Merge pull request #552 from ArighnaIITG/ari_algo2

New Greedy Algorithm

dial_algo/dial.cpp

@@ -0,0 +1,144 @@
+// C++ Program for Dijkstra's dial implementation
+#include<bits/stdc++.h>
+using namespace std;
+# define INF 0x3f3f3f3f
+
+// This class represents a directed graph using
+// adjacency list representation
+class Graph
+{
+    int V;  // No. of vertices
+
+    // In a weighted graph, we need to store vertex
+    // and weight pair for every edge
+    list< pair<int, int> > *adj;
+
+public:
+    Graph(int V);  // Constructor
+
+    // function to add an edge to graph
+    void addEdge(int u, int v, int w);
+
+    // prints shortest path from s
+    void shortestPath(int s, int W);
+};
+
+// Allocates memory for adjacency list
+Graph::Graph(int V)
+{
+    this->V = V;
+    adj = new list< pair<int, int> >[V];
+}
+
+//  adds edge between u and v of weight w
+void Graph::addEdge(int u, int v, int w)
+{
+    adj[u].push_back(make_pair(v, w));
+    adj[v].push_back(make_pair(u, w));
+}
+
+// Prints shortest paths from src to all other vertices.
+// W is the maximum weight of an edge
+void Graph::shortestPath(int src, int W)
+{
+    /* With each distance, iterator to that vertex in
+       its bucket is stored so that vertex can be deleted
+       in O(1) at time of updation. So
+    dist[i].first = distance of ith vertex from src vertex
+    dits[i].second = iterator to vertex i in bucket number */
+    vector<pair<int, list<int>::iterator> > dist(V);
+
+    // Initialize all distances as infinite (INF)
+    for (int i = 0; i < V; i++)
+        dist[i].first = INF;
+
+    // Create buckets B[].
+    // B[i] keep vertex of distance label i
+    list<int> B[W * V + 1];
+
+    B[0].push_back(src);
+    dist[src].first = 0;
+
+    //
+    int idx = 0;
+    while (1)
+    {
+        // Go sequentially through buckets till one non-empty
+        // bucket is found
+        while (B[idx].size() == 0 && idx < W*V)
+            idx++;
+
+        // If all buckets are empty, we are done.
+        if (idx == W * V)
+            break;
+
+        // Take top vertex from bucket and pop it
+        int u = B[idx].front();
+        B[idx].pop_front();
+
+        // Process all adjacents of extracted vertex 'u' and
+        // update their distanced if required.
+        for (auto i = adj[u].begin(); i != adj[u].end(); ++i)
+        {
+            int v = (*i).first;
+            int weight = (*i).second;
+
+            int du = dist[u].first;
+            int dv = dist[v].first;
+
+            // If there is shorted path to v through u.
+            if (dv > du + weight)
+            {
+                // If dv is not INF then it must be in B[dv]
+                // bucket, so erase its entry using iterator
+                // in O(1)
+                if (dv != INF)
+                    B[dv].erase(dist[v].second);
+
+                //  updating the distance
+                dist[v].first = du + weight;
+                dv = dist[v].first;
+
+                // pushing vertex v into updated distance's bucket
+                B[dv].push_front(v);
+
+                // storing updated iterator in dist[v].second
+                dist[v].second = B[dv].begin();
+            }
+        }
+    }
+
+    // Print shortest distances stored in dist[]
+    printf("Vertex   Distance from Source\n");
+    for (int i = 0; i < V; ++i)
+        printf("%d     %d\n", i, dist[i].first);
+}
+
+// Driver program to test methods of graph class
+int main()
+{
+    // create the graph given in above fugure
+    int V = 9;
+    Graph g(V);
+
+    //  making above shown graph
+    g.addEdge(0, 1, 4);
+    g.addEdge(0, 7, 8);
+    g.addEdge(1, 2, 8);
+    g.addEdge(1, 7, 11);
+    g.addEdge(2, 3, 7);
+    g.addEdge(2, 8, 2);
+    g.addEdge(2, 5, 4);
+    g.addEdge(3, 4, 9);
+    g.addEdge(3, 5, 14);
+    g.addEdge(4, 5, 10);
+    g.addEdge(5, 6, 2);
+    g.addEdge(6, 7, 1);
+    g.addEdge(6, 8, 6);
+    g.addEdge(7, 8, 7);
+
+    //  maximum weighted edge - 14
+    g.shortestPath(0, 14);
+
+    return 0;
+}