Question

C Programming Question:

Q) Write a C - program to implement an Uprooted version (Save to parent pointer instead of child pointer, ie. parent of top is null) of Kruskal's Minimum Spanning Tree with adjacency list and min-heap as the additional data structure.

Note: Please implement it in C and also keep the above conditions in mind. You can take your time. Thank you.

Answer 1

// C program for Kruskal's algorithm to find Minimum Spanning Tree // of a given connected, undirected and weighted graph #include <stdio.h> #include <stdlib.h> #include <string.h> // a structure to represent a weighted edge in graph struct Edge {     int src, dest, weight; }; // a structure to represent a connected, undirected // and weighted graph struct Graph {     // V-> Number of vertices, E-> Number of edges     int V, E;     // graph is represented as an array of edges.     // Since the graph is undirected, the edge     // from src to dest is also edge from dest     // to src. Both are counted as 1 edge here.     struct Edge* edge; }; // Creates a graph with V vertices and E edges struct Graph* createGraph(int V, int E) {     struct Graph* graph = new Graph;     graph->V = V;     graph->E = E;     graph->edge = new Edge[E];     return graph; } // A structure to represent a subset for union-find struct subset {     int parent;     int rank; }; // A utility function to find set of an element i // (uses path compression technique) int find(struct subset subsets[], int i) {     // find root and make root as parent of i     // (path compression)     if (subsets[i].parent != i)         subsets[i].parent = find(subsets, subsets[i].parent);     return subsets[i].parent; } // A function that does union of two sets of x and y // (uses union by rank) void Union(struct subset subsets[], int x, int y) {     int xroot = find(subsets, x);     int yroot = find(subsets, y);     // Attach smaller rank tree under root of high     // rank tree (Union by Rank)     if (subsets[xroot].rank < subsets[yroot].rank)         subsets[xroot].parent = yroot;     else if (subsets[xroot].rank > subsets[yroot].rank)         subsets[yroot].parent = xroot;     // If ranks are same, then make one as root and     // increment its rank by one     else     {         subsets[yroot].parent = xroot;         subsets[xroot].rank++;     } } // Compare two edges according to their weights. // Used in qsort() for sorting an array of edges int myComp(const void* a, const void* b) {     struct Edge* a1 = (struct Edge*)a;     struct Edge* b1 = (struct Edge*)b;     return a1->weight > b1->weight; } // The main function to construct MST using Kruskal's algorithm void KruskalMST(struct Graph* graph) {     int V = graph->V;     struct Edge result[V]; // Tnis will store the resultant MST     int e = 0; // An index variable, used for result[]     int i = 0; // An index variable, used for sorted edges     // Step 1: Sort all the edges in non-decreasing     // order of their weight. If we are not allowed to     // change the given graph, we can create a copy of     // array of edges     qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp);     // Allocate memory for creating V ssubsets     struct subset *subsets =         (struct subset*) malloc( V * sizeof(struct subset) );     // Create V subsets with single elements     for (int v = 0; v < V; ++v)     {         subsets[v].parent = v;         subsets[v].rank = 0;     }     // Number of edges to be taken is equal to V-1     while (e < V - 1 && i < graph->E)     {         // Step 2: Pick the smallest edge. And increment         // the index for next iteration         struct Edge next_edge = graph->edge[i++];         int x = find(subsets, next_edge.src);         int y = find(subsets, next_edge.dest);         // If including this edge does't cause cycle,         // include it in result and increment the index         // of result for next edge         if (x != y)         {             result[e++] = next_edge;             Union(subsets, x, y);         }         // Else discard the next_edge     }     // print the contents of result[] to display the     // built MST     printf("Following are the edges in the constructed MST\n");     for (i = 0; i < e; ++i)         printf("%d -- %d == %d\n", result[i].src, result[i].dest,                                                  result[i].weight);     return; } // Driver program to test above functions int main() {     /* Let us create following weighted graph              10         0--------1         | \     |        6|   5\   |15         |      \ |         2--------3             4       */     int V = 4; // Number of vertices in graph     int E = 5; // Number of edges in graph     struct Graph* graph = createGraph(V, E);     // add edge 0-1     graph->edge[0].src = 0;     graph->edge[0].dest = 1;     graph->edge[0].weight = 10;     // add edge 0-2     graph->edge[1].src = 0;     graph->edge[1].dest = 2;     graph->edge[1].weight = 6;     // add edge 0-3     graph->edge[2].src = 0;     graph->edge[2].dest = 3;     graph->edge[2].weight = 5;     // add edge 1-3     graph->edge[3].src = 1;     graph->edge[3].dest = 3;     graph->edge[3].weight = 15;     // add edge 2-3     graph->edge[4].src = 2;     graph->edge[4].dest = 3;     graph->edge[4].weight = 4;     KruskalMST(graph);     return 0; }