# Java Program to Implement Hopcroft Algorithm

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This is a Java Program to Implement Hopcroft Karp Algorithm. The Hopcroft–Karp algorithm is an algorithm that takes as input a bipartite graph and produces as output a maximum cardinality matching – a set of as many edges as possible with the property that no two edges share an endpoint.

Here is the source code of the Java Program to Implement Hopcroft Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

1. `/**`
2. ` ** Java Program to Implement Hopcroft Algorithm`
3. ` **/`
4. ` `
5. `import java.util.*;`
6. ` `
7. `/** Class Hopcroft **/`
8. `public class Hopcroft`
9. `{    `
10. `    private final int NIL = 0;`
11. `    private final int INF = Integer.MAX_VALUE;`
12. `    private ArrayList<Integer>[] Adj; `
13. `    private int[] Pair;`
14. `    private int[] Dist;`
15. `    private int cx, cy;`
16. ` `
17. `     /** Function BFS **/`
18. `    public boolean BFS() `
19. `    {`
20. `        Queue<Integer> queue = new LinkedList<Integer>();`
21. `        for (int v = 1; v <= cx; ++v) `
22. `            if (Pair[v] == NIL) `
23. `            { `
24. `                Dist[v] = 0; `
25. `                queue.add(v); `
26. `            }`
27. `            else `
28. `                Dist[v] = INF;`
29. ` `
30. `        Dist[NIL] = INF;`
31. ` `
32. `        while (!queue.isEmpty()) `
33. `        {`
34. `            int v = queue.poll();`
35. `            if (Dist[v] < Dist[NIL]) `
36. `                for (int u : Adj[v]) `
37. `                    if (Dist[Pair[u]] == INF) `
38. `                    {`
39. `                        Dist[Pair[u]] = Dist[v] + 1;`
40. `                        queue.add(Pair[u]);`
41. `                    }           `
42. `        }`
43. `        return Dist[NIL] != INF;`
44. `    }    `
45. `     /** Function DFS **/`
46. `    public boolean DFS(int v) `
47. `    {`
48. `        if (v != NIL) `
49. `        {`
50. `            for (int u : Adj[v]) `
51. `                if (Dist[Pair[u]] == Dist[v] + 1)`
52. `                    if (DFS(Pair[u])) `
53. `                    {`
54. `                        Pair[u] = v;`
55. `                        Pair[v] = u;`
56. `                        return true;`
57. `                    }               `
58. ` `
59. `            Dist[v] = INF;`
60. `            return false;`
61. `        }`
62. `        return true;`
63. `    }`
64. `     /** Function to get maximum matching **/`
65. `    public int HopcroftKarp() `
66. `    {`
67. `        Pair = new int[cx + cy + 1];`
68. `        Dist = new int[cx + cy + 1];`
69. `        int matching = 0;`
70. `        while (BFS())`
71. `            for (int v = 1; v <= cx; ++v)`
72. `                if (Pair[v] == NIL)`
73. `                    if (DFS(v))`
74. `                        matching = matching + 1;`
75. `        return matching;`
76. `    }`
77. `    /** Function to make graph with vertices x , y **/`
78. `    public void makeGraph(int[] x, int[] y, int E)`
79. `    {`
80. `        Adj = new ArrayList[cx + cy + 1];`
81. `        for (int i = 0; i < Adj.length; ++i)`
82. `            Adj[i] = new ArrayList<Integer>();        `
83. `        /** adding edges **/    `
84. `        for (int i = 0; i < E; ++i) `
85. `            addEdge(x[i] + 1, y[i] + 1);    `
86. `    }`
87. `    /** Function to add a edge **/`
88. `    public void addEdge(int u, int v) `
89. `    {`
90. `        Adj[u].add(cx + v);`
91. `        Adj[cx + v].add(u);`
92. `    }    `
93. `    /** Main Method **/`
94. `    public static void main (String[] args) `
95. `    {`
96. `        Scanner scan = new Scanner(System.in);`
97. `        System.out.println("Hopcroft Algorithm Test\n");`
98. `        /** Make an object of Hopcroft class **/`
99. `        Hopcroft hc = new Hopcroft();`
100. ` `
101. `        /** Accept number of edges **/`
102. `        System.out.println("Enter number of edges\n");`
103. `        int E = scan.nextInt();`
104. `        int[] x = new int[E];`
105. `        int[] y = new int[E];`
106. `        hc.cx = 0;`
107. `        hc.cy = 0;`
108. ` `
109. `        System.out.println("Enter "+ E +" x, y coordinates ");`
110. `        for (int i = 0; i < E; i++)`
111. `        {`
112. `            x[i] = scan.nextInt();`
113. `            y[i] = scan.nextInt();`
114. `            hc.cx = Math.max(hc.cx, x[i]);`
115. `            hc.cy = Math.max(hc.cy, y[i]);`
116. `        }`
117. `        hc.cx += 1;`
118. `        hc.cy += 1;`
119. ` `
120. `        /** make graph with vertices **/`
121. `        hc.makeGraph(x, y, E);            `
122. ` `
123. `        System.out.println("\nMatches : "+ hc.HopcroftKarp());            `
124. `    }    `
125. `}`

```Hopcroft Algorithm Test

Enter number of edges

11
Enter 11 x, y coordinates
0 0
0 3
1 0
1 2
1 4
2 1
3 0
3 2
3 3
3 4
4 2

Matches : 5```

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