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Learn Data Structures and Algorithms in C#

Problem: Is Graph Bipartite?

Explore how to verify if a given undirected graph is bipartite by understanding the concept of 2-coloring and BFS traversal. Learn to implement an algorithm that assigns colors to nodes ensuring no two adjacent nodes share the same color, enabling you to identify odd cycles and solve bipartite graph problems efficiently.

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Statement

You are given an undirected graph with n nodes, numbered from 00 to n−1n - 1. The graph is represented as a 22D array graph, where graph[u] contains all nodes adjacent to node u. That is, for every v in graph[u], there exists an undirected edge between node u and node v.

The graph satisfies the following properties:

  • No self-loops exist (graph[u] does not contain u).

  • No parallel edges exist (all values in graph[u] are unique).

  • The graph is undirected: if v appears in graph[u], then u appears in graph[v].

  • The graph is not necessarily connected.

A graph is bipartite if its nodes ...