C++ Programming Code Examples
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C++ Program to Find the Longest Path in a DAG
/* C++ Program to Find the Longest Path in a DAG
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
}
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;
}
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