Queries for DFS of a subtree in a tree

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Given a tree of N nodes and N-1 edges. The task is to print the DFS of the subtree of a given node for multiple queries. The DFS must include the given node as the root of the subtree.

In the above tree, if 1 is given as the node, then the DFS of subtree will be 1 2 4 6 7 5 3.
If 2 is given as the node, then the DFS of the subtree will be 2 4 6 7 5..

Approach:

Add the edges between the nodes in an adjacency list.
Call DFS function to generate the DFS of the complete tree.
Use a under[] array to store the height of the subtree under the given node including the node.
In the DFS function, keep incrementing the size of subtree on every recursive call.
Mark the node index in the DFS of complete using hashing.
The DFS of a subtree of a node will always be a contiguous subarray starting from the node(say index ind) to (ind+height of subtree).
Get the index of node which has been stored using hashing and print the nodes from original DFS till index = ind + height of subtree which has been stored in under[node].

Below is the implementation of the above approach.

C++

// C++ program for Queries
// for DFS of subtree of a node in a tree
#include <bits/stdc++.h>
using namespace std;
const int N = 100000;
 
// Adjacency list to store the
// tree nodes connection
vector<int> v[N];
 
// stores the index of node in DFS
unordered_map<int, int> mp;
 
// stores the index of node in
// original node
vector<int> a;
 
// Function to call DFS and count nodes
// under that subtree
void dfs(int under[], int child, int parent)
{
 
    // stores the DFS of tree
    a.push_back(child);
 
    // height of subtree
    under[child] = 1;
 
    // iterate for children
    for (auto it : v[child]) {
 
        // if not equal to parent
        // so that it does not traverse back
        if (it != parent) {
 
            // call DFS for subtree
            dfs(under, it, child);
 
            // add the height
            under[child] += under[it];
        }
    }
}
 
// Function to print the DFS of subtree of node
void printDFSofSubtree(int node, int under[])
{
    // index of node in the original DFS
    int ind = mp[node];
 
    // height of subtree of node
    int height = under[node];
 
    cout << "The DFS of subtree " << node << ": ";
 
    // print the DFS of subtree
    for (int i = ind; i < ind + under[node]; i++) {
        cout << a[i] << " ";
    }
    cout << endl;
}
 
// Function to add edges to a tree
void addEdge(int x, int y)
{
    v[x].push_back(y);
    v[y].push_back(x);
}
 
// Marks the index of node in original DFS
void markIndexDfs()
{
    int size = a.size();
 
    // marks the index
    for (int i = 0; i < size; i++) {
        mp[a[i]] = i;
    }
}
 
// Driver Code
int main()
{
    int n = 7;
 
    // add edges of a tree
    addEdge(1, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);
    addEdge(4, 6);
    addEdge(4, 7);
 
    // array to store the height of subtree
    // of every node in a tree
    int under[n + 1];
 
    // Call the function DFS to generate the DFS
    dfs(under, 1, 0);
 
    // Function call to mark the index of node
    markIndexDfs();
 
    // Query 1
    printDFSofSubtree(2, under);
 
    // Query 1
    printDFSofSubtree(4, under);
 
    return 0;
}

Java

// Java program for queries for DFS
// of subtree of a node in a tree
import java.util.*;
 
class GFG{
     
static int N = 100000;
 
// Adjacency list to store the
// tree nodes connection
@SuppressWarnings("unchecked")
static Vector<Integer> []v = new Vector[N];
 
// Stores the index of node in DFS
static HashMap<Integer,
               Integer> mp = new HashMap<Integer,
                                         Integer>();
 
// Stores the index of node in
// original node
static Vector<Integer> a = new Vector<>();
 
// Function to call DFS and count nodes
// under that subtree
static void dfs(int under[], int child,
                int parent)
{
     
    // Stores the DFS of tree
    a.add(child);
 
    // Height of subtree
    under[child] = 1;
 
    // Iterate for children
    for(int it : v[child])
    {
         
        // If not equal to parent so that
        // it does not traverse back
        if (it != parent) 
        {
             
            // Call DFS for subtree
            dfs(under, it, child);
 
            // Add the height
            under[child] += under[it];
        }
    }
}
 
// Function to print the DFS of subtree of node
static void printDFSofSubtree(int node, int under[])
{
     
    // Index of node in the original DFS
    int ind = mp.get(node);
 
    // Height of subtree of node
    int height = under[node];
 
