# Farthest distance of a Node from each Node of a Tree

Given a Tree, the task is to find the farthest node from each node to another node in the given tree.
Examples

Input:

Output: 2 3 3 3 4 4 4
Explanation:
Maximum Distance from Node 1 : 2 (Nodes {5, 6, 7} are at a distance 2)
Maximum Distance from Node 2 : 3 (Nodes {6, 7} are at a distance 3)
Maximum Distance from Node 3 : 3 (Nodes {5, 6, 7} are at a distance 3)
Maximum Distance from Node 4 : 3 (Node {5} is at a distance 3)
Maximum Distance from Node 5 : 4 (Nodes {6, 7} are at a distance 4)
Maximum Distance from Node 6 : 4 (Node {5} is at a distance 4)
Maximum Distance from Node 7 : 4 (Node {5} is at a distance 4)
Input:

Output : 3 2 3 3 2 3

Approach:
Follow the steps below to solve the problem:

• Calculate the height of each node of the tree (Assuming the leaf nodes are at height 1) using DFS
• This gives the maximum distance from a Node to all Nodes present in its Subtree.. Store these heights.
• Now, perform DFS to calculate the maximum distance of a Node from all its ancestors. Store these distances.
• For each node, print the maximum of the two distances calculated.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement ` `// the above approach ` `#include ` `using` `namespace` `std; ` ` `  `#define maxN 100001 ` ` `  `// Adjacency List to store the graph ` `vector<``int``> adj[maxN]; ` ` `  `// Stores the height of each node ` `int` `height[maxN]; ` ` `  `// Stores the maximum distance of a ` `// node from its ancestors ` `int` `dist[maxN]; ` ` `  `// Function to add edge between ` `// two vertices ` `void` `addEdge(``int` `u, ``int` `v) ` `{ ` `    ``// Insert edge from u to v ` `    ``adj[u].push_back(v); ` ` `  `    ``// Insert edge from v to u ` `    ``adj[v].push_back(u); ` `} ` ` `  `// Function to calculate height of ` `// each Node ` `void` `dfs1(``int` `cur, ``int` `par) ` `{ ` `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``for` `(``auto` `u : adj[cur]) { ` ` `  `        ``if` `(u != par) { ` ` `  `            ``// Dfs for child node ` `            ``dfs1(u, cur); ` ` `  `            ``// Calculate height of nodes ` `            ``height[cur] ` `                ``= max(height[cur], height[u]); ` `        ``} ` `    ``} ` ` `  `    ``// Increase height ` `    ``height[cur] += 1; ` `} ` ` `  `// Function to calculate the maximum ` `// distance of a node from its ancestor ` `void` `dfs2(``int` `cur, ``int` `par) ` `{ ` `    ``int` `max1 = 0; ` `    ``int` `max2 = 0; ` ` `  `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``for` `(``auto` `u : adj[cur]) { ` ` `  `        ``if` `(u != par) { ` ` `  `            ``// Find two children ` `            ``// with maximum heights ` `            ``if` `(height[u] >= max1) { ` `                ``max2 = max1; ` `                ``max1 = height[u]; ` `            ``} ` `            ``else` `if` `(height[u] > max2) { ` `                ``max2 = height[u]; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``int` `sum = 0; ` ` `  `    ``for` `(``auto` `u : adj[cur]) { ` `        ``if` `(u != par) { ` ` `  `            ``// Calculate the maximum distance ` `            ``// with ancestor for every node ` `            ``sum = ((max1 == height[u]) ? max2 : max1); ` ` `  `            ``if` `(max1 == height[u]) ` `                ``dist[u] ` `                    ``= 1 + max(1 + max2, dist[cur]); ` `            ``else` `                ``dist[u] ` `                    ``= 1 + max(1 + max1, dist[cur]); ` ` `  `            ``// Calculating for children ` `            ``dfs2(u, cur); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 6; ` ` `  `    ``addEdge(1, 2); ` `    ``addEdge(2, 3); ` `    ``addEdge(2, 4); ` `    ``addEdge(2, 5); ` `    ``addEdge(5, 6); ` ` `  `    ``// Calculate height of ` `    ``// nodes of the tree ` `    ``dfs1(1, 0); ` ` `  `    ``// Calculate the maximum ` `    ``// distance with ancestors ` `    ``dfs2(1, 0); ` ` `  `    ``// Print the maximum of the two ` `    ``// distances from each node ` `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``cout << (max(dist[i], height[i]) - 1) << ``" "``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to implement ` `// the above approach ` `import` `java.util.