Bipartite Graph

 

There is an undirected graph with n nodes, where each node is numbered between 0 and n - 1. You are given a 2D array graph, where graph[u] is an array of nodes that node u is adjacent to. More formally, for each v in graph[u], there is an undirected edge between node u and node v. The graph has the following properties:

• There are no self-edges (graph[u] does not contain u).
• There are no parallel edges (graph[u] does not contain duplicate values).
• If v is in graph[u], then u is in graph[v] (the graph is undirected).
• The graph may not be connected, meaning there may be two nodes u and v such that there is no path between them.

A graph is bipartite if the nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A and a node in set B.

Return true if and only if it is bipartite.

 

Example 1:

Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
Output: false
Explanation: There is no way to partition the nodes into two independent sets such that every edge connects a node in one and a node in the other.

Example 2:

Input: graph = [[1,3],[0,2],[1,3],[0,2]]
Output: true
Explanation: We can partition the nodes into two sets: {0, 2} and {1, 3}.

 

Constraints:

• graph.length == n
• 1 <= n <= 100
• 0 <= graph[u].length < n
• 0 <= graph[u][i] <= n - 1
• graph[u] does not contain u.
• All the values of graph[u] are unique.
• If graph[u] contains v, then graph[v] contains u.

refer: 

https://leetcode.com/problems/is-graph-bipartite/solution/

Color a node blue if it is part of the first set, else red. We should be able to greedily color the graph if and only if it is bipartite: one node being blue implies all it's neighbors are red, all those neighbors are blue, and so on.

package practice;

import java.util.*;

public class BipartiteGraph {


    public boolean isBipartite(int[][] graph) {

        int[] color = new int[graph.length];
        Arrays.fill(color, -1);

        for (int start = 0; start < color.length; start++) {

            if (color[start] == -1) {
                Stack<Integer> stk = new Stack<>();
                stk.push(start);
                color[start] = 0;

                while (!stk.isEmpty()) {
                    Integer node = stk.pop();
                    for (int newNode : graph[node]) {
                        if (color[newNode] == -1) {
                            stk.push(newNode);
                            color[newNode] = color[node] ^ 1;
                        } else if (color[newNode] == color[node]) {
                            return false;
                        }

                    }


                }
            }
        }

        return true;
    }


    public static void main(String[] args) {
//      int[][] graph= {{1,2,3},{0,2},{0,1,3},{0,2}};
        int[][] graph = {{1, 3}, {0, 2}, {1, 3}, {0, 2}};

        BipartiteGraph bg = new BipartiteGraph();
        System.out.println(bg.isBipartite(graph));
    }


}