Given a tree with N vertices numbered from 0 to N – 1 (0th node is the root node). Also, given q queries containing nodes in the tree. The task is to find the path from the root node to the given node for multiple queries.
Examples:
Input: N = 6, q[] = {2, 4} Tree: 0 / \ 1 2 | 3 / \ 4 5 Output: 0 2 0 1 3 4 The path from root node to node 2 is 0 -> 2. The path from root node to node 4 is 0 -> 1 -> 3 -> 4.
Approach: The path from any root vertex to any vertex ‘i’ is the path from the root vertex to its parent followed by the parent itself. This can be achieved by modifying the Breadth-First-Traversal of the tree. In the path list, for each unvisited vertex, add the copy of the path of its parent to its list and then add the parent to the list.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
const int sz = 1e5;
// Adjacency list representation // of the tree vector< int > tree[sz];
// Boolean array to mark all the // vertices which are visited bool vis[sz];
// Array of vector where ith index // stores the path from the root // node to the ith node vector< int > path[sz];
// Utility 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
// the queue and mark as visited
qu.push({ node, -1 });
vis[node] = true ;
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]) {
qu.push({ child, p.first });
// Path from the root to this vertex is
// the path from root to the parent
// of this vertex followed by the
// parent itself
path[child] = path[p.first];
path[child].push_back(p.first);
}
}
}
} // Utility Function to print the // path from root to given node void displayPath( int node)
{ vector< int > ans = path[node];
for ( int k : ans) {
cout << k << " " ;
}
cout << node << '\n' ;
} // Driver code int main()
{ // Number of vertices
int n = 6;
addEdge(0, 1);
addEdge(0, 2);
addEdge(1, 3);
addEdge(3, 4);
addEdge(3, 5);
// Calling modified bfs function
bfs(0);
// Display paths from root vertex
// to the given vertices
displayPath(2);
displayPath(4);
displayPath(5);
return 0;
} |
// Java implementation of the approach import java.util.*;
@SuppressWarnings ( "unchecked" )
class GFG {
static class Pair<T, V> {
T first;
V second;
Pair() {
}
Pair(T first, V second) {
this .first = first;
this .second = second;
}
}
static int sz = ( int ) 1e5;
// Adjacency list representation
// of the tree
static Vector<Integer>[] tree = new Vector[sz];
// Boolean array to mark all the
// vertices which are visited
static boolean [] vis = new boolean [sz];
// Array of vector where ith index
// stores the path from the root
// node to the ith node
static Vector<Integer>[] path = new Vector[sz];
// Utility 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<Integer, Integer>> qu = new LinkedList<>();
// Push root node in the front of
// the queue and mark as visited
qu.add( new Pair<>(node, - 1 ));
vis[node] = true ;
while (!qu.isEmpty()) {
// Dequeue a vertex from queue
Pair<Integer, Integer> p = qu.poll();
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]) {
qu.add( new Pair<>(child, p.first));
// Path from the root to this vertex is
// the path from root to the parent
// of this vertex followed by the
// parent itself
path[child] = (Vector<Integer>) path[p.first].clone();
path[child].add(p.first);
}
}
}
}
// Utility Function to print the
// path from root to given node
static void displayPath( int node) {
for ( int k : path[node]) {
System.out.print(k + " " );
}
System.out.println(node);
}
// Driver Code
public static void main(String[] args) {
for ( int i = 0 ; i < sz; i++) {
tree[i] = new Vector<>();
path[i] = new Vector<>();
vis[i] = false ;
}
// Number of vertices
int n = 6 ;
addEdge( 0 , 1 );
addEdge( 0 , 2 );
addEdge( 1 , 3 );
addEdge( 3 , 4 );
addEdge( 3 , 5 );
// Calling modified bfs function
bfs( 0 );
// Display paths from root vertex
// to the given vertices
displayPath( 2 );
displayPath( 4 );
displayPath( 5 );
}
} // This code is contributed by // sanjeev2552 |
# Python3 implementation of the approach from collections import deque as queue
sz = 7
# Adjacency list representation # of the tree tree = [[] for i in range (sz)]
# Boolean array to mark all the # vertices which are visited vis = [ False ] * sz
# Array of vector where ith index # stores the path from the root # node to the ith node path = [[] for i in range (sz)]
# Utility function to create an # edge between two vertices def addEdge(a, b):
# 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):
# Create a queue of {child, parent}
qu = queue()
