# 766. Toeplitz Matrix 托普利茨矩阵

@TOC

## # 题目描述

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:
In the above grid, the diagonals are:
"[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]".
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].

## # 解题方法

### # 方法一：两两比较

``````class Solution(object):
def isToeplitzMatrix(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: bool
"""
for row in xrange(len(matrix) - 1):
for col in xrange(len(matrix[0]) - 1):
if matrix[row][col] != matrix[row+1][col+1]:
return False
return True
``````

### # 方法二：切片相等

``````class Solution(object):
def isToeplitzMatrix(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: bool
"""
return all(matrix[row+1][1:] == matrix[row][:-1] for row in range(len(matrix)-1))
``````

### # 方法三：判断每条对角线

``````class Solution:
def isToeplitzMatrix(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: bool
"""
M, N = len(matrix), len(matrix[0])
for row in range(M):
first = matrix[row][0]
j = 0
for i in range(row, M):
if 0 <= j < N:
if matrix[i][j] != first:
return False
j += 1
for col in range(N):
first = matrix[0][col]
i = 0
for j in range(col, N):
if 0 <= i < M:
if matrix[i][j] != first:
return False
i += 1
return True
``````

## # 日期

2018 年 1 月 22 日 2018 年 11 月 8 日 —— 项目进展缓慢