107 lines
3.4 KiB
Java
107 lines
3.4 KiB
Java
package DataStructures.Graphs;
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/**
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* A Java program for Prim's Minimum Spanning Tree (MST) algorithm.
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* adjacency matrix representation of the graph
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*/
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class PrimMST {
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// Number of vertices in the graph
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private static final int V = 5;
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// A utility function to find the vertex with minimum key
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// value, from the set of vertices not yet included in MST
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int minKey(int key[], Boolean mstSet[]) {
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// Initialize min value
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int min = Integer.MAX_VALUE, min_index = -1;
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for (int v = 0; v < V; v++)
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if (mstSet[v] == false && key[v] < min) {
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min = key[v];
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min_index = v;
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}
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return min_index;
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}
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// A utility function to print the constructed MST stored in
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// parent[]
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void printMST(int parent[], int n, int graph[][]) {
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System.out.println("Edge Weight");
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for (int i = 1; i < V; i++)
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System.out.println(parent[i] + " - " + i + " " +
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graph[i][parent[i]]);
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}
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// Function to construct and print MST for a graph represented
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// using adjacency matrix representation
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void primMST(int graph[][]) {
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// Array to store constructed MST
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int parent[] = new int[V];
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// Key values used to pick minimum weight edge in cut
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int key[] = new int[V];
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// To represent set of vertices not yet included in MST
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Boolean mstSet[] = new Boolean[V];
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// Initialize all keys as INFINITE
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for (int i = 0; i < V; i++) {
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key[i] = Integer.MAX_VALUE;
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mstSet[i] = false;
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}
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// Always include first 1st vertex in MST.
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key[0] = 0; // Make key 0 so that this vertex is
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// picked as first vertex
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parent[0] = -1; // First node is always root of MST
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// The MST will have V vertices
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for (int count = 0; count < V - 1; count++) {
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// Pick thd minimum key vertex from the set of vertices
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// not yet included in MST
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int u = minKey(key, mstSet);
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// Add the picked vertex to the MST Set
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mstSet[u] = true;
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// Update key value and parent index of the adjacent
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// vertices of the picked vertex. Consider only those
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// vertices which are not yet included in MST
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for (int v = 0; v < V; v++)
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// graph[u][v] is non zero only for adjacent vertices of m
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// mstSet[v] is false for vertices not yet included in MST
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// Update the key only if graph[u][v] is smaller than key[v]
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if (graph[u][v] != 0 && mstSet[v] == false &&
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graph[u][v] < key[v]) {
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parent[v] = u;
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key[v] = graph[u][v];
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}
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}
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// print the constructed MST
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printMST(parent, V, graph);
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}
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public static void main(String[] args) {
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/* Let us create the following graph
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2 3
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(0)--(1)--(2)
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| / \ |
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6| 8/ \5 |7
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| / \ |
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(3)-------(4)
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9 */
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PrimMST t = new PrimMST();
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int graph[][] = new int[][]{{0, 2, 0, 6, 0},
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{2, 0, 3, 8, 5},
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{0, 3, 0, 0, 7},
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{6, 8, 0, 0, 9},
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{0, 5, 7, 9, 0},
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};
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// Print the solution
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t.primMST(graph);
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}
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}
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