Update 48. Rotate Image

Notes:
----------
* easily understandable logic.
* rotate clock-wise = 1. transpose matrix => 2. reverse(matrix[i])
* detailed explanation in comment.
* passes all testcases.

Time Complexity  : O(N)
Space Complexity : O(1)

leetcode/0048.Rotate-Image/48. Rotate Image.go

@@ -1,17 +1,45 @@
+// Time: O(N) Space: O(1)
+
 package leetcode
 
 func rotate(matrix [][]int) {
-	length := len(matrix)
-	// rotate by diagonal 对角线变换
-	for i := 0; i < length; i++ {
-		for j := i + 1; j < length; j++ {
-			matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
-		}
+	n := len(matrix)
+	if n == 1 {
+		return
 	}
-	// rotate by vertical centerline 竖直轴对称翻转
-	for i := 0; i < length; i++ {
-		for j := 0; j < length/2; j++ {
-			matrix[i][j], matrix[i][length-j-1] = matrix[i][length-j-1], matrix[i][j]
+	/* rotate clock-wise = 1. transpose matrix => 2. reverse(matrix[i])
+
+	1   2  3  4      1   5  9  13        13  9  5  1
+	5   6  7  8  =>  2   6  10 14  =>    14  10 6  2
+	9  10 11 12      3   7  11 15        15  11 7  3
+	13 14 15 16      4   8  12 16        16  12 8  4
+
+	*/
+
+	for i := 0; i < n; i++ {
+		// transpose, i=rows, j=columns
+		// j = i+1, coz diagonal elements didn't change in a square matrix
+		for j := i + 1; j < n; j++ {
+			swap(matrix, i, j)
 		}
+		// reverse each row of the image
+		matrix[i] = reverse(matrix[i])
 	}
 }
+
+// swap changes original slice's i,j position
+func swap(nums [][]int, i, j int) {
+	nums[i][j], nums[j][i] = nums[j][i], nums[i][j]
+}
+
+// reverses a row of image, matrix[i]
+func reverse(nums []int) []int {
+	var lp, rp = 0, len(nums) - 1
+
+	for lp < rp {
+		nums[lp], nums[rp] = nums[rp], nums[lp]
+		lp++
+		rp--
+	}
+	return nums
+}