Merge pull request #40 from pb-10/master

Dijkstra Shortest Path added.

Author: darpanjbora

Greedy Algorithms/dijkstra shortest path.java

@@ -0,0 +1,95 @@
+// A Java program for Dijkstra's single source shortest path algorithm. 
+// The program is for adjacency matrix representation of the graph 
+import java.util.*; 
+import java.lang.*; 
+import java.io.*; 
+  
+class ShortestPath { 
+    // A utility function to find the vertex with minimum distance value, 
+    // from the set of vertices not yet included in shortest path tree 
+    static final int V = 9; 
+    int minDistance(int dist[], Boolean sptSet[]) 
+    { 
+        // Initialize min value 
+        int min = Integer.MAX_VALUE, min_index = -1; 
+  
+        for (int v = 0; v < V; v++) 
+            if (sptSet[v] == false && dist[v] <= min) { 
+                min = dist[v]; 
+                min_index = v; 
+            } 
+  
+        return min_index; 
+    } 
+  
+    // A utility function to print the constructed distance array 
+    void printSolution(int dist[]) 
+    { 
+        System.out.println("Vertex \t\t Distance from Source"); 
+        for (int i = 0; i < V; i++) 
+            System.out.println(i + " \t\t " + dist[i]); 
+    } 
+  
+    // Function that implements Dijkstra's single source shortest path 
+    // algorithm for a graph represented using adjacency matrix 
+    // representation 
+    void dijkstra(int graph[][], int src) 
+    { 
+        int dist[] = new int[V]; // The output array. dist[i] will hold 
+        // the shortest distance from src to i 
+  
+        // sptSet[i] will true if vertex i is included in shortest 
+        // path tree or shortest distance from src to i is finalized 
+        Boolean sptSet[] = new Boolean[V]; 
+  
+        // Initialize all distances as INFINITE and stpSet[] as false 
+        for (int i = 0; i < V; i++) { 
+            dist[i] = Integer.MAX_VALUE; 
+            sptSet[i] = false; 
+        } 
+  
+        // Distance of source vertex from itself is always 0 
+        dist[src] = 0; 
+  
+        // Find shortest path for all vertices 
+        for (int count = 0; count < V - 1; count++) { 
+            // Pick the minimum distance vertex from the set of vertices 
+            // not yet processed. u is always equal to src in first 
+            // iteration. 
+            int u = minDistance(dist, sptSet); 
+  
+            // Mark the picked vertex as processed 
+            sptSet[u] = true; 
+  
+            // Update dist value of the adjacent vertices of the 
+            // picked vertex. 
+            for (int v = 0; v < V; v++) 
+  
+                // Update dist[v] only if is not in sptSet, there is an 
+                // edge from u to v, and total weight of path from src to 
+                // v through u is smaller than current value of dist[v] 
+                if (!sptSet[v] && graph[u][v] != 0 && dist[u] != Integer.MAX_VALUE && dist[u] + graph[u][v] < dist[v]) 
+                    dist[v] = dist[u] + graph[u][v]; 
+        } 
+  
+        // print the constructed distance array 
+        printSolution(dist); 
+    } 
+  
+    // Driver method 
+    public static void main(String[] args) 
+    { 
+        /* Let us create the example graph discussed above */
+        int graph[][] = new int[][] { { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, 
+                                      { 4, 0, 8, 0, 0, 0, 0, 11, 0 }, 
+                                      { 0, 8, 0, 7, 0, 4, 0, 0, 2 }, 
+                                      { 0, 0, 7, 0, 9, 14, 0, 0, 0 }, 
+                                      { 0, 0, 0, 9, 0, 10, 0, 0, 0 }, 
+                                      { 0, 0, 4, 14, 10, 0, 2, 0, 0 }, 
+                                      { 0, 0, 0, 0, 0, 2, 0, 1, 6 }, 
+                                      { 8, 11, 0, 0, 0, 0, 1, 0, 7 }, 
+                                      { 0, 0, 2, 0, 0, 0, 6, 7, 0 } }; 
+        ShortestPath t = new ShortestPath(); 
+        t.dijkstra(graph, 0); 
+    } 
+}