# Number of Provinces

Category

Graphs - DFS

Checkbox

Checkbox

Difficulty

Medium

Index

44

Key Ideas

The key idea to solve this problem is to use a depth-first search (DFS) or a breadth-first search (BFS) algorithm to traverse the graph and count the number of connected components.

Problem Number

547

Problem Summary

# Number of Provinces
In this LeetCode-75 curated problem, the task is to determine the number of provinces in a given graph. Each province represents a connected component in the graph, and the goal is to count the number of such components. Key pitfalls to watch out for include properly implementing the depth-first search (DFS) or union-find algorithms to identify connected components and handling edge cases such as an empty or null graph input.

Solution Summary

The best solution to solve this problem involves using Union Find algorithm. First, we initialize a parent array to keep track of the parent of each province. Then, we iterate through the given connections and merge the provinces that are connected. After merging all the connections, we count the number of unique parent provinces to determine the total number of provinces. This solution has a time complexity of O(n), where n is the number of connections, as we perform a union operation for each connection. It efficiently identifies the number of provinces by grouping connected provinces together.

Tags

Depth-First Search

Breadth-First Search

Union Find