Updated problem 1 algorithm

ProjectEulerCS/Problems/Problem1.cs

@@ -1,7 +1,7 @@
 //ProjectEuler/ProjectEulerCS/src/Problems/Problem1.cs
 //Matthew Ellison
 // Created: 08-14-20
-//Modified: 08-27-20
+//Modified: 10-26-20
 //What is the sum of all the multiples of 3 or 5 that are less than 1000
 //Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/CSClasses
 /*
@@ -22,6 +22,9 @@
 */
 
 
+using System;
+
+
 namespace ProjectEulerCS.Problems{
 	public class Problem1 : Problem{
 		//Variables
@@ -64,15 +67,8 @@ namespace ProjectEulerCS.Problems{
 			//Start the timer
 			timer.Start();
 
-			//Check every number < 1000 to see if it is a multiple of 3 or 5. If it is add it to the running sum
-			for (int cnt = 1; cnt <= TOP_NUM; ++cnt){
-				if ((cnt % 3) == 0){
-					fullSum += cnt;
-				}
-				else if ((cnt % 5) == 0){
-					fullSum += cnt;
-				}
-			}
+			//Get the sum of the progressions of 3 and 5 and remove the sum of progressions of the overlap
+			fullSum = SumOfProgression(3) + SumOfProgression(5) - SumOfProgression(3 * 5);
 
 			//Stop the timer
 			timer.Stop();
@@ -85,10 +81,15 @@ namespace ProjectEulerCS.Problems{
 			base.Reset();
 			fullSum = 0;
 		}
+		private int SumOfProgression(double multiple){
+			double numTerms = Math.Floor(TOP_NUM / multiple);	//This gets the number of multiples of a particular number that is < MAX_NUMBER
+			//The sum of progression formula is (n / 2)(a + l). n = number of terms, a = multiple, l = last term
+			return (int)(numTerms / 2.0 * (multiple + (numTerms * multiple)));
+		}
 	}
 }
 
 /* Results:
 The sum of all numbers < 1000 is 233168
-It took an average of 1.430 microseconds to run this problem through 100 iterations
+It took an average of 1.351 microseconds to run this problem through 100 iterations
 */