diff --git a/graphs/README.md b/graphs/README.md new file mode 100644 index 00000000..edddf0fc --- /dev/null +++ b/graphs/README.md @@ -0,0 +1,7 @@ +# Graphs + +### C or C++ + +1. [Kruskal Algorithm](c-or-cpp/kruskal-algorithm.cpp) + + diff --git a/graphs/c-or-cpp/kruskal-algorithm.cpp b/graphs/c-or-cpp/kruskal-algorithm.cpp new file mode 100644 index 00000000..70532e1b --- /dev/null +++ b/graphs/c-or-cpp/kruskal-algorithm.cpp @@ -0,0 +1,173 @@ +//Graph Kruskal algorithm +#include +using namespace std; + +class Edge { +public: + int src, dest, weight; +}; + +class Graph { +public: + + int V, E; + 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; +}; + + +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; + + + 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; + } + + while (e < V - 1 && i < graph->E) + { + + Edge next_edge = graph->edge[i++]; + + int x = find(subsets, next_edge.src); + int y = find(subsets, next_edge.dest); + + + if (x != y) { + result[e++] = next_edge; + Union(subsets, x, y); + } + // Else discard the next_edge + } + + + cout << "Following are the edges in the " + "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; + } + cout << "Minimum Cost Spanning Tree: " << minimumCost + << endl; +} + +// Driver code +int main() +{ + + + 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; + + + + KruskalMST(graph); + + return 0; +} + + diff --git a/linked-lists/README.md b/linked-lists/README.md index 1565603c..5d632318 100644 --- a/linked-lists/README.md +++ b/linked-lists/README.md @@ -9,6 +9,10 @@ 3. [Circular Linked List](c-or-cpp/circular.cpp) +2. [Doubly Linked List](c-or-cpp/doubly.cpp) + +3. [Circular Linked List](c-or-cpp/circular.cpp) + ### Java 1. [Singly Linked List](java/singly.cpp)