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

/**
 * @file
 * @brief An algorithm to calculate the sum LCM(1,n) + LCM(2,n) + .. + LCM(n,n), where LCM(i,n)
 * 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:
 * ∑LCM(i, n) = ((∑(d * ETF(d)) + 1) * n) / 2
 *
 * @author [Chesta Mittal](https://github.com/chestamittal)
 */

#include <iostream> /// for std::cin and std::cout
#include <cassert>  /// for assert
#include <vector>   /// for std::vector

/**
 * 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
 */
int lcmSum(int num) {
   
    int i=0, j=0;
    int limit = 1000;
    std::vector <int> eulerTotient(limit);
    std::vector <int> sumOfEulerTotient(limit);
   
    // storing initial values in eulerTotient vector
    for(i=1; i<=limit; i++) {
        eulerTotient[i] = i;
    }

    // applying totient sieve  
    for(i=2; i<=limit; i++) {
        if(eulerTotient[i] == i) {
            for(j=i; j<=limit; j+=i) {
                eulerTotient[j] = eulerTotient[j]/i;
                eulerTotient[j] = eulerTotient[j]*(i-1);
            }
        }
    }

    // computing sum of euler totients
    for(i=1; i<=limit; i++) {
        for(j=i; j <=limit; j+=i) {
            sumOfEulerTotient[j] += eulerTotient[i]*i;
        }
    }
   
    return ((sumOfEulerTotient[num] + 1 ) * num) / 2;
}

/**
 * Function for testing lcmSum function.
 * test cases and assert statement.
 * @returns `void`
*/
static void test() {
    int n = 2;
    int test_1 = lcmSum(n);
    assert(test_1 == 4);
    std::cout << "Passed Test 1!" << std::endl;

    n = 5;
    int test_2 = math::lcmSum(n);
    assert(test_2 == 55);
    std::cout << "Passed Test 2!" << std::endl;

    n = 10;
    int test_3 = math::lcmSum(n);
    assert(test_3 == 320);
    std::cout << "Passed Test 3!" << std::endl;

    n = 11;
    int test_4 = math::lcmSum(n);
    assert(test_4 == 616);
    std::cout << "Passed Test 4!" << std::endl;

    n = 15;
    int test_5 = math::lcmSum(n);
    assert(test_5 == 1110);
    std::cout << "Passed Test 5!" << std::endl;
}

/**
 * @brief Main function
 * @returns 0 on exit
 */
int main() {
    test();  // execute the tests
    return 0;
}