How do you approach 01 Matrix?

Run BFS from all 0-cells at once (multi-source).

What are common mistakes on 01 Matrix?

Building the adjacency list in one direction on an undirected graph. Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest. Ignoring self-loops and parallel edges when the constraints allow them.

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01 Matrix

MediumAlgorithms

Description

Given an `m x n` binary matrix `mat`, return a matrix of the same size where each cell holds the distance to the **nearest** `0`. The distance between two adjacent cells is `1` (4-directional).

Example 1

Input: mat = [[0,0,0],[0,1,0],[1,1,1]]

Output: [[0,0,0],[0,1,0],[1,2,1]]

Explanation: Each 1 is labeled with its distance to the closest 0.

Constraints

- m == mat.length - n == mat[i].length - 1 <= m, n <= 10^4, with m * n <= 10^4 - There is at least one 0

01 Matrix: approach, complexity and pitfalls

A medium graphs problem, graded against 3 test cases (1 of them hidden).

The pattern: Graphs

Nodes and edges - traversal, connectivity, cycles, and shortest paths.

Reach for it when you see: Explicit edges, a grid treated as a graph, or dependencies between items.

More Graphsproblems →

If you are stuck

Show the 2-step hint ladder

Run BFS from all 0-cells at once (multi-source).
The first time you reach a cell is its shortest distance.

The optimal approach

Show the approach: The approach

Multi-source BFS. Initialize the distance of every `0` to 0 and enqueue them. BFS outward; the first time a `1`-cell is reached gives its minimum distance.

Time: O(m·n). Space: O(m·n).

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Single element. A one-element case is included. Two-pointer and window solutions frequently return the wrong thing when the two indices start out equal.
Duplicate values. Repeated values appear in the input, so any logic that assumes distinct elements - or that skips over equal neighbours - is exercised.
Zero. Zero appears in the input, which is the value most likely to break a truthiness check used in place of an explicit comparison.

Common Graphs mistakes

These apply to the pattern as a whole, not just this problem.

Building the adjacency list in one direction on an undirected graph.
Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest.
Ignoring self-loops and parallel edges when the constraints allow them.