73. Set Matrix Zeroes

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

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
• 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?

Approach

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

Explanation