OpenSoure_Repos/TheAlgorithms-C-Plus-Plus
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Update math/lcm_sum.cpp

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Co-authored-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
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chestamittal 2020-10-21 22:15:20 +05:30 committed by chestamittal
parent 1af94ccf6f
commit 997404b48a
1 changed files with 12 additions and 12 deletions
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math/lcm_sum.cpp
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@ -1,13 +1,13 @@
/**
* @file
* @brief An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\f$
* @brief An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + .. + \mathrm{LCM}(n,n)\f$
* @details An algorithm to calculate the sum of LCM: \f$\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + .. + \mathrm{LCM}(n,n)\f$ 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)
*/
@ -25,11 +25,11 @@ namespace math {
* @param num input number
* @returns int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num
*/
int lcmSum(int num) {
uint64_t lcmSum(uint64_t num) {
int i=0, j=0;
std::vector <int> eulerTotient(num+1);
std::vector <int> sumOfEulerTotient(num+1);
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++) {
@ -63,28 +63,28 @@ namespace math {
* @returns `void`
*/
static void test() {
int n = 2;
int test_1 = math::lcmSum(n);
uint64_t n = 2;
uint64_t test_1 = math::lcmSum(n);
assert(test_1 == 4);
std::cout << "Passed Test 1!" << std::endl;
n = 5;
int test_2 = math::lcmSum(n);
uint64_t test_2 = math::lcmSum(n);
assert(test_2 == 55);
std::cout << "Passed Test 2!" << std::endl;
n = 10;
int test_3 = math::lcmSum(n);
uint64_t test_3 = math::lcmSum(n);
assert(test_3 == 320);
std::cout << "Passed Test 3!" << std::endl;
n = 11;
int test_4 = math::lcmSum(n);
uint64_t test_4 = math::lcmSum(n);
assert(test_4 == 616);
std::cout << "Passed Test 4!" << std::endl;
n = 15;
int test_5 = math::lcmSum(n);
uint64_t test_5 = math::lcmSum(n);
assert(test_5 == 1110);
std::cout << "Passed Test 5!" << std::endl;
}