【LeetCode】48. Rotate Image

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