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++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;const int sz = 1e5;// Adjacency list representation// of the treevector<int> tree[sz];// Boolean array to mark all the// vertices which are visitedbool vis[sz];// Array of vector where ith index// stores the path from the root// node to the ith nodevector<int> path[sz];// Utility function to create an// edge between two verticesvoid 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 Functionvoid 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 nodevoid displayPath(int node){ vector<int> ans = path[node]; for (int k : ans) { cout << k << " "; } cout << node << '\n';}// Driver codeint 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
// Java implementation of the approachimport 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
# Python3 implementation of the approachfrom collections import deque as queuesz = 7# Adjacency list representation# of the treetree = [[] for i in range(sz)]# Boolean array to mark all the# vertices which are visitedvis = [False] * sz# Array of vector where ith index# stores the path from the root# node to the ith nodepath = [[] for i in range(sz)]# Utility function to create an# edge between two verticesdef 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 Functiondef 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 nodedef displayPath(node): ans = path[node] for k in ans: print(k, end = " ") print(node)# Driver codeif __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#
// C# implementation of the approachusing 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. |
Javascript
<script>// JavaScript implementation of the approachlet sz = 7;// Adjacency list representation // of the treelet tree = new Array(sz);// Boolean array to mark all the // vertices which are visitedlet vis = new Array(sz);// Array of vector where ith index // stores the path from the root // node to the ith nodelet path = new Array(sz);// Utility function to create an // edge between two verticesfunction 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 Functionfunction 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 nodefunction displayPath(node){ for (let k=0;k<path[node].length;k++) { document.write(path[node][k] + " "); } document.write(node+"<br>");}// Driver Codefor (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> |
Output:
0 2 0 1 3 4 0 1 3 5
Time Complexity: O(N).
Auxiliary Space: O(N).
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