Find the node whose sum with X has maximum set bits

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 has the maximum set bits. If two or more nodes have the same count of set bits when added with x then find the one with the minimum value.

Examples:

Input:

x = 15
Output: 4
Node 1: setbits(5 + 15) = 2
Node 2: setbits(10 + 15) = 3
Node 3: setbits(11 + 15) = 3
Node 4: setbits(8 + 15) = 4
Node 5: setbits(6 + 15) = 3



Approach: Perform dfs on the tree and keep track of the node whose sum with x has maximum set bits. If two or more nodes have equal count of set bits then choose the one with the minimum number.

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 = INT_MAX;
  
vector<int> graph[100];
vector<int> weight(100);
  
// Function to perform dfs to find
// the maximum set bits value
void dfs(int node, int parent)
{
    // If current set bits value is greater than
    // the current maximum
    int a = __builtin_popcount(weight[node] + x);
    if (maximum < a) {
        maximum = a;
        ans = node;
    }
  
    // If count is equal to the maximum
    // then choose the node with minimum value
    else if (maximum == a)
        ans = min(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 = Integer.MAX_VALUE;  


  


static Vector<Vector<Integer>> graph = new Vector<Vector<Integer>>();  


static Vector<Integer> weight = new Vector<Integer>();  


  


//number of set bits 


static int __builtin_popcount(int x) 


{ 


    int c = 0; 


    for(int i = 0; i < 60; i++) 


    if(((x>>i)&1) != 0)c++; 


      


    return c; 


} 


  


// Function to perform dfs to find  


// the maximum value  


static void dfs(int node, int parent)  


{  


    // If current set bits value is greater than 


    // the current maximum 


    int a = __builtin_popcount(weight.get(node) + x); 


    if (maximum < a)  


    { 


        maximum = a; 


        ans = node; 


    } 


  


    // If count is equal to the maximum 


    // then choose the node with minimum value 


    else if (maximum == a) 


        ans = Math.min(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 


  


maximum, x, ans = -maxsize, None, maxsize 


  


graph = [[] for i in range(100)] 


weight = [0] * 100


  


# Function to perform dfs to find 


# the maximum set bits value 


def dfs(node, parent): 


    global x, ans, graph, weight, maximum 


  


    # If current set bits value is greater than 


    # the current maximum 


    a = bin(weight[node] + x).count('1') 


  


    if maximum < a: 


        maximum = a 


        ans = node 


  


    # If count is equal to the maximum 


    # then choose the node with minimum value 


    elif maximum == a: 


        ans = min(ans, node) 


  


    for to in graph[node]: 


        if to == parent: 


            continue


        dfs(to, node) 


  


# Driver Code 


if __name__ == "__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].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 = int.MaxValue;  


  


static List<List<int>> graph = new List<List<int>>(); 


static List<int> weight = new List<int>(); 


  


// number of set bits 


static int __builtin_popcount(int x) 


{ 


    int c = 0; 


    for(int i = 0; i < 60; i++) 


    if(((x>>i)&1) != 0)c++; 


      


    return c; 


} 


  


// Function to perform dfs to find  


// the maximum value  


static void dfs(int node, int parent)  


{  


    // If current set bits value is greater than 


    // the current maximum 


    int a = __builtin_popcount(weight[node] + x); 


    if (maximum < a)  


    { 


        maximum = a; 


        ans = node; 


    } 


  


    // If count is equal to the maximum 


    // then choose the node with minimum value 


    else if (maximum == a) 


        ans = Math.Min(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() 


{  


    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.Write( ans);  


} 


}  


  


// This code is contributed by mits 



















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Output:


4







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