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

Given a tree with **N** vertices numbered from **0** to **N – 1** (0^{th} 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 5Output: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; ` `} ` |

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**Output:**

0 2 0 1 3 4 0 1 3 5

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