LeetCode.48

　　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]
　　]

 　　题意：题目就是说把一个n×n的矩阵旋转90°。

　　我的算法测试的时候都是正确的，但测试样本都是12345....这样的，而不是LeetCode给的那种测试数据：

{

{10,151,33,143,165,11,13,28,69,159,194,16,108,53},

{8,67,159,59,114,13,24,121,16,13,71,122,158,187},

{85,160,147,52,116,181,1,86,194,167,71,24,131,26},

{41,1,81,7,69,1,67,184,15,49,66,32,19,94},

{111,134,87,154,100,39,11,21,177,13,65,132,138,93},

{114,74,121,112,76,7,120,147,9,189,92,25,-1,116},

{15,19,15,127,154,59,42,59,55,55,38,190,25,60},

{83,164,154,2,0,80,116,77,44,41,181,10,187,35},

{189,187,108,161,163,80,49,123,141,93,139,1,149,134},

{148,131,-1,37,57,111,40,58,148,157,92,194,156,35},

{161,104,71,111,97,180,77,21,65,128,145,163,178,46},

{122,88,181,75,24,138,113,82,54,155,97,7,73,191},

{158,186,31,81,96,59,193,150,44,76,172,66,161,79},

{35,144,126,158,37,112,38,18,55,109,58,66,69,156}

};

 

　　这样运行时就发现出现了一些问题。。。

　　我先说说我的算法思路：就是按照旋转的意思，把正方形的矩阵中对应位置上的数进行交换来实现旋转，如图：

　　每个位置上的与根据计算得到的对应位置上的进行交换，并逐渐向内层递进。

　　代码：

#include <iostream>
#include <vector>
using namespace std;

class Solution {
public:
    void rotate(vector<vector<int> >& matrix) {
        int row = matrix.size();
        for(int i = 0; (row%2 == 0) ? (row > 5 ? i < row/2 : i <= row/2 ) : i <= row/2; i++) {
            for(int j = 0; (row%2 == 0 && row > 5) ? j < row/2 : (row < 5 ? j <= i : j < row/2); j++) {
                int cont = (row%2 == 0) ? matrix[row/2 - 1][row/2] : matrix[j][j];
                if((i != j && cont == matrix[j][i]))
                    break;
                swap(matrix[i][j], matrix[j][row - 1 - i]);
                swap(matrix[i][j], matrix[row - 1 - j][i]);
                swap(matrix[row - 1 - j][i], matrix[row - 1 - i][row - 1 - j]);
            }
        }
    }
};

#define N 14
int main() {
    int nums[][N] = 
    {
        {10,151,33,143,165,11,13,28,69,159,194,16,108,53},
        {8,67,159,59,114,13,24,121,16,13,71,122,158,187},
        {85,160,147,52,116,181,1,86,194,167,71,24,131,26},
        {41,1,81,7,69,1,67,184,15,49,66,32,19,94},
        {111,134,87,154,100,39,11,21,177,13,65,132,138,93},
        {114,74,121,112,76,7,120,147,9,189,92,25,-1,116},
        {15,19,15,127,154,59,42,59,55,55,38,190,25,60},
        {83,164,154,2,0,80,116,77,44,41,181,10,187,35},
        {189,187,108,161,163,80,49,123,141,93,139,1,149,134},
        {148,131,-1,37,57,111,40,58,148,157,92,194,156,35},
        {161,104,71,111,97,180,77,21,65,128,145,163,178,46},
        {122,88,181,75,24,138,113,82,54,155,97,7,73,191},
        {158,186,31,81,96,59,193,150,44,76,172,66,161,79},
        {35,144,126,158,37,112,38,18,55,109,58,66,69,156}
    };
    
    vector<vector<int> > matrix(N, vector<int> (N));
    Solution so;

    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            matrix[i][j] = nums[i][j];
        }
    }

    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            cout << matrix[i][j] << '	';
        }
        cout << endl;
    }

    cout << endl;

    so.rotate(matrix);

    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            cout << matrix[i][j] << '	';
        }
        cout << endl;
    }

    return 0;
}

　　但并没有通过...至少给的测试数据没通过的原因是，我的算法最多进行到层数的一半，也就是左上角的分块矩阵部分，所以无法进行到120,49,55,123这几个的位置...但对于12345...这样的14*14的矩阵却很正确的实现了。代码或许看着有些复杂，其实时间复杂度也不怎么样，O(n^2)。

　　题目来源：Rotate Image