Leetcode-48-Rotate-Image

Leetcode-48-Rotate-Image

ou 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 :

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]
]

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]
]

這個乍一看覺得不難，但是寫的時候又不知道怎麼回事，其實旋轉，對於我們寫程序來說，其實就是不停的調換位置，但是怎麼調換是個問題。

觀察發現，第一個矩陣，最角上的四個1,3,7,9。轉完之後，還是這四個數字，只不過是位置變了，接下來這樣的四個是：2,4,6,8.最後一個5.再看一下4x4的其實也差不多。

所以想法就是直接每次四個數字進行換，換三次，就能換回來，然後進行下一次調換。 代碼如下：

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        if(matrix.size()<=0)
            return;
        int a=0,b=matrix.size()-1;
        while(a<b){
            for(int i=0;i<b-a;++i){
                swap(matrix[a][a+i],matrix[a+i][b]);
                swap(matrix[a][a+i],matrix[b][b-i]);
                swap(matrix[a][a+i],matrix[b-i][a]);
            }
            ++a;
            --b;
        }
    }
};