diff --git a/C++/Algorithms/Graph Theory Algorithms/kruskal.cpp b/C++/Algorithms/Graph Theory Algorithms/kruskal.cpp new file mode 100644 index 000000000..54a8b8f00 --- /dev/null +++ b/C++/Algorithms/Graph Theory Algorithms/kruskal.cpp @@ -0,0 +1,200 @@ +// C++ program for Kruskal's algorithm +// to find Minimum Spanning Tree of a +// given connected, undirected and weighted +// graph +#include +using namespace std; + +// a structure to represent a +// weighted edge in graph +class Edge { +public: + int src, dest, weight; +}; + +// a structure to represent a connected, +// undirected and weighted graph +class Graph { +public: + + // 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. + Edge* edge; +}; + +// Creates a graph with V vertices and E edges +Graph* createGraph(int V, int E) +{ + 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 +class subset { +public: + int parent; + int rank; +}; + +// A utility function to find set of an element i +// (uses path compression technique) +int find(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(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) +{ + Edge* a1 = (Edge*)a; + Edge* b1 = (Edge*)b; + return a1->weight > b1->weight; +} + +// The main function to construct MST using Kruskal's +// algorithm +void KruskalMST(Graph* graph) +{ + int V = graph->V; + 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 + subset* subsets = new subset[(V * sizeof(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 + 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 + cout << "Following are the edges in the constructed " + "MST\n"; + int minimumCost = 0; + for (i = 0; i < e; ++i) + { + cout << result[i].src << " -- " << result[i].dest + << " == " << result[i].weight << endl; + minimumCost = minimumCost + result[i].weight; + } + // return; + cout << "Minimum Cost Spanning Tree: " << minimumCost + << endl; +} + +// Driver code +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 + 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; + + + // Function call + KruskalMST(graph); + + return 0; +} \ No newline at end of file