Refactor with mathematical formulas

difference_of_squares.go

@@ -6,21 +6,14 @@ package diffsquares
 // SquareOfSums returns the square of the sum of the range of natural
 // numbers from 1 to the given value.
 func SquareOfSums(n int) int {
-	var s int
-	for i := 1; i <= n; i++ {
-		s += i
-	}
+	s := n * (n + 1) / 2
 	return s * s
 }
 
 // SumOfSquares returns the sum of the squares of the range of natural
 // numbers from 1 to the given value.
 func SumOfSquares(n int) int {
-	var s int
-	for i := 1; i <= n; i++ {
-		s += i * i
-	}
-	return s
+	return n * (n + 1) * (2*n + 1) / 6
 
 }
 
@@ -30,9 +23,14 @@ func Difference(n int) int {
 	return SquareOfSums(n) - SumOfSquares(n)
 }
 
-// Iteration 1 benchmark:
+// Iteration 2 benchmark:
 //
 // PASS
-// BenchmarkSquareOfSums-12	30000000	        56.5 ns/op
-// BenchmarkSumOfSquares-12	20000000	        63.8 ns/op
-// BenchmarkDifference-12  	20000000	       113 ns/op
+// BenchmarkSquareOfSums-12	2000000000	         1.04 ns/op
+// BenchmarkSumOfSquares-12	2000000000	         1.89 ns/op
+// BenchmarkDifference-12  	1000000000	         2.75 ns/op
+//
+// benchmark                    old ns/op     new ns/op     delta
+// BenchmarkSquareOfSums-12     55.6          1.04          -98.13%
+// BenchmarkSumOfSquares-12     63.4          1.89          -97.02%
+// BenchmarkDifference-12       114           2.75          -97.59%