C++ Program to Find Shortest Path in a DAG using Topological Sorting

This is a C++ Program to find shortest path for DAG using topological sorting. For a general weighted graph, we can calculate single source shortest distances in O(VE) time using Bellman–Ford Algorithm. For a graph with no negative weights, we can do better and calculate single source shortest distances in O(E + VLogV) time using Dijkstra’s algorithm. Can we do even better for Directed Acyclic Graph (DAG)? We can calculate single source shortest distances in O(V+E) time for DAGs. The idea is to use Topological Sorting.

Here is source code of the C++ Program to Implement Shortest Path Algorithm for DAG Using Topological Sorting. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

// A C++ program to find single source shortest paths for Directed Acyclic Graphs

```
#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<AdjListNode> *adj;
```
```
 
```

        // A function used by shortestPath

        void topologicalSortUtil(int v, bool visited[], stack<int> &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<AdjListNode> [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<int> &Stack)

```
{
```
```
    // Mark the current node as visited
```
```
    visited[v] = true;
```
```
 
```

    // Recur for all the vertices adjacent to this vertex

```
    list<AdjListNode>::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<int> 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<AdjListNode>::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:

$ g++ ShortestPathDAG.cpp
$ a.out
 
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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