*; ` ` `  `class` `GFG{ ` ` `  `static` `final` `int` `maxN = ``100001``; ` ` `  `// Adjacency List to store the graph ` `@SuppressWarnings``(``"unchecked"``) ` `static` `Vector []adj = ``new` `Vector[maxN]; ` ` `  `// Stores the height of each node ` `static` `int` `[]height = ``new` `int``[maxN]; ` ` `  `// Stores the maximum distance of a ` `// node from its ancestors ` `static` `int` `[]dist = ``new` `int``[maxN]; ` ` `  `// Function to add edge between ` `// two vertices ` `static` `void` `addEdge(``int` `u, ``int` `v) ` `{ ` `     `  `    ``// Insert edge from u to v ` `    ``adj[u].add(v); ` ` `  `    ``// Insert edge from v to u ` `    ``adj[v].add(u); ` `} ` ` `  `// Function to calculate height of ` `// each Node ` `static` `void` `dfs1(``int` `cur, ``int` `par) ` `{ ` `     `  `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``for``(``int` `u : adj[cur])  ` `    ``{ ` `        ``if` `(u != par) ` `        ``{ ` `             `  `            ``// Dfs for child node ` `            ``dfs1(u, cur); ` ` `  `            ``// Calculate height of nodes ` `            ``height[cur] = Math.max(height[cur], ` `                                   ``height[u]); ` `        ``} ` `    ``} ` ` `  `    ``// Increase height ` `    ``height[cur] += ``1``; ` `} ` ` `  `// Function to calculate the maximum ` `// distance of a node from its ancestor ` `static` `void` `dfs2(``int` `cur, ``int` `par) ` `{ ` `    ``int` `max1 = ``0``; ` `    ``int` `max2 = ``0``; ` ` `  `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``for``(``int` `u : adj[cur]) ` `    ``{ ` `        ``if` `(u != par) ` `        ``{ ` `             `  `            ``// Find two children ` `            ``// with maximum heights ` `            ``if` `(height[u] >= max1) ` `            ``{ ` `                ``max2 = max1; ` `                ``max1 = height[u]; ` `            ``} ` `            ``else` `if` `(height[u] > max2)  ` `            ``{ ` `                ``max2 = height[u]; ` `            ``} ` `        ``} ` `    ``} ` `    ``int` `sum = ``0``; ` ` `  `    ``for``(``int` `u : adj[cur]) ` `    ``{ ` `        ``if` `(u != par)  ` `        ``{ ` `             `  `            ``// Calculate the maximum distance ` `            ``// with ancestor for every node ` `            ``sum = ((max1 == height[u]) ?  ` `                    ``max2 : max1); ` ` `  `            ``if` `(max1 == height[u]) ` `                ``dist[u] = ``1` `+ Math.max(``1` `+ max2,  ` `                                       ``dist[cur]); ` `            ``else` `                ``dist[u] = ``1` `+ Math.max(``1` `+ max1, ` `                                       ``dist[cur]); ` ` `  `            ``// Calculating for children ` `            ``dfs2(u, cur); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``6``; ` `    ``for``(``int` `i = ``0``; i < adj.length; i++) ` `        ``adj[i] = ``new` `Vector(); ` `         `  `    ``addEdge(``1``, ``2``); ` `    ``addEdge(``2``, ``3``); ` `    ``addEdge(``2``, ``4``); ` `    ``addEdge(``2``, ``5``); ` `    ``addEdge(``5``, ``6``); ` ` `  `    ``// Calculate height of ` `    ``// nodes of the tree ` `    ``dfs1(``1``, ``0``); ` ` `  `    ``// Calculate the maximum ` `    ``// distance with ancestors ` `    ``dfs2(``1``, ``0``); ` ` `  `    ``// Print the maximum of the two ` `    ``// distances from each node ` `    ``for``(``int` `i = ``1``; i <= n; i++) ` `        ``System.out.print((Math.max(dist[i],  ` `                                 ``height[i]) - ``1``) + ``" "``); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## C#

