Updated problem 1 algorithm

src/Problems/Problem1.rs

@@ -1,7 +1,7 @@
 //ProjectEulerRust/src/Problems/Problems1.rs
 //Matthew Ellison
 // Created: 06-12-20
-//Modified: 07-21-20
+//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/RustClasses
 /*
@@ -31,26 +31,28 @@ pub fn getDescription() -> &'static str{
 }
 
 pub fn solve() -> Answer{
-	let mut fullSum = 0;
 	let mut timer = myClasses::Stopwatch::Stopwatch::new();
+
+	//Start the timer
 	timer.start();
-	//Set through every number < 1000 and see if either 3 or 5 divide it evenly
-	for cnt in 1..1000{
-		//If either divides it then add it to the vector
-		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
+	let fullSum = sumOfProgression(3.0) + sumOfProgression(5.0) - sumOfProgression(3.0 * 5.0);
+
+	//Top the timer
 	timer.stop();
 
 	//Return the answer
 	return Answer::new("The sum of all numbers < 1000 is ".to_string() + &fullSum.to_string(), timer.getString(), timer.getNano());
 }
 
+fn sumOfProgression(multiple: f64) -> i64{
+	let numTerms = (999f64 / multiple).floor();	//Get the sum of the progressions of 3 and 5 and remove the sum of progressions of the overlap
+	//The sum of progression formula is (n / 2)(a + l). n = number of terms, a = multiple, l = last term
+	return ((numTerms / 2f64) * (multiple + (numTerms * multiple))) as i64;
+}
+
 /* Results:
 The sum of all numbers < 1000 is 233168
-It took an average of 893.000 nanoseconds to run this problem through 100 iterations
+It took an average of 868.000 nanoseconds to run this problem through 100 iterations
 */