C++ Program to Check Whether Topological Sorting can be Performed in a Graph

In a Directed Acyclic Graph, we can sort vertices in linear order using topological sort.

Topological sort is only work on Directed Acyclic Graph. In a Directed Acyclic Graph (DAG), there can be more than one topological sort.

In the following C++ program, we shall perform topological sort to check existence of a cycle in a graph.

Algorithms

For function Topo_Sort

Begin
   Define function Topo_Sort()
      Declare x to the integer datatype, vstd[] of the Boolean array and Stack as a stack.
         Pass them as parameter.
      Initialize vstd[x] = true to mark the current node as vstd.
      Declare an iterator i.
      for (i = a[x].begin(); i != a[x].end(); ++i)
         if (!vstd[*i]) then
      Call Topo_Sort(*i, vstd, Stack) function.
   Call push() function to insert values into stack.
End.

Example

#include<iostream>
#include <list>
#include <stack>
using namespace std;
class grph { // Class to represent a graph
   int ver;
   list<int> *a; // Pointer to an array containing adjacency listsList
   void Topo_Sort(int x, bool vstd[], stack<int> &Stack); // A function used by TopologicalSort
   public:
      grph(int ver); // Constructor of grpf
   void Insert_Edge(int x, int y); // to insert an edge to graph
   void Topol_Sort(); // prints a Topological Sort of the complete graph
};
grph::grph(int ver) {
   this->ver = ver;
   a = new list<int>[ver];
}
void grph::Insert_Edge(int x, int y) {
   a[x].push_back(y); // Add y to x’s list.
}
// A recursive function used by Topol_Sort
void grph::Topo_Sort(int x, bool vstd[], stack<int> &Stack) {
   vstd[x] = true; // Mark the current node as vstd.
   list<int>::iterator i;
   for (i = a[x].begin(); i != a[x].end(); ++i)
      if (!vstd[*i])
         Topo_Sort(*i, vstd, Stack);
   // Push current vertex to stack which stores result
   Stack.push(x);
}
void grph::Topol_Sort() {
   stack<int> Stack;
   // Mark all the vertices as not vstd
   bool *vstd = new bool[ver];
   for (int i = 0; i < ver; i++)
      vstd[i] = false;
   for (int i = 0; i < ver; i++)
      if (vstd[i] == false)
         Topo_Sort(i, vstd, Stack);
   while (Stack.empty() == false) {
      cout << Stack.top() << " ";
      Stack.pop();
   }
}
int main() {
   grph g(6); // Create a graph given in the above diagram
   g.Insert_Edge(5, 2);
   g.Insert_Edge(5, 0);
   g.Insert_Edge(4, 0);
   g.Insert_Edge(4, 1);
   g.Insert_Edge(2, 3);
   g.Insert_Edge(3, 1);
   cout << "Topological Sort of the graph is: \n";
   g.Topol_Sort();
   return 0;
}

Output

Topological Sort of the graph is:
5 4 2 3 1 0