☀️ Bipartite Graph

Author: darpanjbora

Graph Algorithms/Bipartite.java

@@ -0,0 +1,79 @@
+/**
+ * A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V
+ *  such that every edge (u, v) either connects a vertex from U to V or a vertex from V to U. 
+ * In other words, for every edge (u, v), either u belongs to U and v to V, 
+ * or u belongs to V and v to U. 
+ * We can also say that there is no edge that connects vertices of same set.
+ * 
+ * 
+ * Time Complexity of the above approach is same as that Breadth First Search.
+ * O(V^2) where V is number of vertices. 
+ * If graph is represented using adjacency list, 
+ * then the complexity becomes O(V+E).
+ */
+
+
+import java.util.*;
+import java.io.*;
+
+class Bipartite {
+
+    public static boolean isBipartiteUtil(int G[][], int index, int colorArray[], int V) {
+
+        colorArray[index] = 1;
+
+        LinkedList<Integer> queue = new LinkedList<Integer>();
+
+        queue.add(index);
+
+        while (!queue.isEmpty()) {
+
+            int elem = queue.pop();
+
+            if (G[elem][elem] == 1) {
+                return false;
+            }
+
+            for (int i = 0; i < V; i++) {
+
+                if (G[elem][i] == 1 && colorArray[i] == -1) {
+
+                    colorArray[i] = 1 - colorArray[elem];
+                    queue.push(i);
+                }
+
+                else if(G[elem][i] == 1 && colorArray[i] == colorArray[elem]){
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+
+    public static boolean isBipartite(int V, int G[][]) {
+
+        int[] colorArray = new int[V];
+        Arrays.fill(colorArray, -1);
+
+        for (int i = 0; i < V; i++) {
+            if (colorArray[i] == -1) {
+                if (isBipartiteUtil(G, i, colorArray, V) == false) {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    public static void main(String[] args) {
+
+        int G[][] = { { 0, 1, 0, 1 }, { 1, 0, 1, 0 }, { 0, 1, 0, 1 }, { 1, 0, 1, 0 } }; // Adjacency Matrix
+        int V = 4; // Vertices
+
+        if (isBipartite(V, G))
+            System.out.println("Yes, the graph is bipartite.");
+        else
+            System.out.println("No, it's not!");
+    }
+}