0048. Rotate Image

48. Rotate Image #

题目 #

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 NOT allocate 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]
]

题目大意 #

给定一个 n × n 的二维矩阵表示一个图像。将图像顺时针旋转 90 度。说明:你必须在原地旋转图像,这意味着你需要直接修改输入的二维矩阵。请不要使用另一个矩阵来旋转图像。

解题思路 #

  • 给出一个二维数组,要求顺时针旋转 90 度。
  • 这一题比较简单,按照题意做就可以。这里给出 2 种旋转方法的实现,顺时针旋转和逆时针旋转。

    /*
     * clockwise rotate 顺时针旋转
     * first reverse up to down, then swap the symmetry 
     * 1 2 3     7 8 9     7 4 1
     * 4 5 6  => 4 5 6  => 8 5 2
     * 7 8 9     1 2 3     9 6 3
    */
    void rotate(vector<vector<int> > &matrix) {
        reverse(matrix.begin(), matrix.end());
        for (int i = 0; i < matrix.size(); ++i) {
            for (int j = i + 1; j < matrix[i].size(); ++j)
                swap(matrix[i][j], matrix[j][i]);
        }
    }
    
    /*
     * anticlockwise rotate 逆时针旋转
     * first reverse left to right, then swap the symmetry
     * 1 2 3     3 2 1     3 6 9
     * 4 5 6  => 6 5 4  => 2 5 8
     * 7 8 9     9 8 7     1 4 7
    */
    void anti_rotate(vector<vector<int> > &matrix) {
        for (auto vi : matrix) reverse(vi.begin(), vi.end());
        for (int i = 0; i < matrix.size(); ++i) {
            for (int j = i + 1; j < matrix[i].size(); ++j)
                swap(matrix[i][j], matrix[j][i]);
        }
    }
    

代码 #


package leetcode

func rotate(matrix [][]int) {
	row := len(matrix)
	if row <= 0 {
		return
	}
	column := len(matrix[0])
	// rotate by diagonal 对角线变换
	for i := 0; i < row; i++ {
		for j := i + 1; j < column; j++ {
			tmp := matrix[i][j]
			matrix[i][j] = matrix[j][i]
			matrix[j][i] = tmp
		}
	}
	// rotate by vertical centerline 竖直轴对称翻转
	halfColumn := column / 2
	for i := 0; i < row; i++ {
		for j := 0; j < halfColumn; j++ {
			tmp := matrix[i][j]
			matrix[i][j] = matrix[i][column-j-1]
			matrix[i][column-j-1] = tmp
		}
	}
}



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