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] ]
There are 3 solutions.
1: use extra space O(n^2)
2. transpose + flip horizontally
class Solution { void left2Right(int[][] matrix){ int n = matrix.length; for(int i = 0; i<n; i++){// for(int j = 0; j<(n/2); j++){//-> int temp = matrix[i][j]; matrix[i][j] = matrix[i][n-1-j]; matrix[i][n-1-j] = temp; } } } void up2Down(int[][] matrix){ int n = matrix.length; for(int i = 0; i<n; i++){//-> for(int j = 0; j<(n/2); j++){// int temp = matrix[j][i]; matrix[j][i] = matrix[n-1-j][i]; matrix[n-1-j][i] = temp; } } } void transpose(int[][] matrix){ int n = matrix.length; for(int i = 0; i<n; i++){//-> for(int j = 0; j<i; j++){// int temp = matrix[i][j]; matrix[i][j] = matrix[j][i]; matrix[j][i] = temp; } } } public void rotate(int[][] matrix) { //up2Down(matrix); transpose(matrix); left2Right(matrix); } }
3: just one operation (pattern among the in-place element)
reference: https://blog.csdn.net/happyaaaaaaaaaaa/article/details/51563752
class Solution { public void rotate(int[][] matrix) { //three solutions int n = matrix.length; for(int i = 0; i<=n/2; i++){//why n/2 for(int j = i; j<n-1-i; j++){//why i < j int temp = matrix[i][j]; matrix[i][j] = matrix[n-1-j][i]; matrix[n-1-j][i] = matrix[n-1-i][n-1-j]; matrix[n-1-i][n-1-j] = matrix[j][n-1-i]; matrix[j][n-i-1] = temp; } } } }
Caution: the boundary(pick the diagnosis)
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] ]