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Learn Data Structures and Algorithms in Go

Problem: Is Graph Bipartite?

Explore how to verify if an undirected graph is bipartite by applying breadth-first search for 2-coloring. Understand how to assign colors to nodes so that no two adjacent nodes share the same color, and learn to identify an odd cycle that breaks bipartite conditions. This lesson guides you through implementing the algorithm with BFS, managing disconnected components, and analyzing time and space complexity.

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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 can be ...