    System.out.print("The DFS of subtree " +  
                      node + ": ");
 
    // Print the DFS of subtree
    for(int i = ind; i < ind + under[node]; i++)
    {
        System.out.print(a.get(i) + " ");
    }
    System.out.println();
}
 
// Function to add edges to a tree
static void addEdge(int x, int y)
{
    v[x].add(y);
    v[y].add(x);
}
 
// Marks the index of node in original DFS
static void markIndexDfs()
{
    int size = a.size();
 
    // Marks the index
    for(int i = 0; i < size; i++) 
    {
        mp.put(a.get(i), i);
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 7;
     
    for(int i = 0; i < v.length; i++)
        v[i] = new Vector<Integer>();
         
    // Add edges of a tree
    addEdge(1, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);
    addEdge(4, 6);
    addEdge(4, 7);
 
    // Array to store the height of
    // subtree of every node in a tree
    int []under = new int[n + 1];
 
    // Call the function DFS to
    // generate the DFS
    dfs(under, 1, 0);
 
    // Function call to mark the
    // index of node
    markIndexDfs();
 
    // Query 1
    printDFSofSubtree(2, under);
 
    // Query 1
    printDFSofSubtree(4, under);
}
}
 
// This code is contributed by Amit Katiyar

Python3

# Python3 program for Queries 
# for DFS of subtree of a node in a tree 
N = 100000
 
# Adjacency list to store the 
# tree nodes connection 
v = [[]for i in range(N)]
 
# stores the index of node in DFS 
mp = {}
 
# stores the index of node in 
# original node 
a = []
 
# Function to call DFS and count nodes 
# under that subtree 
def dfs(under, child, parent):
     
    # stores the DFS of tree 
    a.append(child) 
     
    # height of subtree 
    under[child] = 1
     
    # iterate for children 
    for it in v[child]:
         
        # if not equal to parent 
        # so that it does not traverse back 
        if (it != parent):
             
            # call DFS for subtree 
            dfs(under, it, child) 
             
            # add the height 
            under[child] += under[it] 
             
# Function to return the DFS of subtree of node 
def printDFSofSubtree(node, under):
     
    # index of node in the original DFS 
    ind = mp[node] 
     
    # height of subtree of node 
    height = under[node]
     
    print("The DFS of subtree", node, ":", end=" ")
     
    # print the DFS of subtree 
    for i in range(ind,ind + under[node]):
        print(a[i], end=" ") 
    print()
     
# Function to add edges to a tree 
def addEdge(x, y):
    v[x].append(y) 
    v[y].append(x) 
 
# Marks the index of node in original DFS 
def markIndexDfs():
     
    size = len(a)
     
    # marks the index 
    for i in range(size):
        mp[a[i]] = i 
     
# Driver Code 
 
n = 7
 
# add edges of a tree 
addEdge(1, 2) 
addEdge(1, 3) 
addEdge(2, 4) 
addEdge(2, 5) 
addEdge(4, 6) 
addEdge(4, 7) 
 
# array to store the height of subtree 
# of every node in a tree 
under = [0]*(n + 1)
 
# Call the function DFS to generate the DFS 
dfs(under, 1, 0) 
 
# Function call to mark the index of node 
markIndexDfs() 
 
# Query 1 
printDFSofSubtree(2, under)
 
# Query 2 
printDFSofSubtree(4, under)
 
# This code is contributed by SHUBHAMSINGH10

C#

// C# program for queries for DFS
// of subtree of a node in a tree
using System;
using System.Collections.Generic;
class GFG{
     
static int N = 100000;
 
// Adjacency list to 
// store the tree nodes 
// connection
static List<int> []v = 
       new List<int>[N];
 
// Stores the index of node in DFS
static Dictionary<int,
                  int> mp = new Dictionary<int,
                                           int>();
 
// Stores the index of node in
// original node
static List<int> a = new List<int>();
 
// Function to call DFS and 
// count nodes under that 
// subtree
static void dfs(int []under, 
                int child,
                int parent)
{    
  // Stores the DFS of tree
  a.Add(child);
 
  // Height of subtree
  under[child] = 1;
 
  // Iterate for children
  foreach(int it in v[child])
  {
    // If not equal to parent 
    // so that it does not 
    // traverse back
    if (it != parent) 
    {
      // Call DFS for subtree
      dfs(under, it, child);
 
