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Graph / BFS•Pattern: Multi-Source BFS•Medium

Walls and gates — fill distance to nearest gate

Problem Intuition & Objective

Fill each empty room with the distance to its nearest gate using multi-source BFS.

Time ComplexityO(m×n)
Optimal
Space ComplexityO(m×n)
Memory Bounds
Optimal Algorithmic Approach

Multi-source BFS from all gates at once.

Core Invariants & Edge Cases

  • Start BFS from all gates (value 0) simultaneously
  • The first time a cell is reached is its shortest distance
  • Walls (value -1) block propagation
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