Problem
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:
- 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].
Solution
Analysis
Iterate each element in the matrix and check whether it equals to its top-left neighbor. Because there is no top-left neighbor for elements in the first row and first column, just traverse elements from the second row and second column.
Python implementation
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Java implementation
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Time complexity
O(MN).
Space complexity
O(1).
Link
766. Toeplitz Matrix
(中文版) 算法笔记: 力扣#766 托普利茨矩阵
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