From c06c47159a33e4d09f8d6d19e72287b374196bf1 Mon Sep 17 00:00:00 2001
From: Ahmad Hamdi <6674568+theHamdiz@users.noreply.github.com>
Date: Sun, 2 Feb 2025 23:37:13 +0300
Subject: [PATCH] Fixed negative sum issues, thanks u/Skeeve-on-git

---
 math/math.go      | 25 +++++++++++++++--
 math/math_test.go | 70 ++++++++++++++++++++++++++++++++++++++---------
 2 files changed, 79 insertions(+), 16 deletions(-)

diff --git a/math/math.go b/math/math.go
index 3a68f69..2028b58 100644
--- a/math/math.go
+++ b/math/math.go
@@ -7,10 +7,16 @@ import (
 	"golang.org/x/exp/constraints"
 )
 
-// Sum calculates the sum of numbers from 1 to n in O(1) time
+// Sum calculates the sum of numbers from 1 to n (or n to 1 if n is negative) in O(1) time
 // because who needs loops when you have math from 300 BC?
 // Gauss would be proud, or maybe just mildly amused.
 func Sum[T constraints.Integer](n T) T {
+	// For n = 0, because sometimes nothing plus nothing is... nothing
+	// Thanks to to u/Skeeve-on-git for highlighting negative sum bug.
+	if n == 0 {
+		return 0
+	}
+
 	// If you're wondering why this works:
 	// 1. Gauss figured this out when he was 8
 	// 2. You're probably older than 8
@@ -23,8 +29,20 @@ func Sum[T constraints.Integer](n T) T {
 // obviously this should not be used, it's just here for the memes.
 func SumSlow[T constraints.Integer](n T) T {
 	var total T
-	for i := T(1); i <= n; i++ {
-		total += i
+	// Explicitly cast 1 to type T
+	one := T(1)
+	// Thanks to to u/Skeeve-on-git for highlighting this.
+	// Compute -1 as type T
+	negOne := -one
+
+	if n > 0 {
+		for i := one; i <= n; i++ {
+			total += i
+		}
+	} else {
+		for i := n; i <= negOne; i++ {
+			total += i
+		}
 	}
 	return total
 }
@@ -38,6 +56,7 @@ func SumRange[T constraints.Integer](start, end T) T {
 		start, end = end, start
 	}
 
+	// One formula to rule them all
 	// The formula is: (end * (end + 1) / 2) - (start * (start - 1) / 2)
 	// Don't worry if you don't understand it, neither do most people
 	return Sum(end) - Sum(start-1)
diff --git a/math/math_test.go b/math/math_test.go
index 15ab8b4..6155f4e 100644
--- a/math/math_test.go
+++ b/math/math_test.go
@@ -62,32 +62,76 @@ func TestCorrectness(t *testing.T) {
 // TestSumRangeCorrectness checks that SumRange and SumRangeSlow produce
 // the same results, even for negative values.
 func TestSumRangeCorrectness(t *testing.T) {
+	// Thanks to to u/Skeeve-on-git for highlighting negative sum bug.
 	type testCase struct {
 		start int64
 		end   int64
-		want  int64 // optional: if you already know the correct result
+		want  int64
 	}
+
 	cases := []testCase{
+		// Zero cases
 		{start: 0, end: 0, want: 0},
+		{start: -0, end: 0, want: 0},
+		{start: 0, end: -0, want: 0},
+
+		// Single number cases
 		{start: 1, end: 1, want: 1},
-		{start: 1, end: 10, want: 55}, // 1+2+3+...+10
-		{start: -5, end: 5, want: 0},  // -5..5 sums to 0
-		{start: 999, end: 1000, want: 999 + 1000},
-		{start: 100, end: 50},          // reversed, tests the swap logic
-		{start: -3, end: -1, want: -6}, // -3 + -2 + -1
+		{start: -1, end: -1, want: -1},
+		{start: 42, end: 42, want: 42},
+
+		// Small positive ranges
+		{start: 1, end: 5, want: 15},
+		{start: 3, end: 7, want: 25},
+		{start: 1, end: 10, want: 55},
+
+		// Small negative ranges
+		{start: -5, end: -1, want: -15},
+		{start: -7, end: -3, want: -25},
+		{start: -10, end: -1, want: -55},
+
+		// Mixed ranges crossing zero
+		{start: -5, end: 5, want: 0},
+		{start: -3, end: 3, want: 0},
+		{start: -2, end: 2, want: 0},
+		{start: -10, end: 10, want: 0},
+
+		// Asymmetric mixed ranges
+		{start: -3, end: 5, want: 9},
+		{start: -7, end: 4, want: -18},
+		{start: -2, end: 8, want: 33},
+
+		// Reversed ranges (testing swap logic)
+		{start: 5, end: 1, want: 15},
+		{start: -1, end: -5, want: -15},
+		{start: 5, end: -5, want: 0},
+		{start: 10, end: -10, want: 0},
+
+		// Larger ranges
+		{start: 1, end: 100, want: 5050},
+		{start: -100, end: -1, want: -5050},
+		{start: -50, end: 50, want: 0},
+		{start: 999, end: 1000, want: 1999},
+
+		// Adjacent numbers
+		{start: -2, end: -1, want: -3},
+		{start: -1, end: 0, want: -1},
+		{start: 0, end: 1, want: 1},
+		{start: 1, end: 2, want: 3},
+
+		// Gaps
+		{start: -10, end: -5, want: -45},
+		{start: 5, end: 10, want: 45},
+		{start: -3, end: 2, want: -3},
 	}
 
 	for _, c := range cases {
 		gotSlow := sumRangeSlow(c.start, c.end)
 		gotFast := math2.SumRange[int64](c.start, c.end)
 
-		// If "want" is 0, we either didn't provide it or we think it might not matter.
-		// We'll just compare slow vs fast. Otherwise, we check the known value.
-		if c.want != 0 {
-			if gotSlow != c.want {
-				t.Errorf("sumRangeSlow(%d, %d) = %d; want %d",
-					c.start, c.end, gotSlow, c.want)
-			}
+		if gotSlow != c.want {
+			t.Errorf("sumRangeSlow(%d, %d) = %d; want %d",
+				c.start, c.end, gotSlow, c.want)
 		}
 		if gotSlow != gotFast {
 			t.Errorf("SumRange mismatch for start=%d end=%d: slow=%d fast=%d",