This is a premium problem. We're working on making it available for free soon.
Use these hints if you're stuck. Try solving on your own first.
Consider each cell containing a 1 as a vertex whose neighbors are the cells 4-directionally connected to it. The grid then becomes a bipartite graph.
You want to find the smallest set of vertices such that every edge in the graph has an endpoint in this set. If you remove every vertex in this set from the graph, then all the 1’s will be disconnected. Are there any well-known algorithms for finding this set?
This set of vertices is called a minimum vertex cover. You can find the size of a minimum vertex cover by finding the size of a maximum matching (Konig’s theorem).
There are well-known algorithms such as Kuhn’s algorithm and Hopcroft-Karp-Karzanov algorithm which can find a maximum matching in a bipartite graph quickly.
Solutions for this premium problem will be available for free soon.
Browse Free ProblemsWatch expert explanations and walkthroughs
Practice problems asked by these companies to ace your technical interviews.
Explore More ProblemsJot down your thoughts, approach, and key learnings
Problems involving grid graphs, bipartite matching, and minimum vertex cover are common in advanced coding interviews. Variants of this problem may appear in FAANG-style interviews to test graph modeling and algorithm optimization skills.
An adjacency list representation of a graph works best because it efficiently stores connections between cells containing 1. Combined with queues and arrays used in Hopcroft–Karp or BFS/DFS traversals, it supports fast matching operations.
The optimal approach models the matrix as a bipartite graph where cells containing 1 are nodes and edges connect adjacent ones. The task becomes finding the minimum vertex cover, which equals the maximum bipartite matching. Using algorithms like Hopcroft–Karp efficiently computes the result.
The grid can be colored like a chessboard, making it naturally bipartite. Adjacent cells always belong to opposite partitions, allowing the problem to be transformed into a bipartite matching problem. This structure enables efficient computation of the minimum operations required.