题目
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:
-
matrix will be a 2D array of integers. -
matrix will have a number of rows and columns in range [1, 20]. -
matrix[i][j] will be integers in range [0, 99].
思路
本题我们先举个例子，加入存在一个3*3的Toeplitz矩阵，那么该矩阵如下所示：
1 | 2 | 3 |
5 | 1 | 2 |
9 | 5 | 1 |
我们发现，数字1对应的坐标如下所示：
(0,0)、（1,1）、(2,2)
数字2对应的坐标：
(0,1)、（1,2）
数字5对应的坐标：
(1,0)、（2,1）
很明显我们发现凡是数字相同的坐标都是x与y坐标自增1的
所以我们只要遍历完整个数组，并检查当前坐标（x,y）与（x+1,y+1)的关系即可。一旦发现不想等直接返回false，否则一直循环直至退出，返回true。
代码
class Solution {
public:
bool isToeplitzMatrix(vector<vector<int>>& matrix) {
int n = matrix.size();
int m = matrix[0].size();
for(int i=0;i<n-1;i++)
{
for(int j=0;j<m-1;j++)
{
if(matrix[i][j]!=matrix[i+1][j+1])
return false;
}
}
return true;
}
};
