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:

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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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Output:

1


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