Add Dijkstra's shortest path algorithm. (#21)

Author: ilimugur

graph/c++/dijkstra.cpp

@@ -0,0 +1,94 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+
+
+class DirectedGraph
+{
+    typedef vector< vector < pair<int, long long> > > AdjList;
+
+    int V;    // Number of vertices
+  
+    AdjList adjList;
+public:
+    DirectedGraph(int V);
+
+    void addEdge(int u, int v, long long w);
+
+    // Finds the shortest path from source to destination
+    long long shortestPathDijkstra(int source, int destination, vector<int>& path);
+};
+
+DirectedGraph::DirectedGraph(int n) : adjList(n), V(n)
+{
+}
+ 
+void DirectedGraph::addEdge(int u, int v, long long w)
+{
+    adjList[u].emplace_back(v, w);
+}
+  
+long long DirectedGraph::shortestPathDijkstra(int source, int destination, vector<int>& path)
+{
+    vector< int > parent(V, -1);
+    vector< long long > minCost(V, LLONG_MAX);
+    set< pair<long long, int> > pq;
+
+    minCost[source] = 0LL;
+    pq.insert( make_pair(0LL, source) );
+
+    while(!pq.empty())
+    {
+        set< pair<long long, int> >::iterator it = pq.begin();
+        int u = it->second;
+        pq.erase(it);
+
+        if(u == destination)
+            break;
+
+        for(int i=0; i < adjList[u].size(); ++i)
+        {
+            int v = adjList[u][i].first;
+            long long w = adjList[u][i].second;
+            if(minCost[v] > minCost[u] + w)
+            {
+                pq.erase( make_pair(minCost[v], v) );
+                minCost[v] = minCost[u] + w;
+                pq.insert( make_pair(minCost[v], v) );
+                parent[v] = u;
+            }
+        }
+    }
+
+    int tmp = destination;
+    while(tmp != -1)
+    {
+        path.push_back(tmp);
+        tmp = parent[tmp];
+    }
+    reverse(path.begin(), path.end());
+
+    return minCost[destination];
+}
+
+// Driver program to test methods of graph class
+int main()
+{
+    // Create a graph given in the above diagram
+    DirectedGraph g(5);
+    g.addEdge(0, 1, 3LL);
+    g.addEdge(1, 3, 6LL);
+    g.addEdge(3, 4, 2LL);
+    g.addEdge(1, 2, 4LL);
+    g.addEdge(2, 3, 1LL);
+
+    vector<int> path;
+    long long cost = g.shortestPathDijkstra(0, 4, path);
+    cout << "Shortest path from vertex 0 to vertex 4 costs " << cost << " and follows the vertices:" << endl;
+    for(int i = 0; i < path.size(); ++i)
+    {
+        cout << path[i] << endl;
+    }
+
+    return 0;
+}