Algorithms for Coding Interviews in C++/

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Solution: Topological Sorting of a Graph

Solution: Topological Sorting of a Graph

This review provides a detailed analysis of the solution to perform topological sorting of a graph.

We'll cover the following...

Solution #1: Using Graph Traversal

We can modify graph traversal algorithms to find Topological Sorting of a graph.

C++
#include "Graph.h"
void Graph::utilityFunction(int v, vector<bool>& visited, stack<int> &myStack) { 
	visited[v] = true; 
  list<int>::iterator i; 
	for (i = adjacencyList[v].begin(); i != adjacencyList[v].end(); ++i) 
		if (!visited[*i]) 
			utilityFunction(*i, visited, myStack); 
	myStack.push(v); 
} 
void Graph::topologicalSort() { 
	vector<bool> visited(this -> vertices, false); 
  stack<int> myStack; 
	for (int i = 0; i < this -> vertices; i++) 
	if (visited[i] == false) 
		utilityFunction(i, visited, myStack); 
	while (myStack.empty() == false) { 
		cout << myStack.top() << " "; 
		myStack.pop(); 
	} 
}  
int main() { 
	Graph g(6); 
	g.addEdge(5, 0); 
	g.addEdge(5, 2); 
	g.addEdge(4, 2); 
	g.addEdge(4, 1); 
	g.addEdge(2, 3); 
	g.addEdge(3, 1); 
	cout << "Graph1 Topological Sort: "; 
	g.topologicalSort(); 
  cout << endl << endl;
  
  Graph g1(5);
  g1.addEdge(0 ,1);
  g1.addEdge(1 ,2);
  g1.addEdge(2 ,3);
  g1.addEdge(2 ,4);
  g1.addEdge(3, 4);
  g1.addEdge(0, 3);
  
  cout << "Graph2 Topological Sort: "; 
	g1.topologicalSort(); 
	return 0; 
}

While traversing a graph, we start from a vertex. First, print it and then recursively call the utility function for its adjacent vertices.

In topological sorting, we use a temporary stack. We do not print the vertex immediately; before that, we recursively call topological sorting for all its adjacent vertices, then push it to a stack. Finally, print contents of the stack.

Note: A vertex is pushed to stack only when all of its adjacent vertices are already in the stack.

Pseudocode

function utilityFunction(v)
    mark v visited
    for each node i with an edge from v to i
        utilityFunction(i)
    add v to head to myStack

function topologicalSort()

  myStack ← Empty list that will contain the sorted 
  nodes
  while there are unvisited nodes do
      select an unvisited node i
      utilityFunction(i)

 print myStack

The pseudocode is mapped in the solution above.

Time Complexity

The above algorithm is a modified version of DFS with an extra stack, so time complexity is the same as DFS with O(V+E)O(V+E).

Solution

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