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C++ Program to Apply DFS to Perform the Topological Sorting of a Directed Acyclic Graph
Topological sorting of DAG (Directed Acyclic Graph) is a linear ordering of vertices such that for every directed edge uv, where vertex u comes before v in the ordering. If the graph is not a DAG, Topological Sorting for a graph is not possible.
Functions and pseudocodes
Begin function topologicalSort(): a) Mark the current node as visited. b) Recur for all the vertices adjacent to this vertex. c) Push current vertex to stack which stores result. End Begin function topoSort() which uses recursive topological sort() function: a) Mark all the vertices which are not visited. b) Call the function topologicalSort(). c) Print the content. End
Example
#include<iostream> #include <list> #include <stack> using namespace std; class G { int n; list<int> *adj; //declaration of functions void topologicalSort(int v, bool visited[], stack<int> &Stack); public: G(int n); //constructor void addEd(int v, int w); void topoSort(); }; G::G(int n) { this->n = n; adj = new list<int> [n]; } void G::addEd(int v, int w) // add the edges to the graph. { adj[v].push_back(w); //add w to v’s list } void G::topologicalSort(int v, bool visited[], stack<int> &Stack) { visited[v] = true; //mark current node as visited list<int>::iterator i; //Recur for all the vertices adjacent to this vertex. for (i = adj[v].begin(); i != adj[v].end(); ++i) if (!visited[*i]) topologicalSort(*i, visited, Stack); Stack.push(v); } void G::topoSort() { stack<int> Stack; bool *visited = new bool[n]; //Mark all the vertices which are not visited. for (int i = 0; i < n; i++) visited[i] = false; for (int i = 0; i < n; i++) if (visited[i] == false) //Call the function topologicalSort(). topologicalSort(i, visited, Stack); while (Stack.empty() == false) { cout << Stack.top() << " "; //print the element Stack.pop(); } } int main() { G g(6); g.addEd(4, 2); g.addEd(5, 1); g.addEd(4, 0); g.addEd(3, 1); g.addEd(1, 3); g.addEd(3, 2); cout << " Topological Sort of the given graph \n"; g.topoSort(); return 0; }
Output
Topological Sort of the given graph 5 4 1 3 2 0
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