# Find the node whose absolute difference with X gives minimum value

Given a tree, and the weights of all the nodes and an integer x, the task is to find a node i such that |weight[i] – x| is minimum.

Examples:

Input:

x = 15
Output: 3
Node 1: |5 – 15| = 10
Node 2: |10 – 15| = 5
Node 3: |11 -15| = 4
Node 4: |8 – 15| = 7
Node 5: |6 -15| = 9

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Perform dfs on the tree and keep track of the node whose weighted absolute difference with x gives the minimum value.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `int` `minimum = INT_MAX, x, ans; ` ` `  `vector<``int``> graph[100]; ` `vector<``int``> weight(100); ` ` `  `// Function to perform dfs to find ` `// the minimum value ` `void` `dfs(``int` `node, ``int` `parent) ` `{ ` `    ``// If current value is less than ` `    ``// the current minimum ` `    ``if` `(minimum > ``abs``(weight[node] - x)) { ` `        ``minimum = ``abs``(weight[node] - x); ` `        ``ans = node; ` `    ``} ` `    ``for` `(``int` `to : graph[node]) { ` `        ``if` `(to == parent) ` `            ``continue``; ` `        ``dfs(to, node); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``x = 15; ` ` `  `    ``// Weights of the node ` `    ``weight[1] = 5; ` `    ``weight[2] = 10; ` `    ``weight[3] = 11; ` `    ``weight[4] = 8; ` `    ``weight[5] = 6; ` ` `  `    ``// Edges of the tree ` `    ``graph[1].push_back(2); ` `    ``graph[2].push_back(3); ` `    ``graph[2].push_back(4); ` `    ``graph[1].push_back(5); ` ` `  `    ``dfs(1, 1); ` ` `  `    ``cout << ans; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` `import` `java.lang.*; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``static` `int` `minimum = Integer.MAX_VALUE, x, ans; ` ` `  `    ``@SuppressWarnings``(``"unchecked"``) ` `    ``static` `Vector[] graph = ``new` `Vector[``100``]; ` `    ``static` `int``[] weight = ``new` `int``[``100``]; ` ` `  `    ``// This block is executed even before main() function ` `    ``// This is necessary otherwise this program will ` `    ``// throw "NullPointerException" ` `    ``static` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < ``100``; i++) ` `            ``graph[i] = ``new` `Vector<>(); ` `    ``} ` ` `  `    ``// Function to perform dfs to find ` `    ``// the minimum xored value ` `    ``static` `void` `dfs(``int` `node, ``int` `parent)  ` `    ``{ ` ` `  `        ``// If current value is less than ` `        ``// the current minimum ` `        ``if` `(minimum > Math.abs(weight[node] - x))  ` `        ``{ ` `            ``minimum = Math.abs(weight[node] - x); ` `            ``ans = node; ` `        ``} ` `        ``for` `(``int` `to : graph[node])  ` `        ``{ ` `            ``if` `(to == parent) ` `                ``continue``; ` `            ``dfs(to, node); ` `        ``} ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``x = ``15``; ` ` `  `        ``// Weights of the node ` `        ``weight[``1``] = ``5``; ` `        ``weight[``2``] = ``10``; ` `        ``weight[``3``] = ``11``; ` `        ``weight[``4``] = ``8``; ` `        ``weight[``5``] = ``6``; ` ` `  `        ``// Edges of the tree ` `        ``graph[``1``].add(``2``); ` `        ``graph[``2``].add(``3``); ` `        ``graph[``2``].add(``4``); ` `        ``graph[``1``].add(``5``); ` ` `  `        ``dfs(``1``, ``1``); ` ` `  `        ``System.out.println(ans); ` `    ``} ` `} ` ` `  `// This code is contributed by SHUBHAMSINGH10 `

## Python3

 `# Python3 implementation of the approach ` `from` `sys ``import` `maxsize ` ` `  `# Function to perform dfs to find ` `# the minimum value ` `def` `dfs(node, parent): ` `    ``global` `minimum, graph, weight, x, ans ` ` `  `    ``# If current value is less than ` `    ``# the current minimum ` `    ``if` `minimum > ``abs``(weight[node] ``-` `x): ` `        ``minimum ``=` `abs``(weight[node] ``-` `x) ` `        ``ans ``=` `node ` ` `  `    ``for` `to ``in` `graph[node]: ` `        ``if` `to ``=``=` `parent: ` `            ``continue` `        ``dfs(to, node) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``minimum ``=` `maxsize ` `    ``graph ``=` `[[] ``for` `i ``in` `range``(``100``)] ` `    ``weight ``=` `[``0``] ``*` `100` `    ``x ``=` `15` `    ``ans ``=` `0` ` `  `    ``# Weights of the node ` `    ``weight[``1``] ``=` `5` `    ``weight[``2``] ``=` `10` `    ``weight[``3``] ``=` `11` `    ``weight[``4``] ``=` `8` `    ``weight[``5``] ``=` `6` ` `  `    ``# Edges of the tree ` `    ``graph[``1``].append(``2``) ` `    ``graph[``2``].append(``3``) ` `    ``graph[``2``].append(``4``) ` `    ``graph[``1``].append(``5``) ` ` `  `    ``dfs(``1``, ``1``) ` ` `  `    ``print``(ans) ` ` `  `# This code is contributed by ` `# sanjeev2552 `

Output:

```3
```

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.