Printing pre and post visited times in DFS of a graph

Depth First Search (DFS) marks all the vertices of a graph as visited. So for making DFS useful, some additional information can also be stored. For instance, the order in which the vertices are visited while running DFS.

Pre-visit and Post-visit numbers are the extra information that can be stored while running a DFS on a graph and which turns out to be really useful. Pre-visit number tells the time at which the node gets into the recursion stack and Post-visit number tells the time at which the node comes out from recursion stack of DFS.

Example:

The numbers written in brackets denote [Pre-visit number, Post-visit number].

Pre and Post numbers are widely used in graph algorithms. For example, they can be used to find out whether a particular node lies in the sub-tree of another node.
To find whether u lies in the sub-tree of v or not we just compare the pre and post number of u and v. If pre[u] > pre[v] and post[u] < post[v] then u lies in the sub-tree of v otherwise not. You can see above example for more clarification.

Pre-visit and Post-visit numbers can be found by simple DFS. We will take two arrays one for storing pre numbers and one for post numbers and by taking a variable that will keep track of the time. The implementation of the same is given below:

Implementation:

C++

#include <bits/stdc++.h>
using namespace std;

// Variable to keep track of time
int Time = 1;

// Function to perform DFS starting from node u
void dfs(int u, vector<vector<int>> aList,
                       vector<int> &pre, 
                       vector<int> &post, 
                       vector<int> &vis)
{
    
    // Storing the pre number whenever
    // the node comes into recursion stack
    pre[u] = Time;

    // Increment time
    Time++;
    vis[u] = 1;
    
    for(int v : aList[u]) 
    {
        if (vis[v] == 0)
            dfs(v, aList, pre, post, vis);
    }

    // Storing the post number whenever
    // the node goes out of recursion stack
    post[u] = Time;
    Time++;
}

// Driver Code    
int main()
{
    
    // Number of nodes in graph
    int n = 6;

    // Adjacency list
    vector<vector<int>> aList(n + 1);
    
    vector<int> pre(n + 1);
    vector<int> post(n + 1);

    // Visited array
    vector<int> vis(n + 1);

    // Edges
    aList[1].push_back(2);
    aList[2].push_back(1);
    aList[2].push_back(4);
    aList[4].push_back(2);
    aList[1].push_back(3);
    aList[3].push_back(1);
    aList[3].push_back(4);
    aList[4].push_back(3);
    aList[3].push_back(5);
    aList[5].push_back(3);
    aList[5].push_back(6);
    aList[6].push_back(5);

    // DFS starting at Node 1
    dfs(1, aList, pre, post, vis);

    // Number of nodes in graph
    for(int i = 1; i <= n; i++)
        cout << "Node " << i << " Pre number "
             << pre[i] << " Post number " 
             << post[i] << endl;

    return 0;
}

// This code is contributed by divyesh072019

Java

import java.util.*;
public class GFG {

    // Variable to keep track of time
    static int time = 1;

    // Function to perform DFS starting from node u
    static void dfs(int u, ArrayList<ArrayList<Integer> > aList,
                    int pre[], int post[], int vis[])
    {

        // Storing the pre number whenever
        // the node comes into recursion stack
        pre[u] = time;

        // Increment time
        time++;
        vis[u] = 1;
        for (int v : aList.get(u)) {
            if (vis[v] == 0)
                dfs(v, aList, pre, post, vis);
        }

        // Storing the post number whenever
        // the node goes out of recursion stack
        post[u] = time;
        time++;
    }

    // Driver code
    public static void main(String args[])
    {

        // Number of nodes in graph
        int n = 6;

        // Adjacency list
        ArrayList<ArrayList<Integer> > aList
            = new ArrayList<ArrayList<Integer> >(n + 1);
        for (int i = 1; i <= n; i++) {
            ArrayList<Integer> list = new ArrayList<>();
            aList.add(list);
        }
        aList.add(new ArrayList<Integer>());
        int pre[] = new int[n + 1];
        int post[] = new int[n + 1];

        // Visited array
        int vis[] = new int[n + 1];

        // Edges
        aList.get(1).add(2);
        aList.get(2).add(1);
        aList.get(2).add(4);
        aList.get(4).add(2);
        aList.get(1).add(3);
        aList.get(3).add(1);
        aList.get(3).add(4);
        aList.get(4).add(3);
        aList.get(3).add(5);
        aList.get(5).add(3);
        aList.get(5).add(6);
        aList.get(6).add(5);

        // DFS starting at Node 1
        dfs(1, aList, pre, post, vis);

        // Number of nodes in graph
        for (int i = 1; i <= n; i++)
            System.out.println("Node " + i + " Pre number "
                               + pre[i] + " Post number " + post[i]);
    }
}

Python3

# Variable to keep track of time 
time = 1

# Function to perform DFS starting 
# from node u 
def dfs(u, aList, pre, post, vis):
    
    global time
    
    # Storing the pre number whenever 
    # the node comes into recursion stack 
    pre[u] = time

    # Increment time 
    time += 1 
    
    vis[u] = 1
    
    for v in aList[u]:
        if (vis[v] == 0):
            dfs(v, aList, pre, post, vis)
            
