Leetcode: Toeplitz Matrix

Toeplitz Matrix



Similar Problems:


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].

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.


## Blog link: https://code.dennyzhang.com/toeplitz-matrix
## Basic Ideas: Check all m[i][j] with m[i+1][j+1]
##
##            (0,0)  (1,0)  (2,0)  (3,0)
##              1     2       3     4
##              5     1       2     3
##              9     5       1     2
##            (0,2)  (1,2)  (2,2)  (3,2)
##
## Complexity: Time O(m*n), Space O(1)
class Solution(object):
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        row_count = len(matrix)
        if row_count == 0: return True
        col_count = len(matrix[0])
        for i in xrange(row_count-1):
            for j in xrange(col_count-1):
                if matrix[i][j] != matrix[i+1][j+1]:
                    return False
        return True
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