Find distance of nodes from root in a tree for multiple queries

Last Updated : 08 Mar, 2023

Given a tree with N vertices numbered from 0 to N – 1 and Q queries containing nodes in the tree, the task is to find the distance of given node from root node for multiple queries. Consider 0th node as the root node and take the distance of the root node from itself as 0.
Examples:

Tree:
      0
     /  \
    1    2
    |   / \
    3  4   5
Input: 2
Output: 1
Explanation:
Distance of node 2 from root is 1

Input: 3
Output: 2
Explanation:
Distance of node 3 from root is 2

Approach:
Start by assigning the distance of the root node as 0. Then, traverse the tree using Breadth First Traversal(BFS). When marking the children of the node N as visited, also assign the distance of these children as the distance[N] + 1. Finally, for different queries, the value of the distance array of the node is printed.
Below is the implementation of above approach:

C++

// C++ implementation for
// the above approach
#include <bits/stdc++.h>
using namespace std;

const int sz = 1e5;

// Adjacency list representation
// of the tree
vector<int> tree[sz + 1];

// Boolean array to mark all the
// vertices which are visited
bool vis[sz + 1];

// Array of vector where ith index
// stores the path from the root
// node to the ith node
int dis[sz + 1];

// Function to create an
// edge between two vertices
void addEdge(int a, int b)
{
    // Add a to b's list
    tree[a].push_back(b);

    // Add b to a's list
    tree[b].push_back(a);
}

// Modified Breadth-First Function
void bfs(int node)
{
    // Create a queue of {child, parent}
    queue<pair<int, int> > qu;

    // Push root node in the front of
    qu.push({ node, 0 });
    dis[0] = 0;

    while (!qu.empty()) {
        pair<int, int> p = qu.front();

        // Dequeue a vertex from queue
        qu.pop();
        vis[p.first] = true;

        // Get all adjacent vertices of the dequeued
        // vertex s. If any adjacent has not
        // been visited then enqueue it
        for (int child : tree[p.first]) {
            if (!vis[child]) {
                dis[child] = dis[p.first] + 1;
                qu.push({ child, p.first });
            }
        }
    }
}

// Driver code
int main()
{
    // Number of vertices
    int n = 6;

    addEdge(0, 1);
    addEdge(0, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);

    // Calling modified bfs function
    bfs(0);

    int q[] = { 2, 4 };

    for (int i = 0; i < 2; i++) {
        cout << dis[q[i]] << '\n';
    }

    return 0;
}

Java

// Java implementation for
// the above approach
import java.util.*;

class GFG
{
static int sz = (int) 1e5;

// Adjacency list representation
// of the tree
static Vector<Integer> []tree = new Vector[sz + 1];

// Boolean array to mark all the
// vertices which are visited
static boolean []vis = new boolean[sz + 1];

// Array of vector where ith index
// stores the path from the root
// node to the ith node
static int []dis = new int[sz + 1];

static class pair
{ 
    int first, second; 
    public pair(int first, int second) 
    { 
        this.first = first; 
        this.second = second; 
    } 
}

// Function to create an
// edge between two vertices
static void addEdge(int a, int b)
{

    // Add a to b's list
    tree[a].add(b);

    // Add b to a's list
    tree[b].add(a);
}

// Modified Breadth-First Function
static void bfs(int node)
{
    // Create a queue of {child, parent}
    Queue<pair> qu = new LinkedList<>();

    // Push root node in the front of
    qu.add(new pair(node, 0 ));
    dis[0] = 0;

    while (!qu.isEmpty()) 
    {
        pair p = qu.peek();

        // Dequeue a vertex from queue
        qu.remove();
        vis[p.first] = true;

        // Get all adjacent vertices of the dequeued
        // vertex s. If any adjacent has not
        // been visited then enqueue it
        for (int child : tree[p.first])
        {
            if (!vis[child]) 
            {
                dis[child] = dis[p.first] + 1;
                qu.add(new pair(child, p.first));
            }
        }
    }
}

// Driver code
public static void main(String[] args)
{
    
    // Number of vertices
    int n = 6;
    for (int i = 0; i < sz + 1; i++) 
        tree[i] = new Vector<Integer>();
        
    addEdge(0, 1);
    addEdge(0, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);

    // Calling modified bfs function
    bfs(0);

    int q[] = { 2, 3 };

    for (int i = 0; i < 2; i++) 
    {
        System.out.println(dis[q[i]]);
    }
}
}

// This code is contributed by 29AjayKumar

Python3

# Python implementation for
# the above approach

from collections import deque

sz = int(1e5)

# Adjacency list representation
# of the tree
tree = [0] * (sz + 1)
for i in range(sz + 1):
    tree[i] = []

# Boolean array to mark all the
# vertices which are visited
vis = [False] * (sz + 1)

# Array of vector where ith index
# stores the path from the root
# node to the ith node
dis = [0] * sz

# Function to create an
# edge between two vertices
def addEdge(a: int, b: int):
    global tree

    # Add a to b's list
    tree[a].append(b)

    # Add b to a's list
    tree[b].append(a)

# Modified Breadth-First Function
def bfs(node: int):
    global dis, vis

    # Create a queue of {child, parent}
    qu = deque()

    # Push root node in the front of
    qu.append((node, 0))
    dis[0] = 0

    while qu:
        p = qu[0]

