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Kahns_Algorithm_Topological_sort.cpp
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Kahns_Algorithm_Topological_sort.cpp
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// Kahns's Algorithm for Topological sort :
//STEP 1: Push (Enqueue) nodes having in-degree == 0 in Queue.
//STEP 2: Remove Edges associated with that node.
//STEP 3: Perform steps 1 & 2, until Queue gets empty.
// Topological Sort
// Def : Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices
// such that for every directed edge uv, vertex u comes before v in the ordering.
// Topological Sorting for a graph is not possible if graph is not DAG.
//Note : There can be multiple Topological sorts for a given DAG.
#include<iostream>
#include<algorithm>
#include<vector>
#include<set>
#include<iterator>
#include<math.h>
#include<queue>
#include<stack>
using namespace std;
#define SIZE 100001
vector<int>adj[SIZE];
int in_degree[SIZE];
queue<int>q;
vector<int>answer;
void kahns_topo(int N){
for(int i=1;i<=N;i++)
if(in_degree[i]==0) //Pushing all nodes having in-degree == 0
q.push(i);
while(!q.empty()){
int u=q.front();
answer.push_back(u); //Adding node in Final answer, as Queue has nodes having in-degree == 0
q.pop();
for(int child:adj[u]){
in_degree[child]--; //Removing Edges associated with that node
if(in_degree[child]==0) //Pushing node in Queue having in-degree == 0
q.push(child);
}
}
if(answer.size()!=N) //It means graph is not DAG,it has Cycle.
cout<<"Cycle Present : Topological Sort Not Possible\n";
else
for(int node:answer) //Printing Final Answer i.e. Topological sort
cout<<node<<" ";
cout<<"\n";
}
int main()
{
int N,M;
cin>>N>>M;
int i,j,x,y;
while(M--){
cin>>x>>y;
adj[x].push_back(y); //Directed graph
in_degree[y]++; //Calculating in-degree of every node
}
kahns_topo(N);
return 0;
}