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Learn Data Structures and Algorithms in JavaScript

Problem: Is Graph Bipartite?

Explore how to determine if an undirected graph is bipartite through a breadth-first search approach that assigns two colors to nodes ensuring no adjacent nodes share the same color. Understand the step-by-step method, including initialization, BFS traversal, and color assignments, to detect odd cycles and verify bipartite conditions in possibly disconnected graphs.

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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 partitioned into two independent sets A and B such that every edge in the graph connects a node in set A to a node in set B.

Return true if and only if the given graph is bipartite.

Constraints:

  • graph.length ==n== n ...