      // Add the height
      under[child] += under[it];
    }
  }
}
 
// Function to print the DFS of 
// subtree of node
static void printDFSofSubtree(int node,
                              int []under)
{    
  // Index of node in the 
  // original DFS
  int ind = mp[node];
 
  // Height of subtree of node
  int height = under[node];
 
  Console.Write("The DFS of subtree " +  
                 node + ": ");
 
  // Print the DFS of subtree
  for(int i = ind; 
          i < ind + under[node]; i++)
  {
    Console.Write(a[i] + " ");
  }
  Console.WriteLine();
}
 
// Function to add edges
// to a tree
static void addEdge(int x, 
                    int y)
{
  v[x].Add(y);
  v[y].Add(x);
}
 
// Marks the index of node 
// in original DFS
static void markIndexDfs()
{
  int size = a.Count;
 
  // Marks the index
  for(int i = 0; i < size; i++) 
  {
    mp.Add(a[i], i);
  }
}
 
// Driver Code
public static void Main(String[] args)
{
  int n = 7;
 
  for(int i = 0; i < v.Length; i++)
    v[i] = new List<int>();
 
  // Add edges of a tree
  addEdge(1, 2);
  addEdge(1, 3);
  addEdge(2, 4);
  addEdge(2, 5);
  addEdge(4, 6);
  addEdge(4, 7);
 
  // Array to store the height 
  // of subtree of every node 
  // in a tree
  int []under = new int[n + 1];
 
  // Call the function DFS to
  // generate the DFS
  dfs(under, 1, 0);
 
  // Function call to mark the
  // index of node
  markIndexDfs();
 
  // Query 1
  printDFSofSubtree(2, under);
 
  // Query 1
  printDFSofSubtree(4, under);
}
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
 
// Javascript program for queries for DFS
// of subtree of a node in a tree
var N = 100000;
 
// Adjacency list to 
// store the tree nodes 
// connection
var v = Array.from(Array(N), () => Array());
 
// Stores the index of node in DFS
var mp = new Map();
 
// Stores the index of node in
// original node
var a = [];
 
// Function to call DFS and 
// count nodes under that 
// subtree
function dfs(under, child, parent)
{ 
     
    // Stores the DFS of tree
    a.push(child);
     
    // Height of subtree
    under[child] = 1;
     
    // Iterate for children
    for(var it of v[child])
    {
         
        // If not equal to parent 
        // so that it does not 
        // traverse back
        if (it != parent) 
        {
             
            // Call DFS for subtree
            dfs(under, it, child);
             
            // push the height
            under[child] += under[it];
        }
    }
}
 
// Function to print the DFS of 
// subtree of node
function printDFSofSubtree(node, under)
{ 
     
    // Index of node in the 
    // original DFS
    var ind = mp.get(node);
     
    // Height of subtree of node
    var height = under[node];
     
    document.write("The DFS of subtree " +  
                   node + ": ");
     
    // Print the DFS of subtree
    for(var i = ind; 
            i < ind + under[node]; i++)
    {
        document.write(a[i] + " ");
    }
    document.write("<br>");
}
 
// Function to add edges
// to a tree
function addEdge(x, y)
{
    v[x].push(y);
    v[y].push(x);
}
 
// Marks the index of node 
// in original DFS
function markIndexDfs()
{
    var size = a.length;
     
    // Marks the index
    for(var i = 0; i < size; i++) 
    {
        mp.set(a[i], i);
    }
}
 
// Driver Code
var n = 7;
for(var i = 0; i < v.length; i++)
    v[i] = Array();
     
// push edges of a tree
addEdge(1, 2);
addEdge(1, 3);
addEdge(2, 4);
addEdge(2, 5);
addEdge(4, 6);
addEdge(4, 7);
 
// Array to store the height 
// of subtree of every node 
// in a tree
var under = Array(n + 1);
 
// Call the function DFS to
// generate the DFS
dfs(under, 1, 0);
 
// Function call to mark the
// index of node
markIndexDfs();
 
// Query 1
printDFSofSubtree(2, under);
 
// Query 1
printDFSofSubtree(4, under);
 
// This code is contributed by rutvik_56
 
</script>

Output:

The DFS of subtree 2: 2 4 6 7 5 
The DFS of subtree 4: 4 6 7

Time Complexity: O( N + M ), where N is the number of nodes and M is the number of edges for pre-calculation, and O(N) for queries in the worst case.
Auxiliary Space: O(N)

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