        # Dequeue a vertex from queue
        qu.popleft()
        vis[p[0]] = True

        # Get all adjacent vertices of the dequeued
        # vertex s. If any adjacent has not
        # been visited then enqueue it
        for child in tree[p[0]]:
            if not vis[child]:
                dis[child] = dis[p[0]] + 1
                qu.append((child, p[0]))

# Driver Code
if __name__ == "__main__":

    # Number of vertices
    n = 6

    addEdge(0, 1)
    addEdge(0, 2)
    addEdge(1, 3)
    addEdge(2, 4)
    addEdge(2, 5)

    # Calling modified bfs function
    bfs(0)

    q = [2, 4]

    for i in range(2):
        print(dis[q[i]])

# This code is contributed by
# sanjeev2552

// C# implementation for
// the above approach
using System;
using System.Collections.Generic;
    
class GFG
{
static int sz = (int) 1e5;

// Adjacency list representation
// of the tree
static List<int> []tree = new List<int>[sz + 1];

// Boolean array to mark all the
// vertices which are visited
static Boolean []vis = new Boolean[sz + 1];

// Array of vector where ith index
// stores the path from the root
// node to the ith node
static int []dis = new int[sz + 1];

public class pair
{ 
    public int first, second; 
    public pair(int first, int second) 
    { 
        this.first = first; 
        this.second = second; 
    } 
}

// Function to create an
// edge between two vertices
static void addEdge(int a, int b)
{

    // Add a to b's list
    tree[a].Add(b);

    // Add b to a's list
    tree[b].Add(a);
}

// Modified Breadth-First Function
static void bfs(int node)
{
    // Create a queue of {child, parent}
    Queue<pair> qu = new Queue<pair>();

    // Push root node in the front of
    qu.Enqueue(new pair(node, 0 ));
    dis[0] = 0;

    while (qu.Count != 0) 
    {
        pair p = qu.Peek();

        // Dequeue a vertex from queue
        qu.Dequeue();
        vis[p.first] = true;

        // Get all adjacent vertices of the dequeued
        // vertex s. If any adjacent has not
        // been visited then enqueue it
        foreach (int child in tree[p.first])
        {
            if (!vis[child]) 
            {
                dis[child] = dis[p.first] + 1;
                qu.Enqueue(new pair(child, p.first));
            }
        }
    }
}

// Driver code
public static void Main(String[] args)
{
    
    // Number of vertices
    for (int i = 0; i < sz + 1; i++) 
        tree[i] = new List<int>();
        
    addEdge(0, 1);
    addEdge(0, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);

    // Calling modified bfs function
    bfs(0);

    int []q = { 2, 3 };

    for (int i = 0; i < 2; i++) 
    {
        Console.WriteLine(dis[q[i]]);
    }
}
}

// This code is contributed by Rajput-Ji

JavaScript

<script>
    
    // JavaScript implementation for the above approach
    
    let sz = 1e5;
  
    // Adjacency list representation
    // of the tree
    let tree = new Array(sz + 1);

    // Boolean array to mark all the
    // vertices which are visited
    let vis = new Array(sz + 1);

    // Array of vector where ith index
    // stores the path from the root
    // node to the ith node
    let dis = new Array(sz + 1);

    // Function to create an
    // edge between two vertices
    function addEdge(a, b)
    {

        // Add a to b's list
        tree[a].push(b);

        // Add b to a's list
        tree[b].push(a);
    }

    // Modified Breadth-First Function
    function bfs(node)
    {
        // Create a queue of {child, parent}
        let qu = [];

        // Push root node in the front of
        qu.push([node, 0]);
        dis[0] = 0;

        while (qu.length > 0) 
        {
            let p = qu[0];

            // Dequeue a vertex from queue
            qu.shift();
            vis[p[0]] = true;

            // Get all adjacent vertices of the dequeued
            // vertex s. If any adjacent has not
            // been visited then enqueue it
            for (let child = 0; child < tree[p[0]].length; child++)
            {
                if (!vis[tree[p[0]][child]]) 
                {
                    dis[tree[p[0]][child]] = dis[p[0]] + 1;
                    qu.push([tree[p[0]][child], p[0]]);
                }
            }
        }
    }
    
    // Number of vertices
    let n = 6;
    for (let i = 0; i < sz + 1; i++) 
        tree[i] = [];
          
    addEdge(0, 1);
    addEdge(0, 2);
    addEdge(1, 3);
    addEdge(2, 4);
    addEdge(2, 5);
  
    // Calling modified bfs function
    bfs(0);
  
    let q = [ 2, 3 ];
  
    for (let i = 0; i < 2; i++) 
    {
        document.write(dis[q[i]] + "</br>");
    }

</script>

Output:

1
2

Time Complexity: O(n+m) where n is the number of vertices and m is the number of edges in the tree.
Space Complexity: O(n)

Find the path from root to the given nodes of a tree for multiple queries

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Find distance of nodes from root in a tree for multiple queries

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