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 2020-10-20 14:19:29 +05:30 committed by chestamittal
parent e466714e27
commit b1e2d1ed8e
1 changed files with 10 additions and 9 deletions
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math/lcm_sum.cpp
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@ -4,7 +4,9 @@
* @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$\mathrm{LCM}(i,n)\f$ * @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. * 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: * The value of the sum is calculated by formula:
* ∑LCM(i, n) = ((∑(d * ETF(d)) + 1) * n) / 2 * \f[
* \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d * \mathrm{ETF}(d)) + 1\right) * n\right]
* \f]
* *
* @author [Chesta Mittal](https://github.com/chestamittal) * @author [Chesta Mittal](https://github.com/chestamittal)
*/ */
@ -26,19 +28,18 @@ namespace math {
int lcmSum(int num) { int lcmSum(int num) {
int i=0, j=0; int i=0, j=0;
int limit = 1000; std::vector <int> eulerTotient(num+1);
std::vector <int> eulerTotient(limit); std::vector <int> sumOfEulerTotient(num+1);
std::vector <int> sumOfEulerTotient(limit);
// storing initial values in eulerTotient vector // storing initial values in eulerTotient vector
for(i=1; i<=limit; i++) { for(i=1; i<=num; i++) {
eulerTotient[i] = i; eulerTotient[i] = i;
} }
// applying totient sieve // applying totient sieve
for(i=2; i<=limit; i++) { for(i=2; i<=num; i++) {
if(eulerTotient[i] == i) { if(eulerTotient[i] == i) {
for(j=i; j<=limit; j+=i) { for(j=i; j<=num; j+=i) {
eulerTotient[j] = eulerTotient[j]/i; eulerTotient[j] = eulerTotient[j]/i;
eulerTotient[j] = eulerTotient[j]*(i-1); eulerTotient[j] = eulerTotient[j]*(i-1);
} }
@ -46,8 +47,8 @@ namespace math {
} }
// computing sum of euler totients // computing sum of euler totients
for(i=1; i<=limit; i++) { for(i=1; i<=num; i++) {
for(j=i; j <=limit; j+=i) { for(j=i; j <=num; j+=i) {
sumOfEulerTotient[j] += eulerTotient[i]*i; sumOfEulerTotient[j] += eulerTotient[i]*i;
} }
} }