The Algorithms logo
The Algorithms

Tarjans Algorithm

package com.thealgorithms.datastructures.graphs;

import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Stack;

 * Java program that implements Tarjan's Algorithm.
 * @author Shivanagouda S A (

 * Tarjan's algorithm is a linear time algorithm to find the strongly connected components of a 
   directed graph, which, from here onwards will be referred as SCC. 
 * A graph is said to be strongly connected if every vertex is reachable from every other vertex. 
   The SCCs of a directed graph form a partition into subgraphs that are themselves strongly connected.
   Single node is always a SCC.

 * Example:
    0 --------> 1 -------> 3 --------> 4
    ^          /
    |         /
    |        /
    |       /
    |      /
    |     /
    |    /
    |   /
    |  /
    | /

    For the above graph, the SCC list goes as follows:
    1, 2, 0
    We can also see that order of the nodes in an SCC doesn't matter since they are in cycle.

    Tarjan's Algorithm: 
    * DFS search produces a DFS tree 
    * Strongly Connected Components form subtrees of the DFS tree. 
    * If we can find the head of these subtrees, we can get all the nodes in that subtree (including the head)
      and that will be one SCC. 
    * There is no back edge from one SCC to another (here can be cross edges, but they will not be used).

    * Kosaraju Algorithm aims at doing the same but uses two DFS traversalse whereas Tarjan’s algorithm does 
      the same in a single DFS, which leads to much lower constant factors in the latter.

public class TarjansAlgorithm {

    //Timer for tracking lowtime and insertion time
    private int Time;

    private List<List<Integer>> SCClist = new ArrayList<List<Integer>>();

    public List<List<Integer>> stronglyConnectedComponents(int V, List<List<Integer>> graph) {

        // Initially all vertices as unvisited, insertion and low time are undefined

        // insertionTime:Time when a node is visited 1st time while DFS traversal

        // lowTime: indicates the earliest visited vertex (the vertex with minimum insertion time) that can 
        // be reached from a subtree rooted with a particular node.
        int lowTime[] = new int[V];
        int insertionTime[] = new int[V];
        for (int i = 0; i < V; i++) {
            insertionTime[i] = -1;
            lowTime[i] = -1;
        // To check if element is present in stack
        boolean isInStack[] = new boolean[V];

        // Store nodes during DFS
        Stack<Integer> st = new Stack<Integer>();

        for (int i = 0; i < V; i++) {
            if (insertionTime[i] == -1)
                stronglyConnCompsUtil(i, lowTime, insertionTime, isInStack, st, graph);

        return SCClist;

    private void stronglyConnCompsUtil(int u, int lowTime[], int insertionTime[],
            boolean isInStack[], Stack<Integer> st, List<List<Integer>> graph) {

        // Initialize insertion time and lowTime value of current node
        insertionTime[u] = Time;
        lowTime[u] = Time;
        Time += 1;

        //Push current node into stack
        isInStack[u] = true;

        int n;

        // Go through all vertices adjacent to this
        Iterator<Integer> i = graph.get(u).iterator();

        while (i.hasNext()) {
            n =;

            //If the adjacent node is unvisited, do DFS
            if (insertionTime[n] == -1) {
                stronglyConnCompsUtil(n, lowTime, insertionTime, isInStack, st, graph);
                //update lowTime for the current node comparing lowtime of adj node
                lowTime[u] = Math.min(lowTime[u], lowTime[n]);
            } else if (isInStack[n] == true) {
                //If adj node is in stack, update low 
                lowTime[u] = Math.min(lowTime[u], insertionTime[n]);
        //If lowtime and insertion time are same, current node is the head of an SCC
        // head node found, get all the nodes in this SCC
        if (lowTime[u] == insertionTime[u]) {
            int w = -1;
            var scc = new ArrayList<Integer>();

            //Stack has all the nodes of the current SCC
            while (w != u) {
                w = st.pop();
                isInStack[w] = false;