[leetcode]48. Rotate Image旋转图像

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]
]

题意：

In-place 顺时针旋转90度

Solution1: Try a simulation by matrix [2X2],  find the principle how to rotate

i.e:

Original:
1 2
4

Rotated:
1
4 2

Q:  How do we get value 3 from (1,0) to (0,0) ?

A:  flip matrix from up to down

Flip up down from original:

3
2

Q: How do we put values 1 and 4 to their own places?

A:  flip matrix by diagonal

Flip matrix by diagonal:

3 1
4 2

code

 /*
 Time:O(n^2). We use nested 2 for loop.
 Space: O(1). We only used constant extra space.
 */
 class Solution {
     public void rotate(int[][] matrix) {
         int n = matrix.length;
         // flip  matrix from up to down
         for(int i = 0; i < n/2; i++){
             for(int j = 0; j< n; j++){
                 swap(matrix, i, j, n-i-1, j);
             }
         }
         //flip matrix by diagonal
         for(int i = 0; i < n; i++){
             for(int j = i+1; j < n; j++){
                  swap(matrix, i, j, j, i);
             }
         }
     }
     private void swap(int[][] matrix, int i, int j, int a, int b){
         int tmp = matrix[i][j];
         matrix[i][j] = matrix[a][b];
         matrix[a][b] = tmp;
     }
 }