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:

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:初始时标志位置为1,遍历整个矩阵, 看每个元素[i,j]的右下方元素[i+1,j+1]是否与其相等即可,若发现一个不相等,标志位置为0.注意边界条件,即最后一行和最后一列不用再与其右下方比较.

    bool isToeplitzMatrix(vector<vector<int>>& matrix) {
        bool flag = true; //标志位
        int m = matrix.size(); //行数
        int n = matrix[0].size(); //列数
        for (int i = 0; i < m-1; i++) {
            for (int j = 0; j < n-1; j++) {
                if (matrix[i][j] != matrix[i+1][j+1]) //若发现不满足,标志位置0
                    flag = false;
            }
        }
        return flag;
    }