Solutions

sheet1/C/main.cpp

@@ -0,0 +1,70 @@
+#include <iostream>
+#include "timing.h"
+
+using namespace std;
+
+
+unsigned long  multiplesOf3Or5(unsigned int n)
+{
+    unsigned long sum = 0;
+    for(unsigned int i=1; i<=n; i++)
+    {
+        if(i % 3 == 0 || i % 5 == 0)
+        {
+            sum += i;
+        }
+    }
+    return sum;
+}
+
+unsigned long gauss_sum(unsigned long n)
+{
+    return n*(n+1)/2;
+}
+
+unsigned long multiplesOf3Or5_noLoop(unsigned int n)
+{
+    /*for n there are floor(n/3) multiples of 3 and floor(n/5) multiples of 5. Calculate them using Gauss summation and subtract the 
+    multiples of 15 (counted twice)*/
+    unsigned long multiples3 = gauss_sum(n/3)*3;
+    unsigned long multiples5 = gauss_sum(n/5)*5;
+    unsigned long multiples15 = gauss_sum(n/15)*15;
+
+    return multiples3 + multiples5 - multiples15;
+
+}
+
+
+int main() {
+
+    unsigned long mA,mB,mC,mD,mE,mF;
+
+    tic();
+    for(unsigned int i = 0; i< 10000; i++)
+    {
+        mA = multiplesOf3Or5(15);
+        mB = multiplesOf3Or5(1001);
+        mC = multiplesOf3Or5(1432987);
+    }
+    double timeA = toc();
+
+    tic();
+    for(unsigned int i = 0; i< 10000; i++)
+    {
+        mD = multiplesOf3Or5_noLoop(15);
+        mE = multiplesOf3Or5_noLoop(1001);
+        mF = multiplesOf3Or5_noLoop(1432987);
+    }
+    double timeB = toc();
+
+    cout << "n = 15, result = " << mA << endl;
+    cout << "n = 1001, result = " << mB << endl;
+    cout << "n = 1432987, result = " << mC << endl;
+    cout << "time: " << timeA << endl;
+    cout << "--------------------------------------------------------------" <<endl;
+    cout << "n = 15, result = " << mD << endl;
+    cout << "n = 1001, result = " << mE << endl;
+    cout << "n = 1432987, result = " << mF << endl;
+    cout << "time: " << timeB << endl;
+    return 0;
+}