48. Rotate Image

Problem

You are given an n x n 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

Note:

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Example 1:

Given input matrix = 
[
  [1,2,3],
  [4,5,6],
  [7,8,9]
],

rotate the input matrix in-place such that it becomes:
[
  [7,4,1],
  [8,5,2],
  [9,6,3]
]

Example 2:

Given input matrix =
[
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
], 

rotate the input matrix in-place such that it becomes:
[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]

Solution

/**
 * @param {number[][]} matrix
 * @return {void} Do not return anything, modify matrix in-place instead.
 */
var rotate = function(matrix) {
  var n = matrix.length;
  var n2 = Math.floor(n / 2);
  // 1 2 3     7 8 9
  // 4 5 6  => 4 5 6
  // 7 8 9     1 2 3
  for (var i = 0; i < n2; i++) {
    for (var j = 0; j < n; j++) {
      swap(matrix, i, j, n - 1 - i, j);
    }
  }
  // 7 8 9     7 4 1
  // 4 5 6  => 8 5 2
  // 1 2 3     9 6 3
  for (var i = 0; i < n; i++) {
    for (var j = i + 1; j < n; j++) {
      swap(matrix, i, j, j, i);
    }
  }
};

var swap = function (matrix, x1, y1, x2, y2) {
  var tmp = matrix[x1][y1];
  matrix[x1][y1] = matrix[x2][y2];
  matrix[x2][y2] = tmp;
};

Explain:

见注释

顺时针 90°：先上下倒置，再对角倒置

逆时针 90°：先左右倒置，再对角倒置

Complexity:

• Time complexity : O(n^2).
• Space complexity : O(1).