# Time:  O(m * n)
# Space: O(1)

# 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:
# - 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].

class Solution(object):
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        return all(i == 0 or j == 0 or matrix[i-1][j-1] == val
                   for i, row in enumerate(matrix)
                   for j, val in enumerate(row))


class Solution2(object):
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        for row_index, row in enumerate(matrix):
            for digit_index, digit in enumerate(row):
                if not row_index or not digit_index:
                    continue
                if matrix[row_index - 1][digit_index - 1] != digit:
                    return False
        return True