add lcm_sum.cpp

math/lcm_sum.cpp

@@ -0,0 +1,90 @@
+/**
+ * @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 std::cout
+#include <cassert>  // for assert
+#include <vector>   // dor std::vector
+
+/**
+ * Function to compute sum of euler totients in sumOfEulerTotient vector
+ * @param num input number
+ * @returns int
+ */
+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 = lcmSum(n);
+    assert(test_2 == 55);
+    std::cout << "Passed Test 2!" << std::endl;
+
+    n = 10;
+    int test_3 = lcmSum(n);
+    assert(test_3 == 320);
+    std::cout << "Passed Test 3!" << std::endl;
+
+    n = 11;
+    int test_4 = lcmSum(n);
+    assert(test_4 == 616);
+    std::cout << "Passed Test 4!" << std::endl;
+
+    n = 15;
+    int test_5 = lcmSum(n);
+    assert(test_5 == 1110);
+    std::cout << "Passed Test 5!" << std::endl;
+}
+
+/**
+* main function
+*/
+int main() {
+    test();
+    return 0;
+}