"""
73. Set Matrix Zeroes
Difficulty: Medium
https://leetcode.com/problems/set-matrix-zeroes/

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Given an m x n integer matrix matrix, if an element is 0, set its
entire row and column to 0's.

You must do it in place.



Example 1:

Input: matrix = [[1,1,1],[1,0,1],[1,1,1]]
Output: [[1,0,1],[0,0,0],[1,0,1]]

Example 2:

Input: matrix = [[0,1,2,0],[3,4,5,2],[1,3,1,5]]
Output: [[0,0,0,0],[0,4,5,0],[0,3,1,0]]



Constraints:

        • m == matrix.length

        • n == matrix[0].length

        • 1 <= m, n <= 200

        • -2^31 <= matrix[i][j] <= 2^31 - 1



Follow up:

• A straightforward solution using O(mn) space is probably a bad
idea.

• A simple improvement uses O(m + n) space, but still not the best
solution.

        • Could you devise a constant space solution?
"""


class Solution:
    def setZeroes(self, matrix: List[List[int]]) -> None:
        """
        Do not return anything, modify matrix in-place instead.
        """
        m, n = len(matrix), len(matrix[0])

        # 1. remember if row 0 or column 0 have their own zeros
        row0_zero = any(matrix[0][c] == 0 for c in range(n))
        col0_zero = any(matrix[r][0] == 0 for r in range(m))

        # 2. use row 0 and column 0 as marker lists
        for r in range(1, m):
            for c in range(1, n):
                if matrix[r][c] == 0:
                    matrix[r][0] = 0
                    matrix[0][c] = 0

        # 3. zero the inner cells from the markers
        for r in range(1, m):
            for c in range(1, n):
                if matrix[r][0] == 0 or matrix[0][c] == 0:
                    matrix[r][c] = 0

        # 4. handle row 0 and column 0 last
        if row0_zero:
            for c in range(n):
                matrix[0][c] = 0
        if col0_zero:
            for r in range(m):
                matrix[r][0] = 0