## 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。

## 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。

## 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):
if len(vmap[y - x]) > 1: return False
return True
``````

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