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



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++

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// C++ implementation of the approach
#include <bits/stdc++.h>
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;
}

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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG
{
  
static int maximum = Integer.MIN_VALUE, x, ans; 
  
static Vector<Vector<Integer>> graph=new Vector<Vector<Integer>>(); 
static Vector<Integer> weight=new Vector<Integer>(); 
  
// 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<Integer>());
  
    // 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

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Python3

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# 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

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C#

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// C# implementation of the approach
using System;
using System.Collections.Generic;
      
class GFG
{
  
static int maximum = int.MinValue, x, ans; 
  
static List<List<int>> graph = new List<List<int>>(); 
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

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Output:

1

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