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



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++

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

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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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Output:

3


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Improved By : sanjeev2552