add kruskal.cpp

C++/Algorithms/Graph Theory Algorithms/kruskal.cpp

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+// C++ program for Kruskal's algorithm
+//  to find Minimum Spanning Tree of a
+//  given connected, undirected and weighted
+//  graph
+#include <bits/stdc++.h>
+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;
+}