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

Given a tree with N vertices numbered from 0 to N â€“ 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 ` `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 > 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 []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 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();` `        `  `    ``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#

 `// 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 qu = ``new` `Queue();`   `    ``// 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

 ``

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)

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