The value of the sum is calculated by formula:
* \f[
* \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d * \mathrm{ETF}(d)) + 1\right) * n\right]
* \f]
* where \mathrm{ETF}(i) represents Euler totient function of i.
* @brief An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) +
* \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\f$
* @details An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) +
* \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\f$ where
* \f$\mathrm{LCM}(i,n)\f$ denotes the Least Common Multiple of the integers i
* and n. For n greater than or equal to 1. The value of the sum is calculated
* by formula: \f[ \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d *
* \mathrm{ETF}(d)) + 1\right) * n\right] \f] where \mathrm{ETF}(i) represents
* Euler totient function of i.
* @author [Chesta Mittal](https://github.com/chestamittal)
*/
#include <iostream> /// for std::cin and std::cout
#include <cassert> /// for assert
#include <vector> /// for std::vector
#include <cassert> /// for assert
#include <iostream> /// for std::cin and std::cout
#include <vector> /// for std::vector
/**
* @namespace math
* @brief Mathematical algorithms
*/
namespace math {
/**
* Function to compute sum of euler totients in sumOfEulerTotient vector
* @param num input number
* @returns int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num
*/
uint64_t lcmSum(const uint16_t& num) {
uint64_t i=0, j=0;
std::vector <uint64_t> eulerTotient(num+1);
std::vector <uint64_t> sumOfEulerTotient(num+1);
// storing initial values in eulerTotient vector
for(i=1; i<=num; i++) {
eulerTotient[i] = i;
}
/**
* Function to compute sum of euler totients in sumOfEulerTotient vector
* @param num input number
* @returns int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num
*/
uint64_t lcmSum(const uint16_t& num) {
uint64_t i = 0, j = 0;
std::vector<uint64_t> eulerTotient(num + 1);
std::vector<uint64_t> sumOfEulerTotient(num + 1);
// applying totient sieve
for(i=2; i<=num; i++) {
if(eulerTotient[i] == i) {
for(j=i; j<=num; j+=i) {
eulerTotient[j] = eulerTotient[j]/i;
eulerTotient[j] = eulerTotient[j]*(i-1);
}
}
}
// computing sum of euler totients
for(i=1; i<=num; i++) {
for(j=i; j <=num; j+=i) {
sumOfEulerTotient[j] += eulerTotient[i]*i;
}
}
return ((sumOfEulerTotient[num] + 1 ) * num) / 2;
// storing initial values in eulerTotient vector
for (i = 1; i <= num; i++) {
eulerTotient[i] = i;
}
// applying totient sieve
for (i = 2; i <= num; i++) {
if (eulerTotient[i] == i) {
for (j = i; j <= num; j += i) {
eulerTotient[j] = eulerTotient[j] / i;
eulerTotient[j] = eulerTotient[j] * (i - 1);
}
}
}
// computing sum of euler totients
for (i = 1; i <= num; i++) {
for (j = i; j <= num; j += i) {
sumOfEulerTotient[j] += eulerTotient[i] * i;
}
}
return ((sumOfEulerTotient[num] + 1) * num) / 2;
}
} // namespace math
/**
* Function for testing lcmSum function.
* test cases and assert statement.
* @returns `void`
*/
*/
static void test() {
uint64_t n = 2;
uint64_t test_1 = math::lcmSum(n);