# Find the node whose absolute difference with X gives maximum 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 maximum.

Examples:

Input:

x = 15
Output: 1
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 maximum value.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `int` `maximum = INT_MIN, x, ans; ` ` `  `vector<``int``> graph[100]; ` `vector<``int``> weight(100); ` ` `  `// Function to perform dfs to find ` `// the maximum value ` `void` `dfs(``int` `node, ``int` `parent) ` `{ ` `    ``// If current value is more than ` `    ``// the current maximum ` `    ``if` `(maximum < ``abs``(weight[node] - x)) { ` `        ``maximum = ``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.*; ` ` `  `class` `GFG ` `{ ` ` `  `static` `int` `maximum = Integer.MIN_VALUE, x, ans;  ` ` `  `static` `Vector> graph=``new` `Vector>();  ` `static` `Vector weight=``new` `Vector();  ` ` `  `// Function to perform dfs to find  ` `// the maximum value  ` `static` `void` `dfs(``int` `node, ``int` `parent)  ` `{  ` `    ``// If current value is more than  ` `    ``// the current maximum  ` `    ``if` `(maximum < Math.abs(weight.get(node) - x))  ` `    ``{  ` `        ``maximum = Math.abs(weight.get(node) - x);  ` `        ``ans = node;  ` `    ``}  ` `    ``for` `(``int` `i = ``0``; i < graph.get(node).size(); i++)  ` `    ``{  ` `        ``if` `(graph.get(node).get(i) == parent)  ` `            ``continue``;  ` `        ``dfs(graph.get(node).get(i), node);  ` `    ``}  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``x = ``15``;  ` ` `  `    ``// Weights of the node  ` `    ``weight.add(``0``);  ` `    ``weight.add(``5``);  ` `    ``weight.add(``10``);;  ` `    ``weight.add(``11``);;  ` `    ``weight.add(``8``);  ` `    ``weight.add(``6``);  ` `     `  `    ``for``(``int` `i = ``0``; i < ``100``; i++) ` `    ``graph.add(``new` `Vector()); ` ` `  `    ``// Edges of the tree  ` `    ``graph.get(``1``).add(``2``);  ` `    ``graph.get(``2``).add(``3``);  ` `    ``graph.get(``2``).add(``4``);  ` `    ``graph.get(``1``).add(``5``);  ` ` `  `    ``dfs(``1``, ``1``);  ` ` `  `    ``System.out.println( ans);  ` `} ` `}  ` ` `  `// This code is contributed by Arnab Kundu `

## Python3

 `# Python 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 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` `     `  `class` `GFG ` `{ ` ` `  `static` `int` `maximum = ``int``.MinValue, x, ans;  ` ` `  `static` `List> graph = ``new` `List>();  ` `static` `List<``int``> weight = ``new` `List<``int``>();  ` ` `  `// Function to perform dfs to find  ` `// the maximum value  ` `static` `void` `dfs(``int` `node, ``int` `parent)  ` `{  ` `    ``// If current value is more than  ` `    ``// the current maximum  ` `    ``if` `(maximum < Math.Abs(weight[node] - x))  ` `    ``{  ` `        ``maximum = Math.Abs(weight[node] - x);  ` `        ``ans = node;  ` `    ``}  ` `    ``for` `(``int` `i = 0; i < graph[node].Count; i++)  ` `    ``{  ` `        ``if` `(graph[node][i] == parent)  ` `            ``continue``;  ` `        ``dfs(graph[node][i], node);  ` `    ``}  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(String []args) ` `{  ` `    ``x = 15;  ` ` `  `    ``// Weights of the node  ` `    ``weight.Add(0);  ` `    ``weight.Add(5);  ` `    ``weight.Add(10);;  ` `    ``weight.Add(11);;  ` `    ``weight.Add(8);  ` `    ``weight.Add(6);  ` `     `  `    ``for``(``int` `i = 0; i < 100; i++) ` `    ``graph.Add(``new` `List<``int``>()); ` ` `  `    ``// Edges of the tree  ` `    ``graph[1].Add(2);  ` `    ``graph[2].Add(3);  ` `    ``graph[2].Add(4);  ` `    ``graph[1].Add(5);  ` ` `  `    ``dfs(1, 1);  ` ` `  `    ``Console.WriteLine( ans);  ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```1
```

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