Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Python/Java solution

Python and Java implementations typically encode the matrix as a bitmask integer and run BFS over possible states. Each step toggles the current cell and its neighbors using XOR operations. The queue tracks states with their flip counts until the zero mask is reached or all states are explored.

What is the best approach for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?

Breadth-First Search with bitmask state encoding is the most efficient approach. The matrix is encoded into an integer where each bit represents a cell. BFS explores all reachable states and guarantees the first time the zero matrix appears is the minimum number of flips. Time complexity is O(2^(m*n)) with the same order of space.

Is Minimum Number of Flips to Convert Binary Matrix to Zero Matrix asked at Google/Amazon/Meta?

Grid state search problems using BFS and bitmasking frequently appear in interviews at companies like Google, Amazon, and Meta. This problem tests graph modeling, state compression, and shortest-path reasoning, which are common themes in technical interviews.

What data structure is used in Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?

The solution primarily uses a queue for Breadth-First Search and a hash set to track visited states. Many optimized implementations also use integers as bitmasks to encode the matrix. This combines graph traversal with bit manipulation for efficient state transitions.

What is the time complexity of Minimum Number of Flips to Convert Binary Matrix to Zero Matrix?

The optimal BFS solution runs in O(2^(m*n)) time because each matrix configuration is treated as a state in a graph. For a 3x3 grid there are at most 512 states, which keeps the search manageable. Space complexity is also O(2^(m*n)) for the visited set and queue.

Description Hints 1 Solution Video 10:09

1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix

Q: How to solve Minimum Number of Flips to Convert Binary Matrix to Zero Matrix in O(n)?

An O(n) solution does not exist for the general problem because every matrix configuration may need to be explored. The practical optimal solution models the matrix as a graph of states and runs BFS over encoded states. Using bitmask compression keeps transitions fast and avoids large memory overhead.

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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). A pair of cells are called neighbors if they share one edge.

Return the minimum number of steps required to convert mat to a zero matrix or -1 if you cannot.

A binary matrix is a matrix with all cells equal to 0 or 1 only.

A zero matrix is a matrix with all cells equal to 0.

Example 1:

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.

Example 2:

Input: mat = [[0]]
Output: 0
Explanation: Given matrix is a zero matrix. We do not need to change it.

Example 3:

Input: mat = [[1,0,0],[1,0,0]]
Output: -1
Explanation: Given matrix cannot be a zero matrix.

Constraints:

m == mat.length
n == mat[i].length
1 <= m, n <= 3
mat[i][j] is either 0 or 1.

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Hint 1

Flipping same index two times is like not flipping it at all. Each index can be flipped one time. Try all possible combinations. O(2^(n*m)).

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