Rotate Image

You are given an n x n 2D matrix representing an image.
Rotate the image by 90 degrees (clockwise).

 

Example

Given a matrix

[
    [1,2],
    [3,4]
]

rotate it by 90 degrees (clockwise), return

[
    [3,1],
    [4,2]
]
分析：
本题的关键是找到几个互换点之间位置的关系。

public class Solution {
    /**
     * @param matrix:
     *            A list of lists of integers
     * @return: Void
     */
    public void rotate(int[][] matrix) {
        if (matrix == null || matrix.length == 0) return;
        int n = matrix.length - 1;
        for (int i = 0; i < (n + 1) / 2; ++i) {
            for (int j = i; j < n - i; ++j) {
                int t = matrix[i][j];
                matrix[i][j] = matrix[n - j][i];
                matrix[n - j][i] = matrix[n - i][n - j];
                matrix[n - i][n - j] = matrix[j][n - i];
                matrix[j][n - i] = t;
            }
        }
    }
}

 对于一个正方形边上的四个对应点，它们有下面的关系：n = 边长 - 1

上： (x, y)

下：(n - x, n - y)

左：(n - y, x)

右：(y, n - x)

另一种解法：

The idea was firstly transpose the matrix and then flip it symmetrically. For instance,

1  2  3             
4  5  6
7  8  9

after transpose, it will be swap(matrix[i][j], matrix[j][i])

1  4  7
2  5  8
3  6  9

Then flip the matrix horizontally. (swap(matrix[i][j], matrix[i][matrix.length-1-j])

7  4  1
8  5  2
9  6  3

Hope this helps.

public class Solution {
    public void rotate(int[][] matrix) {
        for(int i = 0; i<matrix.length; i++){
            for(int j = i; j<matrix[0].length; j++){
                int temp = 0;
                temp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = temp;
            }
        }
        for(int i =0 ; i<matrix.length; i++){
            for(int j = 0; j<matrix.length/2; j++){
                int temp = 0;
                temp = matrix[i][j];
                matrix[i][j] = matrix[i][matrix.length-1-j];
                matrix[i][matrix.length-1-j] = temp;
            }
        }
    }
}