题目描述：

LeetCode 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].

题目大意：

Toeplitz（托普利茨）矩阵是指各条从左上到右下对角线元素均相等的矩阵。

给定M x N矩阵，判断是否为Toeplitz矩阵。

解题思路：

Map + Set

将矩阵各元素按照其所在位置行与列的差值分组。

遍历矩阵，记行为i，列为j，将元素matrix[i][j]加入i - j对应的集合。

判断各集合元素是否为1

Python代码：

class Solution(object):
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        vmap = collections.defaultdict(set)
        M, N = len(matrix), len(matrix[0])
        for x in range(M):
            for y in range(N):
                vmap[y - x].add(matrix[x][y])
                if len(vmap[y - x]) > 1: return False
        return True

 

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