C++ Program to Create a Random Linear Extension for a DAG

Here we will see how to create Random Linear Extension of a Directed Acyclic Graph (DAG). The Linear extension is basically the topological sorting of DAG. Let us consider the graph is like below −

The topological sorting for a directed acyclic graph is the linear ordering of vertices. For every edge u-v of a directed graph, the vertex u will come before vertex v in the ordering.

As we know that the source vertex will come after the destination vertex, so we need to use a stack to store previous elements. After completing all nodes, we can simply display them from stack.

Input

Output

Nodes after topological sorted order − 5 4 2 3 1 0

Algorithm

topoSort(u, visited, stack)

Input − The start vertex u, An array to keep track which node is visited or not. A stack to store nodes.

Output − Sorting the vertices in topological sequence in the stack.

Begin
   mark u as visited
   for all vertices v which is adjacent with u, do
      if v is not visited, then
         topoSort(c, visited, stack)
      done
      push u into stack
End

performTopologicalSorting(Graph)

Input − The given directed acyclic graph.

Output − Sequence of nodes.

Begin
   initially mark all nodes as unvisited
   for all nodes v of the graph, do
      if v is not visited, then
         topoSort(i, visited, stack)
      done
      pop and print all elements from the stack
End

Example

 Live Demo

#include<iostream>
#include<stack>
#define NODE 6
using namespace std;
int graph[NODE][NODE] = {
   {0, 0, 0, 0, 0, 0},
   {0, 0, 0, 0, 0, 0},
   {0, 0, 0, 1, 0, 0},
   {0, 1, 0, 0, 0, 0},
   {1, 1, 0, 0, 0, 0},
   {1, 0, 1, 0, 0, 0}
};
void topoSort(int u, bool visited[], stack<int> &stk) {
   visited[u] = true; //set as the node v is visited
   for(int v = 0; v<NODE; v++) {
      if(graph[u][v]){ //for allvertices v adjacent to u
         if(!visited[v])
            topoSort(v, visited, stk);
      }
   }
   stk.push(u); //push starting vertex into the stack
}
void performTopologicalSort() {
   stack<int> stk;
   bool vis[NODE];
   for(int i = 0; i<NODE; i++)
      vis[i] = false; //initially all nodes are unvisited
   for(int i = 0; i<NODE; i++)
      if(!vis[i]) //when node is not visited
         topoSort(i, vis, stk);
   while(!stk.empty()) {
      cout << stk.top() << " ";
      stk.pop();
   }
}
main() {
   cout << "Nodes after topological sorted order: ";
   performTopologicalSort();
}

Output

Nodes after topological sorted order: 5 4 2 3 1 0