Number of Provinces

Med
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Solution Guide: Number of Provinces

Approach

Every unvisited city starts a new DFS and one province. DFS marks all cities in that connected component.

Complexity Analysis

Time
O(n²)
Space
O(n)

Pattern

Connected Components in Matrix

Why It Works

A province is exactly one connected component in the undirected city graph, and each node is visited once from its component root.

Updated Feb 2026