# Java Program to Find Minimum Spanning Tree using Kruskal’s Algorithm

This Java program to find mst using kruskal’s algorithm.Kruskal’s algorithm is a greedy algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized

Here is the source code of the Java program to find mst using kruskal’s algorithm. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

1. `import java.util.Collections;`
2. `import java.util.Comparator;`
3. `import java.util.LinkedList;`
4. `import java.util.List;`
5. `import java.util.Scanner;`
6. `import java.util.Stack;`
7. ` `
8. `public class KruskalAlgorithm`
9. `{`
10. `    private List<Edge> edges;`
11. `    private int numberOfVertices;`
12. `    public static final int MAX_VALUE = 999;`
13. `    private int visited[];`
14. `    private int spanning_tree[][];`
15. ` `
16. `    public KruskalAlgorithm(int numberOfVertices)`
17. `    {`
18. `        this.numberOfVertices = numberOfVertices;`
19. `        edges = new LinkedList<Edge>();`
20. `        visited = new int[this.numberOfVertices + 1];`
21. `        spanning_tree = new int[numberOfVertices + 1][numberOfVertices + 1];`
22. `    }`
23. ` `
24. `    public void kruskalAlgorithm(int adjacencyMatrix[][])`
25. `    {`
26. `        boolean finished = false;`
27. `        for (int source = 1; source <= numberOfVertices; source++)`
28. `        {`
29. `            for (int destination = 1; destination <= numberOfVertices; destination++)`
30. `            {`
31. `                if (adjacencyMatrix[source][destination] != MAX_VALUE && source != destination)`
32. `                {`
33. `                    Edge edge = new Edge();`
34. `                    edge.sourcevertex = source;`
35. `                    edge.destinationvertex = destination;`
36. `                    edge.weight = adjacencyMatrix[source][destination];`
37. `                    adjacencyMatrix[destination][source] = MAX_VALUE;`
38. `                    edges.add(edge);`
39. `                }`
40. `            }`
41. `        }`
42. `        Collections.sort(edges, new EdgeComparator());`
43. `        CheckCycle checkCycle = new CheckCycle();`
44. `        for (Edge edge : edges)`
45. `        {`
46. `            spanning_tree[edge.sourcevertex][edge.destinationvertex] = edge.weight;`
47. `            spanning_tree[edge.destinationvertex][edge.sourcevertex] = edge.weight;`
48. `            if (checkCycle.checkCycle(spanning_tree, edge.sourcevertex))`
49. `            {`
50. `                spanning_tree[edge.sourcevertex][edge.destinationvertex] = 0;`
51. `                spanning_tree[edge.destinationvertex][edge.sourcevertex] = 0;`
52. `                edge.weight = -1;`
53. `                continue;`
54. `            }`
55. `            visited[edge.sourcevertex] = 1;`
56. `            visited[edge.destinationvertex] = 1;`
57. `            for (int i = 0; i < visited.length; i++)`
58. `            {`
59. `                if (visited[i] == 0)`
60. `                {`
61. `                    finished = false;`
62. `                    break;`
63. `                } else`
64. `                {`
65. `                    finished = true;`
66. `                }`
67. `            }`
68. `            if (finished)`
69. `                break;`
70. `        }`
71. `        System.out.println("The spanning tree is ");`
72. `        for (int i = 1; i <= numberOfVertices; i++)`
73. `            System.out.print("\t" + i);`
74. `        System.out.println();`
75. `        for (int source = 1; source <= numberOfVertices; source++)`
76. `        {`
77. `            System.out.print(source + "\t");`
78. `            for (int destination = 1; destination <= numberOfVertices; destination++)`
79. `            {`
80. `                System.out.print(spanning_tree[source][destination] + "\t");`
81. `            }`
82. `            System.out.println();`
83. `        }`
84. `    }`
85. ` `
86. `    public static void main(String... arg)`
87. `    {`
88. `        int adjacency_matrix[][];`
89. `        int number_of_vertices;`
90. ` `
91. `        Scanner scan = new Scanner(System.in);`
92. `        System.out.println("Enter the number of vertices");`
93. `        number_of_vertices = scan.nextInt();`
