Tarjans strongly connected components algorithm

#include<bits/stdc++.h>
using namespace std;
#define V 7
#define pb push_back

unordered_map<int,vector<int>> adj;

void DFS(int u,vector<int>& disc,vector<int>& low,stack<int>& mystack,vector<bool>& presentInStack)
{
	static int time = 0;
	disc[u] = low[u] = time;
	time+=1;
	mystack.push(u);
	presentInStack[u] = true;

	for(int v: adj[u])
	{
		if(disc[v]==-1)	//If v is not visited
		{
			DFS(v,disc,low,mystack,presentInStack);
			low[u] = min(low[u],low[v]);
		}
		//Differentiate back-edge and cross-edge
		else if(presentInStack[v])	//Back-edge case
			low[u] = min(low[u],disc[v]);
	}

	if(low[u]==disc[u])	//If u is head node of SCC
	{
		cout<<"SCC is: ";
		while(mystack.top()!=u)
		{
			cout<<mystack.top()<<" ";
			presentInStack[mystack.top()] = false;
			mystack.pop();
		}
		cout<<mystack.top()<<"\n";
		presentInStack[mystack.top()] = false;
		mystack.pop();
	}
}

void findSCCs_Tarjan()
{
	vector<int> disc(V,-1),low(V,-1);
	vector<bool> presentInStack(V,false);	//Avoids cross-edge
	stack<int> mystack;

	for(int i=0;i<V;++i)
		if(disc[i]==-1)
			DFS(i,disc,low,mystack,presentInStack);
}

int main()
{
	adj[0].pb(1);
	adj[1].pb(2);
	adj[1].pb(3);
	adj[3].pb(4);
	adj[4].pb(0);
	adj[4].pb(5);
	adj[4].pb(6);
	adj[5].pb(6);
	adj[6].pb(5);

	findSCCs_Tarjan();
	return 0;
}

//TIME COMPLEXITY: O(V+E)

Thank you for the explanation on YouTube and code here.

Hey Surya - thank you for sharing the code, but I do have a question.

For this input -

adj[0].pb(1);
adj[0].pb(4);
adj[1].pb(2);
adj[2].pb(3);
adj[3].pb(1);
adj[3].pb(0);
adj[1].pb(4);
adj[4].pb(3);

your code return 1->4 as the bridge.
However, removing connection 1->4 does not increase the number of SCC it is still 1 (SCC1 - 0,1,2,3,4).

But removing connection 4->3 does increase the number of SCC, it is now 2 (SCC1 - 0,1,2,3 and SCC2 - 4)

Do you think I'm doing something wrong?

cout<<mystack.top()<<"\n";
presentInStack[mystack.top()] = false;
mystack.pop();

why this is writing again ??
this 3 lines are already put in while condn so! why it's also put outside while loop

@sakshi160722 because you need to pop the head node also. the while loop pops the elements until you see the head node, you write the above code snippet to remove the head node too.

Java Code

import java.util.*;
class Tarjans {
    static final int V = 7;
    static int time=0;
    static List<Integer> graph[];
    public static void main(String[] args) {
        graph = new LinkedList[V];
        for(int i=0;i<V;i++){
            graph[i]=new LinkedList<Integer>();
        }
        graph[0].add(1);
        graph[1].add(2);
        graph[1].add(3);
        graph[3].add(4);
        graph[4].add(0);
        graph[4].add(5);
        graph[4].add(6);
        graph[5].add(6);
        graph[6].add(5);        

        findSCCs_Trajan();
    }
    private static void findSCCs_Trajan() {
        int disc[] = new int[V];
        int low[] = new int[V];
        Arrays.fill(disc, -1);
        Arrays.fill(low, -1);
        boolean presentInStack[] = new boolean[V]; // Avoids cross-edge
        Stack<Integer> st = new Stack<>();
        for(int i=0;i<V;i++){
            if(disc[i]==-1){
                DFS(i,disc,low,st,presentInStack);
            }
        }
    }
    private static void DFS(int u, int[] disc, int[] low, Stack<Integer> st, boolean[] presentInStack) {

        low[u]=disc[u]=time;
        time+=1;
        st.push(u);
        presentInStack[u]=true;
        for(int v:graph[u]){
            if(disc[v]==-1){ // If v is not visited
                DFS(v, disc, low, st, presentInStack);
                low[u]=Math.min(low[u], low[v]);
            }else if(presentInStack[v]){
                low[u]=Math.min(low[u], disc[v]);
            }
        }
        if(low[u]==disc[u]){
            System.out.println("SCC is :");
            while(st.peek()!=u){
                System.out.print(st.peek()+" ");
                presentInStack[st.pop()]=false;
            }
            System.out.print(st.peek()+"\n");
            presentInStack[st.pop()]=false;
        }
    }

}

Can anybody help why this code is not working for a specific test case on geeksforgeeks?

  tarjanDfs(graph, vertex, discoveryTime, lowTime, isVertexInStack, stack, components, time, count) {
    	discoveryTime[vertex] = lowTime[vertex] = time++;
    	
    	stack.push(vertex);
    	isVertexInStack[vertex] = true;
    	
    	for(const neighbour of graph[vertex]) {
    		if(discoveryTime[neighbour] == -1) {
    			this.tarjanDfs(graph, neighbour, discoveryTime, lowTime, isVertexInStack, stack, components, time, count);
    			lowTime[vertex] = Math.min(lowTime[vertex], lowTime[neighbour]);
    		} else if(isVertexInStack[neighbour]) {
    			lowTime[vertex] = Math.min(lowTime[vertex], discoveryTime[neighbour]);
    		}
    	}
    
    	// If vertex is the head of the SCC
    	if(lowTime[vertex] == discoveryTime[vertex]) {
    		const scc = [];
            let node = stack.pop();
    
    		while(node != vertex) {
    			scc.push(node);
    			isVertexInStack[node] = false;
    			node = stack.pop();
    		}
    		scc.push(node);
    		isVertexInStack[node] = false;
    		components.push(scc.sort()) ;
    		 
    	}
    }
    
    tarjans(V,adj)
    {
    	const discoveryTime = new Array(V).fill(-1);
    	const lowTime = new Array(V).fill(-1);
    	const isVertexInStack = new Array(V).fill(false);
    	const stack = [];
    	const components = [];
    
    	for(let vertex = 0; vertex < V; vertex++) {
    		if(discoveryTime[vertex] == -1) {
    			this.tarjanDfs(adj, vertex, discoveryTime, lowTime, isVertexInStack, stack, components, 0);
    		}
    	}
        
    	return components.sort((l1, l2) => l1[0] - l2[0]);
    }

i too am having the same issue

top G channel , hands down