LeetCode 766. Toeplitz Matrix



Given an m x n matrix, return true if the matrix is Toeplitz. Otherwise, return false.

A matrix is Toeplitz if every diagonal from top-left to bottom-right has the same elements.

Example 1:

Input: matrix = [[1,2,3,4],[5,1,2,3],[9,5,1,2]]
Output: true
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
The diagonal "[1, 2]" has different elements.


  • m == matrix.length
  • n == matrix[i].length
  • 1 <= m, n <= 20
  • 0 <= matrix[i][j] <= 99

Follow up:

  • What if the matrix is stored on disk, and the memory is limited such that you can only load at most one row of the matrix into the memory at once?
  • What if the matrix is so large that you can only load up a partial row into the memory at once?


Compare each element with its top-left neighbor to see if the values are the same.

Python Solution

class Solution:
    def isToeplitzMatrix(self, matrix: List[List[int]]) -> bool:
        if not matrix:
            return False

        for i in range(1, len(matrix)):
            for j in range(1, len(matrix[0])):
                if matrix[i][j] != matrix[i - 1][j - 1]:
                    return False

        return True        
  • Time Complexity: O(MN)
  • Space Complexity: O(1)

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