数组+旋转+坐标表示+数组ij交换 48.旋转图像 48. Rotate Image

48. 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 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]
]

来源:力扣(LeetCode)
解题
给定数组,原地顺时针循转90度;

解法1:先ij=ji,然后每行倒叙即可
ij交换只要做斜着一半即可,不然又会交换回来;

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        //先ij=ji交换,再倒叙每一行即可
        int n=matrix.size();
        int tmp;
        for(int i=0;i<n;i++)
            for(int j=i;j<n;j++)
                swap(matrix[i][j],matrix[j][i]);
            
        for(int i=0;i<n;i++)
            reverse(matrix[i].begin(),matrix[i].end());      
    }
};

解法2:用大小为4的数组,存放没边一个数字,从外圈到内圈右移一次

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        rot.resize(4);
        int n=matrix.size();
    for(int j=0;j<(n+1)/2;j++)
        for(int i=j;i<n-1-j;i++)//n-1不用换 //从外圈到内圈
            {
                rot={matrix[j][i],matrix[i][n-1-j],matrix[n-1-j][n-1-i],matrix[n-1-i][j]};
                matrix[j][i]=rot[3];
                matrix[i][n-1-j]=rot[0];
                matrix[n-1-j][n-1-i]=rot[1];
                matrix[n-1-i][j]=rot[2];
            }
    }
private:
    vector<int> rot;
};

解法2优化
用tmp将四个角全部交换即可;

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        int n=matrix.size();
        int tmp;
    for(int j=0;j<(n+1)/2;j++)
        for(int i=j;i<n-1-j;i++)//n-1不用换 //从外圈到内圈
            {
                tmp=matrix[j][i];
                matrix[j][i]=matrix[n-1-i][j];
                matrix[n-1-i][j]=matrix[n-1-j][n-1-i];
                matrix[n-1-j][n-1-i]=matrix[i][n-1-j];
                matrix[i][n-1-j]=tmp;
            }
    }
};

注意点
转圈时注意用ij表示坐标;

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