Remove space from Data Structures package name

DataStructures/Graphs/KruskalsAlgorithm.java

@@ -0,0 +1,174 @@
+// Java program for Kruskal's algorithm to find Minimum Spanning Tree
+// of a given connected, undirected and weighted graph
+import java.util.*;
+import java.lang.*;
+import java.io.*;
+ 
+class Graph
+{
+    // A class to represent a graph edge
+    class Edge implements Comparable<Edge>
+    {
+        int src, dest, weight;
+ 
+        // Comparator function used for sorting edges based on
+        // their weight
+        public int compareTo(Edge compareEdge)
+        {
+            return this.weight-compareEdge.weight;
+        }
+    };
+ 
+    // A class to represent a subset for union-find
+    class subset
+    {
+        int parent, rank;
+    };
+ 
+    int V, E;    // V-> no. of vertices & E->no.of edges
+    Edge edge[]; // collection of all edges
+ 
+    // Creates a graph with V vertices and E edges
+    Graph(int v, int e)
+    {
+        V = v;
+        E = e;
+        edge = new Edge[E];
+        for (int i=0; i<e; ++i)
+            edge[i] = new Edge();
+    }
+ 
+    // 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++;
+        }
+    }
+ 
+    // The main function to construct MST using Kruskal's algorithm
+    void KruskalMST()
+    {
+        Edge result[] = new Edge[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
+        for (i=0; i<V; ++i)
+            result[i] = new Edge();
+ 
+        // 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
+        Arrays.sort(edge);
+ 
+        // Allocate memory for creating V ssubsets
+        subset subsets[] = new subset[V];
+        for(i=0; i<V; ++i)
+            subsets[i]=new subset();
+ 
+        // Create V subsets with single elements
+        for (int v = 0; v < V; ++v)
+        {
+            subsets[v].parent = v;
+            subsets[v].rank = 0;
+        }
+ 
+        i = 0;  // Index used to pick next edge
+ 
+        // Number of edges to be taken is equal to V-1
+        while (e < V - 1)
+        {
+            // Step 2: Pick the smallest edge. And increment the index
+            // for next iteration
+            Edge next_edge = new Edge();
+            next_edge = 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
+        System.out.println("Following are the edges in the constructed MST");
+        for (i = 0; i < e; ++i)
+            System.out.println(result[i].src+" -- "+result[i].dest+" == "+
+                               result[i].weight);
+    }
+ 
+    // Driver Program
+    public static void main (String[] args)
+    {
+ 
+        /* 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 = new Graph(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;
+ 
+        graph.KruskalMST();
+    }
+}