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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