What is the space complexity of LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?

The Python solution on this page uses O(n) auxiliary space.

Minimum Number of Flips to Convert Binary Matrix to Zero Matrix — LeetCode 1284 Python Solution

HardBit ManipulationBreadth-First SearchArrayHash TableMatrix

Problem: #1284
Pattern: Bit Manipulation
Reading time: 5 min
Source: leetcode.com

The problem

Given a m x n binary matrix mat. In one step, you can choose one cell and flip it and all the four neighbors of it if they exist (Flip is changing 1 to 0 and 0 to 1).

Example

Input: mat = [[0,0],[0,1]]
Output: 3
Explanation: One possible solution is to flip (1, 0) then (0, 1) and finally (1, 1) as shown.

Python solution

Python

class Solution:
    def minFlips(self, mat: List[List[int]]) -> int:
        m, n = len(mat), len(mat[0])
        state = sum(1 << (i * n + j) for i in range(m) for j in range(n) if mat[i][j])
        q = deque([state])
        vis = {state}
        ans = 0
        dirs = [0, -1, 0, 1, 0, 0]
        while q:
            for _ in range(len(q)):
                state = q.popleft()
                if state == 0:
                    return ans
                for i in range(m):
                    for j in range(n):
                        nxt = state
                        for k in range(5):
                            x, y = i + dirs[k], j + dirs[k + 1]
                            if not 0 <= x < m or not 0 <= y < n:
                                continue
                            if nxt & (1 << (x * n + y)):
                                nxt -= 1 << (x * n + y)
                            else:
                                nxt |= 1 << (x * n + y)
                        if nxt not in vis:
                            vis.add(nxt)
                            q.append(nxt)
            ans += 1
        return -1

Complexity

Measure	Complexity
Time	O(n)
Space	O(n) auxiliary

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix is filed here because LeetCode tags it Bit Manipulation, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?: LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix is rated Hard on LeetCode.
What is the time complexity of LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?: The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?: The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix cover?: LeetCode 1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix is tagged Bit Manipulation, Breadth-First Search, Array, Hash Table and Matrix on LeetCode.