What is the 01 Matrix pattern?

The 01 Matrix is a common coding interview pattern in Breadth First Search problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use 01 Matrix?

Use the 01 Matrix pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is 01 Matrix asked in FAANG interviews?

Yes, 01 Matrix is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Breadth-First Search

Medium

01 Matrix

Find the distance of the nearest 0 for each cell.

20 min

Solve on LeetCode

Problem Understanding

Given an m x n binary matrix:

0: A goal cell.
1: An empty cell.

For each cell, find the distance to the nearest 0. The distance between adjacent cells is 1.

Algorithm Strategy

A naive BFS from each 1 would be too slow (O((RC)^2)).

Better Approach: Multi-Source BFS

Reverse Thinking: Instead of finding nearest 0 from 1s, let the 0s expand outward like a flood.
Initialization:
- Enqueue ALL cells containing 0 at time=0.
- Mark all 1 cells as Infinity (unvisited).
Expansion: Pop a cell. Visit its unvisited neighbors. Set neighbor dist = current dist + 1. Enqueue neighbor.

Interactive Visualization

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