73. Set Matrix Zeroes

Problem

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.

https://leetcode.com/problems/set-matrix-zeroes/

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?

Test Cases

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

solution_test.py

import copy

import pytest

from solution import Solution
from solution2 import Solution as Solution2


@pytest.mark.parametrize('matrix, expected', [
    ([[1,1,1],[1,0,1],[1,1,1]], [[1,0,1],[0,0,0],[1,0,1]]),
    ([[0,1,2,0],[3,4,5,2],[1,3,1,5]], [[0,0,0,0],[0,4,5,0],[0,3,1,0]]),

    ([[1,2,3,4],[5,0,7,8],[0,10,11,12],[13,14,15,0]], [[0,0,3,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]),
])
class Test:
    def test_solution(self, matrix, expected):
        sol = Solution()
        matrix = copy.deepcopy(matrix)
        sol.setZeroes(matrix)
        assert matrix == expected

    def test_solution2(self, matrix, expected):
        sol = Solution2()
        matrix = copy.deepcopy(matrix)
        sol.setZeroes(matrix)
        assert matrix == expected

Thoughts

用长为 m 的数组记录哪一行需要换成 0，长为 n 的数组记录哪一列需要换成 0。

遍历一遍 grid，如果 grid[i][j] 是 0，则标记 i 行和 j 列。

再遍历一遍 grid，根据行和列的标记，将需要替换的格子的值改成 0。

时间复杂度 O(mn)，空间复杂度 O(m+n)。

Code

solution.py

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

        for i, row in enumerate(matrix):
            for j, v in enumerate(row):
                if v == 0:
                    rows[i] = True
                    cols[j] = True

        for i in range(m):
            for j in range(n):
                if rows[i] or cols[j]:
                    matrix[i][j] = 0

Follow Up

可以直接用 matrix 的第一行和第一列记录需要全部换成 0 的列和行。唯一需要注意的是 matrix[0][0] 是公共的元素，为了避免冲突，可以用单独的变量记录第一行和第一列是否需要换。

solution2.py

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

        for i in range(m):
            if matrix[i][0] == 0:
                first_col = True
                break

        for j in range(n):
            if matrix[0][j] == 0:
                first_row = True
                break

        for i in range(1, m):
            for j in range(1, n):
                if matrix[i][j] == 0:
                    matrix[i][0] = 0
                    matrix[0][j] = 0

        for i in range(1, m):
            for j in range(1, n):
                if matrix[i][0] == 0 or matrix[0][j] == 0:
                    matrix[i][j] = 0

        if first_col:
            for i in range(m):
                matrix[i][0] = 0

        if first_row:
            for j in range(n):
                matrix[0][j] = 0

本文除了题目描述（Problem）部分之外，其他内容由 Calf 原创，采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。