programming-examples/c++/Hard_Graph_Problems/C++ Program to Find the Longest Path in a DAG.cpp

/*This is a C++ Program to find longest path in DAG. Given a Weighted Directed Acyclic Graph (DAG) and a source vertex s in it, find the longest distances from s to all other vertices in the given graph. Following is complete algorithm for finding longest distances.
1) Initialize dist[] = {NINF, NINF, ….} and dist[s] = 0 where s is the source vertex. Here NINF means negative infinite.
2) Create a toplogical order of all vertices.
3) Do following for every vertex u in topological order.
………..Do following for every adjacent vertex v of u
………………if (dist[v] < dist[u] + weight(u, v)) ………………………dist[v] = dist[u] + weight(u, v) */

// A C++ program to find single source longest distances in a DAG
#include <iostream>
#include <list>
#include <stack>
#include <limits.h>
#define NINF INT_MIN
using namespace std;

// Graph is represented using adjacency list. Every node of adjacency list
// contains vertex number of the vertex to which edge connects. It also
// contains weight of the edge
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 longestPath
    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 longest distances from given source vertex
    void longestPath(int s);
};

Graph::Graph(int V) // Constructor
{
    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
}

// A recursive function used by longestPath. See below link for details
// http://www.geeksforgeeks.org/topological-sorting/
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);
}

// The function to find longest distances from a given vertex. It uses
// recursive topologicalSortUtil() to get topological sorting.
void Graph::longestPath(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] = NINF;
    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] != NINF)
                {
                    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 longest distances
    for (int i = 0; i < V; i++)
        (dist[i] == NINF) ? 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, 5, 1);
    g.addEdge(3, 4, -1);
    g.addEdge(4, 5, -2);
    int s = 1;
    cout << "Following are longest distances from source vertex " << s << " \n";
    g.longestPath(s);
    return 0;
}

/*

Following are longest distances from source vertex 1
INF 0 2 9 8 10