C++ Program to Apply the Prim’s Algorithm to Find the Minimum Spanning Tree of a Graph

This is a C++ Program to find the minimum spanning tree of the given graph using Prims algorihtm. In computer science, Prim’s algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted undirected 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 source code of the C++ Program to Apply the Prim’s Algorithm to Find the Minimum Spanning Tree of a Graph. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

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#include <stdio.h>
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#include <limits.h>
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#include <iostream>
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using namespace std;
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// Number of vertices in the graph
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#define V 5
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// A utility function to find the vertex with minimum key value, from

// the set of vertices not yet included in MST

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int minKey(int key[], bool mstSet[])
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{
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    // Initialize min value
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    int min = INT_MAX, min_index;
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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], min_index = v;
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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 parent[]

int printMST(int parent[], int n, int graph[V][V])

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{
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    cout<<"Edge   Weight\n";
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    for (int i = 1; i < V; i++)
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        printf("%d - %d    %d \n", parent[i], i, graph[i][parent[i]]);

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}
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// Function to construct and print MST for a graph represented using adjacency

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// matrix representation
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void primMST(int graph[V][V])
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{
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    int parent[V]; // Array to store constructed MST

    int key[V]; // Key values used to pick minimum weight edge in cut

    bool mstSet[V]; // To represent set of vertices not yet included in MST

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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] = INT_MAX, mstSet[i] = false;

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    // Always include first 1st vertex in MST.

    key[0] = 0; // Make key 0 so that this vertex is picked as first vertex

    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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    {
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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 vertices of

        // the picked vertex. Consider only those vertices which are not yet

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        // 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

            // mstSet[v] is false for vertices not yet included in MST

            // Update the key only if graph[u][v] is smaller than key[v]

            if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v])

                parent[v] = u, key[v] = graph[u][v];

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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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// driver program to test above function

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int main()
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{
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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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    int graph[V][V] = { { 0, 2, 0, 6, 0 }, { 2, 0, 3, 8, 5 },

            { 0, 3, 0, 0, 7 }, { 6, 8, 0, 0, 9 }, { 0, 5, 7, 9, 0 }, };

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    // Print the solution
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    primMST(graph);
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    return 0;
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}
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Output:

$ g++ PrimsMST.cpp
$ a.out
 
Edge   Weight
0 - 1    2 
1 - 2    3 
0 - 3    6 
1 - 4    5 
 
------------------
(program exited with code: 0)
Press return to continue

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