Applications of MST

What is Minimum Spanning Tree in C?

Minimum Spanning Tree in C can be represented in different ways, depending on the algorithm used. Here we use Kruskal’s Algorithm to Implement Minimum Spanning Tree....

C Program to Implement Minimum Spanning Tree

C #include #include // Structure to represent an edge with source, destination, and weight typedef struct Edge { int src; int dest; int weight; } Edge; // Structure to represent a graph with vertices, edges, and an array of edges typedef struct Graph { int V; int E; Edge* edges; } Graph; // Create a new graph with V vertices and E edges Graph* createGraph(int V, int E) { Graph* graph = (Graph*)malloc(sizeof(Graph)); graph->V = V; graph->E = E; graph->edges = (Edge*)malloc(E * sizeof(Edge)); return graph; } // Disjoint Set Union (DSU) structure with parent and rank typedef struct DSU { int* parent; int* rank; } DSU; // Create a new DSU with V vertices DSU* createDSU(int V) { DSU* dsu = (DSU*)malloc(sizeof(DSU)); dsu->parent = (int*)malloc(V * sizeof(int)); dsu->rank = (int*)malloc(V * sizeof(int)); for (int i = 0; i < V; i++) { dsu->parent[i] = i; dsu->rank[i] = 0; } return dsu; } // Find the representative (root) of a set with path compression int find(DSU* dsu, int x) { if (dsu->parent[x] != x) { dsu->parent[x] = find(dsu, dsu->parent[x]); } return dsu->parent[x]; } // Union two sets by rank void unionSets(DSU* dsu, int x, int y) { int rootX = find(dsu, x); int rootY = find(dsu, y); if (rootX != rootY) { if (dsu->rank[rootX] < dsu->rank[rootY]) { dsu->parent[rootX] = rootY; } else if (dsu->rank[rootX] > dsu->rank[rootY]) { dsu->parent[rootY] = rootX; } else { dsu->parent[rootY] = rootX; dsu->rank[rootX]++; } } } // Compare function for sorting edges by weight int compareEdges(const void* a, const void* b) { Edge* edgeA = (Edge*)a; Edge* edgeB = (Edge*)b; return edgeA->weight - edgeB->weight; } // Kruskal's algorithm to find the Minimum Spanning Tree void kruskalMST(Graph* graph) { // Step 1: Sort the edges by weight qsort(graph->edges, graph->E, sizeof(Edge), compareEdges); DSU* dsu = createDSU(graph->V); Edge* result = (Edge*)malloc((graph->V - 1) * sizeof(Edge)); int edgeCount = 0; int i = 0; while (edgeCount < graph->V - 1 && i < graph->E) { Edge nextEdge = graph->edges[i++]; int srcRoot = find(dsu, nextEdge.src); int destRoot = find(dsu, nextEdge.dest); if (srcRoot != destRoot) { result[edgeCount++] = nextEdge; unionSets(dsu, srcRoot, destRoot); } } printf("Edges in the Minimum Spanning Tree:\n"); for (int j = 0; j < edgeCount; j++) { printf("%d -- %d : %d\n", result[j].src, result[j].dest, result[j].weight); } free(result); free(dsu->parent); free(dsu->rank); free(dsu); } int main() { int V = 4; // Number of vertices int E = 5; // Number of edges Graph* graph = createGraph(V, E); // Edges: (src, dest, weight) graph->edges[0].src = 0; graph->edges[0].dest = 1; graph->edges[0].weight = 10; graph->edges[1].src = 0; graph->edges[1].dest = 2; graph->edges[1].weight = 6; graph->edges[2].src = 0; graph->edges[2].dest = 3; graph->edges[2].weight = 5; graph->edges[3].src = 1; graph->edges[3].dest = 3; graph->edges[3].weight = 15; graph->edges[4].src = 2; graph->edges[4].dest = 3; graph->edges[4].weight = 4; kruskalMST(graph); free(graph->edges); free(graph); return 0; }...

Applications of MST

In Networking design mostly The Minimum Spanning Tree is usedFor identifying natural clustering in Graph .Used in approximation algorithms for problems like Travelling Salesman Problem.Constructing efficient road or pipelines network with minimal construction costs....

Conclusion

Prim’s Algorithms is an effective for creating or implementing Minimum Spanning Tree. Kruskal’s Algorithm is typically chosen when edges are already given, and sorting them is efficient. It offers time and space complexity that is well suited for large scale graphs with applications in network designing, clustering, And other optimization problems....