766. Toeplitz Matrix

A matrix is Toeplitz if every diagonal from top-left to bottom-right has the same element.

Now given an M x N matrix, return True if and only if the matrix is Toeplitz.
 

Example 1:

Input: matrix = [[1,2,3,4],[5,1,2,3],[9,5,1,2]]
Output: True
Explanation:
1234
5123
9512

In the above grid, the diagonals are "[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]", and in each diagonal all elements are the same, so the answer is True.

Example 2:

Input: matrix = [[1,2],[2,2]]
Output: False
Explanation:
The diagonal "[1, 2]" has different elements.

Note:

1. matrix will be a 2D array of integers.
2. matrix will have a number of rows and columns in range [1, 20].
3. matrix[i][j] will be integers in range [0, 99].

解题思路：

乍一想可以从底部开始搜索，分两端搜索，一旦一斜行不相等即可返回false，但是这种方法代价太大。试一下：

class Solution {
public:
bool isToeplitzMatrix(vector<vector<int>>& matrix) {

if(matrix.size() == 1) return true;

int temp;
int temp_i,temp_j;
for(int i=matrix[0].size()-2;i>=0;i--){
temp = matrix[0][i];
temp_i = 0;
temp_j = i;
while(temp_j<matrix[0].size()-1&&temp_i<matrix.size()-1){
temp_i++;
temp_j++;
if(matrix[temp_i][temp_j] != temp) return false;
}
}

for(int i=matrix.size()-1;i>0;i--){
temp = matrix[i][0];
temp_i = i;
temp_j = 0;
while(temp_j<matrix[0].size()-1&&temp_i<matrix.size()-1){
temp_i++;
temp_j++;
if(matrix[temp_i][temp_j] != temp) return false;
}
}
return true;

}
};

可以跑了= =，不管了先。