48. Rotate Image (matrix retation, transpose) Amazon problem

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]
]

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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]
]

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