    # Storing the post number whenever 
    # the node goes out of recursion stack 
    post[u] = time
    time += 1

# Driver code 
if __name__=='__main__':
    
    # Number of nodes in graph 
    n = 6 

    # Adjacency list 
    aList = [[] for i in range(n + 1)]
    
    pre = [0 for i in range(n + 1)]
    post = [0 for i in range(n + 1)]

    # Visited array 
    vis = [0 for i in range(n + 1)]
    
    # Edges 
    aList[1].append(2)
    aList[2].append(1) 
    aList[2].append(4) 
    aList[4].append(2) 
    aList[1].append(3) 
    aList[3].append(1) 
    aList[3].append(4) 
    aList[4].append(3) 
    aList[3].append(5) 
    aList[5].append(3) 
    aList[5].append(6)
    aList[6].append(5) 

    # DFS starting at Node 1 
    dfs(1, aList, pre, post, vis)

    # Number of nodes in graph 
    for i in range(1, n + 1):
        print("Node " + str(i) + 
              " Pre number " + str(pre[i]) + 
              " Post number " + str(post[i]))

# This code is contributed by rutvik_56

using System;
using System.Collections;
using System.Collections.Generic; 

class GFG{
 
// Variable to keep track of time
static int time = 1;

// Function to perform DFS starting from node u
static void dfs(int u, ArrayList aList,
                int []pre, int []post, 
                int []vis)
{
    
    // Storing the pre number whenever
    // the node comes into recursion stack
    pre[u] = time;

    // Increment time
    time++;
    vis[u] = 1;
    
    foreach(int v in (ArrayList)aList[u]) 
    {
        if (vis[v] == 0)
            dfs(v, aList, pre, post, vis);
    }

    // Storing the post number whenever
    // the node goes out of recursion stack
    post[u] = time;
    time++;
}

// Driver code
public static void Main(string []args)
{
    
    // Number of nodes in graph
    int n = 6;

    // Adjacency list
    ArrayList aList = new ArrayList(n + 1);
    
    for(int i = 1; i <= n; i++) 
    {
        ArrayList list = new ArrayList();
        aList.Add(list);
    }
    aList.Add(new ArrayList());
    int []pre = new int[n + 1];
    int []post = new int[n + 1];

    // Visited array
    int []vis = new int[n + 1];

    // Edges
    ((ArrayList)aList[1]).Add(2);
    ((ArrayList)aList[2]).Add(1);
    ((ArrayList)aList[2]).Add(4);
    ((ArrayList)aList[4]).Add(2);
    ((ArrayList)aList[1]).Add(3);
    ((ArrayList)aList[3]).Add(1);
    ((ArrayList)aList[3]).Add(4);
    ((ArrayList)aList[4]).Add(3);
    ((ArrayList)aList[3]).Add(5);
    ((ArrayList)aList[5]).Add(3);
    ((ArrayList)aList[5]).Add(6);
    ((ArrayList)aList[6]).Add(5);

    // DFS starting at Node 1
    dfs(1, aList, pre, post, vis);

    // Number of nodes in graph
    for(int i = 1; i <= n; i++)
        Console.WriteLine("Node " + i + 
                          " Pre number " + pre[i] + 
                          " Post number " + post[i]);
}
}

// This code is contributed by pratham76

JavaScript

<script>
    // Variable to keep track of time
    let time = 1;

    // Function to perform DFS starting
    // from node u
    function dfs(u, aList, pre, post, vis)
    {
    
        // Storing the pre number whenever
        // the node comes into recursion stack
        pre[u] = time;

        // Increment time
        time += 1;

        vis[u] = 1;

        for(let v = 0; v < aList[u].length; v++)
        {
            if (vis[aList[u][v]] == 0)
                dfs(aList[u][v], aList, pre, post, vis);
        }

        // Storing the post number whenever
        // the node goes out of recursion stack
        post[u] = time;
        time += 1;
   }
   
  // Number of nodes in graph
  let n = 6;

  // Adjacency list
  let aList = [];
  for(let i = 0; i < (n + 1); i++)
  {
      aList.push([]);
  }

  let pre = new Array(n+1);
  let post = new Array(n+1);
  pre.fill(0);
  post.fill(0);

  // Visited array
  let vis = new Array(n+1);
  vis.fill(0);

  // Edges
  aList[1].push(2);
  aList[2].push(1);
  aList[2].push(4);
  aList[4].push(2);
  aList[1].push(3);
  aList[3].push(1);
  aList[3].push(4);
  aList[4].push(3);
  aList[3].push(5);
  aList[5].push(3);
  aList[5].push(6);
  aList[6].push(5);

  // DFS starting at Node 1
  dfs(1, aList, pre, post, vis);

  // Number of nodes in graph
  for(let i = 1; i < n + 1; i++)
  {
    document.write("Node " + i +
          " Pre number " + pre[i] +
          " Post number " + post[i] + "</br>")
  }
 
 // This code is contributed by suresh07.
</script>

Output

Node 1 Pre number 1 Post number 12
Node 2 Pre number 2 Post number 11
Node 3 Pre number 4 Post number 9
Node 4 Pre number 3 Post number 10
Node 5 Pre number 5 Post number 8
Node 6 Pre number 6 Post number 7

Time complexity: O(V + E), where V is the number of nodes or vertices and E is the number of edges in the graph.
Auxiliary Space: O(V)

Printing pre and post visited times in DFS of a graph

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