 # C++ Programming Code Examples

## C++ > Computer Graphics Code Examples

### Apply the Prim's Algorithm to Find the Minimum Spanning Tree of a Graph

``` 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. #include <stdio.h> #include <limits.h> #include <iostream> using namespace std; // Number of vertices in the graph #define V 5 // A utility function to find the vertex with minimum key value, from // the set of vertices not yet included in MST int minKey(int key[], bool mstSet[]) { // Initialize min value int min = INT_MAX, min_index; for (int v = 0; v < V; v++) if (mstSet[v] == false && key[v] < min) min = key[v], min_index = v; return min_index; } // A utility function to print the constructed MST stored in parent[] int printMST(int parent[], int n, int graph[V][V]) { cout<<"Edge Weight\n"; for (int i = 1; i < V; i++) printf("%d - %d %d \n", parent[i], i, graph[i][parent[i]]); } // Function to construct and print MST for a graph represented using adjacency // matrix representation void primMST(int graph[V][V]) { 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 // Initialize all keys as INFINITE for (int i = 0; i < V; i++) key[i] = INT_MAX, mstSet[i] = false; // Always include first 1st vertex in MST. key = 0; // Make key 0 so that this vertex is picked as first vertex parent = -1; // First node is always root of MST // The MST will have V vertices for (int count = 0; count < V - 1; count++) { // Pick thd minimum key vertex from the set of vertices // not yet included in MST int u = minKey(key, mstSet); // Add the picked vertex to the MST Set mstSet[u] = true; // Update key value and parent index of the adjacent vertices of the picked vertex. Consider only those vertices which are not yet included in MST for (int v = 0; v < V; v++) // 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]; } // print the constructed MST printMST(parent, V, graph); } // driver program to test above function int main() { /* Let us create the following graph 2 3 (0)--(1)--(2) | / \ | 6| 8/ \5 |7 | / \ | (3)-------(4) 9 */ 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 }, }; // Print the solution primMST(graph); return 0; } ``` 