94. `        adjacency_matrix = new int[number_of_vertices + 1][number_of_vertices + 1];`
95. ` `
96. `        System.out.println("Enter the Weighted Matrix for the graph");`
97. `        for (int i = 1; i <= number_of_vertices; i++)`
98. `        {`
99. `            for (int j = 1; j <= number_of_vertices; j++)`
100. `            {`
101. `                adjacency_matrix[i][j] = scan.nextInt();`
102. `                if (i == j)`
103. `                {`
104. `                    adjacency_matrix[i][j] = 0;`
105. `                    continue;`
106. `                }`
107. `                if (adjacency_matrix[i][j] == 0)`
108. `                {`
109. `                    adjacency_matrix[i][j] = MAX_VALUE;`
110. `                }`
111. `            }`
112. `        }`
113. `        KruskalAlgorithm kruskalAlgorithm = new KruskalAlgorithm(number_of_vertices);`
114. `        kruskalAlgorithm.kruskalAlgorithm(adjacency_matrix);`
115. `        scan.close();`
116. `    }`
117. `}`
118. ` `
119. `class Edge`
120. `{`
121. `    int sourcevertex;`
122. `    int destinationvertex;`
123. `    int weight;`
124. `}`
125. ` `
126. `class EdgeComparator implements Comparator<Edge>`
127. `{`
128. `    @Override`
129. `    public int compare(Edge edge1, Edge edge2)`
130. `    {`
131. `        if (edge1.weight < edge2.weight)`
132. `            return -1;`
133. `        if (edge1.weight > edge2.weight)`
134. `            return 1;`
135. `        return 0;`
136. `    }`
137. `}`
138. ` `
139. `class CheckCycle`
140. `{`
141. `    private Stack<Integer> stack;`
142. `    private int adjacencyMatrix[][];`
143. ` `
144. `    public CheckCycle()`
145. `    {`
146. `        stack = new Stack<Integer>();`
147. `    }`
148. ` `
149. `    public boolean checkCycle(int adjacency_matrix[][], int source)`
150. `    {`
151. `        boolean cyclepresent = false;`
152. `        int number_of_nodes = adjacency_matrix[source].length - 1;`
153. ` `
154. `        adjacencyMatrix = new int[number_of_nodes + 1][number_of_nodes + 1];`
155. `        for (int sourcevertex = 1; sourcevertex <= number_of_nodes; sourcevertex++)`
156. `        {`
157. `            for (int destinationvertex = 1; destinationvertex <= number_of_nodes; destinationvertex++)`
158. `            {`
159. `                adjacencyMatrix[sourcevertex][destinationvertex] = adjacency_matrix[sourcevertex[destinationvertex];`
160. `            }`
161. `         }`
162. ` `
163. `         int visited[] = new int[number_of_nodes + 1];`
164. `         int element = source;`
165. `         int i = source;`
166. `         visited[source] = 1;`
167. `         stack.push(source);`
168. ` `
169. `         while (!stack.isEmpty())`
170. `         {`
171. `             element = stack.peek();`
172. `             i = element;`
173. `             while (i <= number_of_nodes)`
174. `             {`
175. `                 if (adjacencyMatrix[element][i] >= 1 && visited[i] == 1)`
176. `                 {`
177. `                     if (stack.contains(i))`
178. `                     {`
179. `                         cyclepresent = true;`
180. `                         return cyclepresent;`
181. `                     }`
182. `                 }`
183. `                 if (adjacencyMatrix[element][i] >= 1 && visited[i] == 0)`
184. `                 {`
185. `                     stack.push(i);`
186. `                     visited[i] = 1;`
187. `                     adjacencyMatrix[element][i] = 0;// mark as labelled;`
188. `                     adjacencyMatrix[i][element] = 0;`
189. `                     element = i;`
190. `                     i = 1;`
191. `                     continue;`
192. `                  }`
193. `                  i++;`
194. `             }`
195. `             stack.pop();`
196. `        }`
197. `        return cyclepresent;`
198. `    }`
199. `}`

```\$javac KruskalAlgorithm.java
\$java KruskalAlgorithm
Enter the number of vertices
6
Enter the Weighted Matrix for the graph
0 6 8 6 0 0
6 0 0 5 10 0
8 0 0 7 5 3
6 5 7 0 0 0
0 10 5 0 0 3
0 0 3 0 3 0
The spanning tree is
1	2	3	4	5	6
1	0	6	0	0	0	0
2	6	0	0	5	0	0
3	0	0	0	7	0	3
4	0	5	7	0	0	0
5	0	0	0	0	0	3
6	0	0	3	0	3	0```

Sanfoundry Global Education & Learning Series – 1000 Java Programs.