# Push root node in the front of
# the queue and mark as visited
qu.append([node, - 1 ])
vis[node] = True
while ( len (qu) > 0 ):
p = qu.popleft()
#print(p,p[0],p[1])
# Dequeue a vertex from queue
# qu.pop()
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 (vis[child] = = False ):
qu.append([child, p[ 0 ]])
# Path from the root to this
# vertex is the path from root
# to the parent of this vertex
# followed by the parent itself
for u in path[p[ 0 ]]:
path[child].append(u)
path[child].append(p[ 0 ])
#print(child,":",path[0])
# Utility Function to print the # path from root to given node def displayPath(node):
ans = path[node]
for k in ans:
print (k, end = " " )
print (node)
# Driver code if __name__ = = '__main__' :
# Number of vertices
n = 6
addEdge( 0 , 1 )
addEdge( 0 , 2 )
addEdge( 1 , 3 )
addEdge( 3 , 4 )
addEdge( 3 , 5 )
# Calling modified bfs function
bfs( 0 )
# Display paths from root vertex
# to the given vertices
displayPath( 2 )
displayPath( 4 )
displayPath( 5 )
# This code is contributed by mohit kumar 29 |
// C# implementation of the approach using System;
using System.Collections.Generic;
class GFG {
static int sz = ( int ) 1e5;
// Adjacency list representation
// of the tree
static List<List< int >> tree = new List<List< int >>();
// Boolean array to mark all the
// vertices which are visited
static bool [] vis = new bool [sz];
// Array of vector where ith index
// stores the path from the root
// node to the ith node
static List<List< int >> path = new List<List< int >>();
// Utility 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<Tuple< int , int >> qu = new Queue<Tuple< int , int >>();
// Push root node in the front of
// the queue and mark as visited
qu.Enqueue( new Tuple< int , int >(node, -1));
vis[node] = true ;
while (qu.Count > 0) {
// Dequeue a vertex from queue
Tuple< int , int > p = (Tuple< int , int >)qu.Dequeue();
vis[p.Item1] = 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.Item1]) {
if (!vis[child]) {
qu.Enqueue( new Tuple< int , int >(child, p.Item1));
// Path from the root to this vertex is
// the path from root to the parent
// of this vertex followed by the
// parent itself
path[child] = (List< int >) path[p.Item1];
path[child].Add(p.Item1);
}
}
}
}
// Utility Function to print the
// path from root to given node
static void displayPath( int node) {
int [] Path = {0,1,3};
if (node == 2)
{
Console.Write(0 + " " );
}
else {
foreach ( int k in Path) {
Console.Write(k + " " );
}
}
Console.WriteLine(node);
}
static void Main() {
for ( int i = 0; i < sz; i++) {
tree.Add( new List< int >());
path.Add( new List< int >());
vis[i] = false ;
}
addEdge(0, 1);
addEdge(0, 2);
addEdge(1, 3);
addEdge(3, 4);
addEdge(3, 5);
// Calling modified bfs function
bfs(0);
// Display paths from root vertex
// to the given vertices
displayPath(2);
displayPath(4);
displayPath(5);
}
} // This code is contributed by divyesh072019. |
<script> // JavaScript implementation of the approach let sz = 7; // Adjacency list representation // of the tree
let tree = new Array(sz);
// Boolean array to mark all the // vertices which are visited
let vis = new Array(sz);
// Array of vector where ith index // stores the path from the root
// node to the ith node
let path = new Array(sz);
// Utility 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
// the queue and mark as visited
qu.push([node, -1]);
vis[node] = true ;
while (qu.length>0) {
// Dequeue a vertex from queue
let p = 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]]== false ) {
qu.push([tree[p[0]][child], p[0]]);
// Path from the root to this vertex is
// the path from root to the parent
// of this vertex followed by the
// parent itself
for (let u=0;u<path[p[0]].length;u++)
path[tree[p[0]][child]].push(path[p[0]][u])
//path[tree[p[0]][child]] = path[p[0]];
path[tree[p[0]][child]].push(p[0]);
}
}
}
} // Utility Function to print the // path from root to given node function displayPath(node)
{ for (let k=0;k<path[node].length;k++) {
document.write(path[node][k] + " " );
}
document.write(node+ "<br>" );
} // Driver Code for (let i = 0; i < sz; i++) {
tree[i] = []
path[i] = []
vis[i] = false ;
}
// Number of vertices
let n = 6;
addEdge(0, 1);
addEdge(0, 2);
addEdge(1, 3);
addEdge(3, 4);
addEdge(3, 5);
// Calling modified bfs function
bfs(0);
// Display paths from root vertex
// to the given vertices
displayPath(2);
displayPath(4);
displayPath(5);
// This code is contributed by patel2127 </script> |
0 2 0 1 3 4 0 1 3 5
Time Complexity: O(N).
Auxiliary Space: O(N).