C++ Program to Implement Shortest Path Algorithm for DAG Using Topological Sorting

Code:

#include   iostream
#include   list
#include   stack
#include   limits.h
#define INF INT_MAX
using namespace std;

class AdjListNode
{
        int v;
        int weight;
    public:
        AdjListNode(int _v, int _w)
        {
            v = _v;
            weight = _w;
        }
        int getV()
        {
            return v;
        }
        int getWeight()
        {
            return weight;
        }
};

// Class to represent a graph using adjacency list representation
class Graph
{
        int V; // No. of vertices'

        // Pointer to an array containing adjacency lists
        list *adj;

        // A function used by shortestPath
        void topologicalSortUtil(int v, bool visited[], stack &Stack);
    public:
        Graph(int V); // Constructor

        // function to add an edge to graph
        void addEdge(int u, int v, int weight);

        // Finds shortest paths from given source vertex
        void shortestPath(int s);
};

Graph::Graph(int V)
{
    this->V = V;
    adj = new list [V];
}

void Graph::addEdge(int u, int v, int weight)
{
    AdjListNode node(v, weight);
    adj[u].push_back(node); // Add v to u's list
}

void Graph::topologicalSortUtil(int v, bool visited[], stack &Stack)
{
    // Mark the current node as visited
    visited[v] = true;

    // Recur for all the vertices adjacent to this vertex
    list::iterator i;
    for (i = adj[v].begin(); i != adj[v].end(); ++i)
    {
        AdjListNode node = *i;
        if (!visited[node.getV()])
            topologicalSortUtil(node.getV(), visited, Stack);
    }

    // Push current vertex to stack which stores topological sort
    Stack.push(v);
}

void Graph::shortestPath(int s)
{
    stack Stack;
    int dist[V];

    // Mark all the vertices as not visited
    bool *visited = new bool[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;

    // Call the recursive helper function to store Topological Sort
    // starting from all vertices one by one
    for (int i = 0; i < V; i++)
        if (visited[i] == false)
            topologicalSortUtil(i, visited, Stack);

    // Initialize distances to all vertices as infinite and distance
    // to source as 0
    for (int i = 0; i < V; i++)
        dist[i] = INF;
    dist[s] = 0;

    // Process vertices in topological order
    while (Stack.empty() == false)
    {
        // Get the next vertex from topological order
        int u = Stack.top();
        Stack.pop();

        // Update distances of all adjacent vertices
        list::iterator i;
        if (dist[u] != INF)
        {
            for (i = adj[u].begin(); i != adj[u].end(); ++i)
                if (dist[i->getV()] > dist[u] + i->getWeight())
                    dist[i->getV()] = dist[u] + i->getWeight();
        }
    }

    // Print the calculated shortest distances
    for (int i = 0; i < V; i++)
        (dist[i] == INF) ? cout << "INF " : cout << dist[i] << " ";
}

// Driver program to test above functions
int main()
{
    // Create a graph given in the above diagram.  Here vertex numbers are
    // 0, 1, 2, 3, 4, 5 with following mappings:
    // 0=r, 1=s, 2=t, 3=x, 4=y, 5=z
    Graph g(6);
    g.addEdge(0, 1, 5);
    g.addEdge(0, 2, 3);
    g.addEdge(1, 3, 6);
    g.addEdge(1, 2, 2);
    g.addEdge(2, 4, 4);
    g.addEdge(2, 5, 2);
    g.addEdge(2, 3, 7);
    g.addEdge(3, 4, -1);
    g.addEdge(4, 5, -2);

    int s = 1;
    cout << "Following are shortest distances from source " << s << " \n";
    g.shortestPath(s);

    return 0;
}


Output:

Following are shortest distances from source 1 
INF 0 2 6 5 3 
------------------
(program exited with code: 0)
Press return to continue


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