 `// C# program to implement ` `// the above approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` ` `  `static` `readonly` `int` `maxN = 100001; ` ` `  `// Adjacency List to store the graph ` `static` `List<``int``> []adj = ``new` `List<``int``>[maxN]; ` ` `  `// Stores the height of each node ` `static` `int` `[]height = ``new` `int``[maxN]; ` ` `  `// Stores the maximum distance of a ` `// node from its ancestors ` `static` `int` `[]dist = ``new` `int``[maxN]; ` ` `  `// Function to add edge between ` `// two vertices ` `static` `void` `addEdge(``int` `u, ``int` `v) ` `{ ` `     `  `    ``// Insert edge from u to v ` `    ``adj[u].Add(v); ` ` `  `    ``// Insert edge from v to u ` `    ``adj[v].Add(u); ` `} ` ` `  `// Function to calculate height of ` `// each Node ` `static` `void` `dfs1(``int` `cur, ``int` `par) ` `{ ` `     `  `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``foreach``(``int` `u ``in` `adj[cur])  ` `    ``{ ` `        ``if` `(u != par) ` `        ``{ ` `             `  `            ``// Dfs for child node ` `            ``dfs1(u, cur); ` ` `  `            ``// Calculate height of nodes ` `            ``height[cur] = Math.Max(height[cur], ` `                                   ``height[u]); ` `        ``} ` `    ``} ` ` `  `    ``// Increase height ` `    ``height[cur] += 1; ` `} ` ` `  `// Function to calculate the maximum ` `// distance of a node from its ancestor ` `static` `void` `dfs2(``int` `cur, ``int` `par) ` `{ ` `    ``int` `max1 = 0; ` `    ``int` `max2 = 0; ` ` `  `    ``// Iterate in the adjacency ` `    ``// list of the current node ` `    ``foreach``(``int` `u ``in` `adj[cur]) ` `    ``{ ` `        ``if` `(u != par) ` `        ``{ ` `             `  `            ``// Find two children ` `            ``// with maximum heights ` `            ``if` `(height[u] >= max1) ` `            ``{ ` `                ``max2 = max1; ` `                ``max1 = height[u]; ` `            ``} ` `            ``else` `if` `(height[u] > max2)  ` `            ``{ ` `                ``max2 = height[u]; ` `            ``} ` `        ``} ` `    ``} ` `    ``int` `sum = 0; ` ` `  `    ``foreach``(``int` `u ``in` `adj[cur]) ` `    ``{ ` `        ``if` `(u != par)  ` `        ``{ ` `             `  `            ``// Calculate the maximum distance ` `            ``// with ancestor for every node ` `            ``sum = ((max1 == height[u]) ?  ` `                    ``max2 : max1); ` ` `  `            ``if` `(max1 == height[u]) ` `                ``dist[u] = 1 + Math.Max(1 + max2,  ` `                                       ``dist[cur]); ` `            ``else` `                ``dist[u] = 1 + Math.Max(1 + max1, ` `                                       ``dist[cur]); ` ` `  `            ``// Calculating for children ` `            ``dfs2(u, cur); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `n = 6; ` `    ``for``(``int` `i = 0; i < adj.Length; i++) ` `        ``adj[i] = ``new` `List<``int``>(); ` `         `  `    ``addEdge(1, 2); ` `    ``addEdge(2, 3); ` `    ``addEdge(2, 4); ` `    ``addEdge(2, 5); ` `    ``addEdge(5, 6); ` ` `  `    ``// Calculate height of ` `    ``// nodes of the tree ` `    ``dfs1(1, 0); ` ` `  `    ``// Calculate the maximum ` `    ``// distance with ancestors ` `    ``dfs2(1, 0); ` ` `  `    ``// Print the maximum of the two ` `    ``// distances from each node ` `    ``for``(``int` `i = 1; i <= n; i++) ` `        ``Console.Write((Math.Max(dist[i],  ` `                                ``height[i]) - 1) + ``" "``); ` `} ` `} ` ` `  `// This code is contributed by Rohit_ranjan  `

Output:

```3 2 3 3 2 3
```

Time Complexity: O(V+E)
Auxiliary Space: O(N)

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