Difficulty:medium

 More:【目录】LeetCode Java实现

Description

https://leetcode.com/problems/rotate-image/

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 NOTallocate 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]

]

Intuition

　　1. transpose the matrix

　　2. flip the matrix horizontally

　　1 2 3 　　1 4 7　　 7 4 1
　　4 5 6  =>  2 5 8  =>  8 5 2
　　7 8 9　　 3 6 9 　　9 6 3

Solution

    public void rotate(int[][] a) {

        int n = a[0].length;

        //transpose the matrix

        for(int i=0; i<n; i++){

            for(int j=i+1; j<n; j++){

                int temp = a[i][j];

                a[i][j]=a[j][i];

                a[j][i]=temp;

            }

        }

        //flip the matrix horizontally

        for(int i=0; i<n; i++){

            for(int j=0; j<n/2; j++){

                int temp = a[i][j];

                a[i][j] = a[i][n-1-j];

                a[i][n-1-j] = temp;

            }

        }

    }

Complexity

Time complexity : O(N)

Space complexity : O(1)

What I've learned

1. When rotating a matrix, we can transpose the matrix firstly, and then find the law.

 More:【目录】LeetCode Java实现