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BipartiteGraph.java
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BipartiteGraph.java
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package Leetcode;
/**
* @author kalpak
*
* Given an undirected graph, return true if and only if it is bipartite.
* Recall that a graph is bipartite if we can split its set of nodes into two independent subsets A and B, such that every edge in the graph has one node in A and another node in B.
*
* The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists.
* Each node is an integer between 0 and graph.length - 1. There are no self edges or parallel edges: graph[i] does not contain i, and it doesn't contain any element twice.
*
*
* Example 1:
* Input: graph = [[1,3],[0,2],[1,3],[0,2]]
* Output: true
* Explanation: We can divide the vertices into two groups: {0, 2} and {1, 3}.
*
* Example 2:
* Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
* Output: false
* Explanation: We cannot find a way to divide the set of nodes into two independent subsets.
*
* Constraints:
*
* 1 <= graph.length <= 100
* 0 <= graph[i].length < 100
* 0 <= graph[i][j] <= graph.length - 1
* graph[i][j] != i
* All the values of graph[i] are unique.
* The graph is guaranteed to be undirected.
*
*/
public class BipartiteGraph {
public static boolean isBipartite(int[][] graph) {
// Merge the visited and color array and maintain the states
// 0: Haven't been colored yet.
// 1: Blue.
// -1: Red.
int[] vertexColors = new int[graph.length];
for (int i = 0; i < graph.length; i++) {
//This graph might be a disconnected graph. So check each unvisited node.
if (vertexColors[i] == 0 && !validColor(graph, vertexColors, 1, i)) {
return false;
}
}
return true;
}
private static boolean validColor(int[][] graph, int[] vertexColors, int color, int startNode) {
if (vertexColors[startNode] != 0) {
return vertexColors[startNode] == color;
}
vertexColors[startNode] = color;
for (int next : graph[startNode]) {
if (!validColor(graph, vertexColors, -color, next)) {
return false;
}
}
return true;
}
public static void main(String[] args) {
int[][] graph = new int[][]{{1,3},{0,2},{1,3},{0,2}};
System.out.println("Is the graph Bipartite ?? " + isBipartite(graph));
}
}