Maximum sum by adding numbers with same number of set bits

Last Updated : 01 Aug, 2022

Given an array of N numbers, the task is to find the maximum sum that can be obtained by adding numbers with the same number of set bits.
Examples:

Input: 32 3 7 5 27 28
Output: 34
Input: 2 3 8 5 6 7
Output: 14

Approach:

Traverse in the array and count the number of set bits for every element.
Initialize an array for 32 bits, assuming the number to have a maximum of 32 set bits.
Iterate in the array and add the array element to the position which indicates the number of set bits.
Traverse and find the maximum sum and return it.

Below is the implementation of the above approach:

C++

// C++ program to find maximum sum // by adding numbers with same number of set bits #include <bits/stdc++.h> using namespace std;  // count the number of bits // for each element of array int bit_count(int n) {     int count = 0;      // Count the number of set bits     while (n) {         count++;          n = n & (n - 1);     }      return count; }  // Function to return the // the maximum sum int maxsum(int arr[], int n) {     int bits[n];      // Calculate the     for (int i = 0; i < n; i++) {         bits[i] = bit_count(arr[i]);     }      // Assuming the number to be     // a maximum of 32 bits     int sum[32] = { 0 };      // Add the number to the     // number of set bits     for (int i = 0; i < n; i++) {         sum[bits[i]] += arr[i];     }      int maximum = 0;      // Find the maximum sum     for (int i = 0; i < 32; i++) {          maximum = max(sum[i], maximum);     }      return maximum; }  // Driver code int main() {      int arr[] = { 2, 3, 8, 5, 6, 7 };     int n = sizeof(arr) / sizeof(arr[0]);     cout << maxsum(arr, n);      return 0; }

// C program to find maximum sum // by adding numbers with same number of set bits #include <stdio.h> #include <stdlib.h> #include<math.h>  //function to find the maximum of two numbers  int max(int a,int b) { if(a>b)     return a; else     return b; }  // count the number of bits // for each element of array  int bit_count(int n) {     int count = 0;      // Count the number of set bits     while (n) {         count++;          n = n & (n - 1);     }      return count; }  // Function to return the // the maximum sum int maxsum(int arr[], int n) {     int bits[n];      // Calculate the     for (int i = 0; i < n; i++) {         bits[i] = bit_count(arr[i]);     }      // Assuming the number to be     // a maximum of 32 bits     int sum[32] = { 0 };      // Add the number to the     // number of set bits     for (int i = 0; i < n; i++) {         sum[bits[i]] += arr[i];     }      int maximum = 0;      // Find the maximum sum     for (int i = 0; i < 32; i++) {          maximum = max(sum[i], maximum);     }      return maximum; }  // Driver code int main() {      int arr[] = { 2, 3, 8, 5, 6, 7 };     int n = sizeof(arr) / sizeof(arr[0]);     int ans=maxsum(arr,n);     printf("%d",ans);     return 0; }

Java

// Java program to find maximum sum // by adding numbers with same number of set bits  class GFG { // count the number of bits // for each element of array static int bit_count(int n) {     int count = 0;      // Count the number of set bits     while (n>0)     {         count++;          n = n & (n - 1);     }      return count; }  // Function to return the // the maximum sum static int maxsum(int[] arr, int n) {     int[] bits=new int[n];      // Calculate the     for (int i = 0; i < n; i++)      {         bits[i] = bit_count(arr[i]);     }      // Assuming the number to be     // a maximum of 32 bits     int[] sum=new int[32];      // Add the number to the     // number of set bits     for (int i = 0; i < n; i++)     {         sum[bits[i]] += arr[i];     }      int maximum = 0;      // Find the maximum sum     for (int i = 0; i < 32; i++)     {          maximum = Math.max(sum[i], maximum);     }      return maximum; }  // Driver code public static void main (String[] args) {     int[] arr = { 2 ,3 , 8, 5, 6, 7 };     int n = arr.length;     System.out.println(maxsum(arr, n));  } }  // This Code is contributed by mits

Python3

# Python3 program to find maximum # sum by adding numbers with # same number of set bits  # count the number of bits # for each element of array def bit_count(n):     count = 0;      # Count the number     # of set bits     while (n > 0):         count += 1;          n = n & (n - 1);      return count;  # Function to return the # the maximum sum def maxsum(arr, n):     bits = [0] * n;      # Calculate the     for i in range(n):          bits[i] = bit_count(arr[i]);      # Assuming the number to be     # a maximum of 32 bits     sum = [0] * 32;      # Add the number to the     # number of set bits     for i in range(n):          sum[bits[i]] += arr[i];      maximum = 0;      # Find the maximum sum     for i in range(32):          maximum = max(sum[i], maximum);      return maximum;  # Driver code arr = [ 2, 3, 8, 5, 6, 7 ]; n = len(arr); print(maxsum(arr, n));  # This code is contributed by mits

// C# program to find maximum  // sum by adding numbers with  // same number of set bits using System;  class GFG { // count the number of bits // for each element of array static int bit_count(int n) {     int count = 0;      // Count the number     // of set bits     while (n > 0)     {         count++;          n = n & (n - 1);     }      return count; }  // Function to return the // the maximum sum static int maxsum(int[] arr, int n) {     int[] bits = new int[n];      // Calculate the     for (int i = 0; i < n; i++)      {         bits[i] = bit_count(arr[i]);     }      // Assuming the number to be     // a maximum of 32 bits     int[] sum = new int[32];      // Add the number to the     // number of set bits     for (int i = 0; i < n; i++)     {         sum[bits[i]] += arr[i];     }      int maximum = 0;      // Find the maximum sum     for (int i = 0; i < 32; i++)     {         maximum = Math.Max(sum[i], maximum);     }      return maximum; }  // Driver code static void Main() {     int[] arr = { 2 ,3 , 8, 5, 6, 7 };     int n = arr.Length;     Console.WriteLine(maxsum(arr, n)); } }  // This Code is contributed by mits

PHP

<?php // PHP program to find maximum // sum by adding numbers with // same number of set bits  // count the number of bits // for each element of array function bit_count($n) {     $count = 0;      // Count the number     // of set bits     while ($n)     {         $count++;          $n = $n & ($n - 1);     }      return $count; }  // Function to return the // the maximum sum function maxsum($arr, $n) {     $bits = array($n);      // Calculate the     for ($i = 0; $i < $n; $i++)      {         $bits[$i] = bit_count($arr[$i]);     }      // Assuming the number to be     // a maximum of 32 bits     $sum = array_fill(0, 32, 0);      // Add the number to the     // number of set bits     for ($i = 0; $i < $n; $i++)      {         $sum[$bits[$i]] += $arr[$i];     }      $maximum = 0;      // Find the maximum sum     for ($i = 0; $i < 32; $i++)     {          $maximum = max($sum[$i],                        $maximum);     }      return $maximum; }  // Driver code $arr = array( 2, 3, 8, 5, 6, 7 ); $n = sizeof($arr); echo maxsum($arr, $n);  // This code is contributed by mits ?>

JavaScript

<script>  // Javascript program to find maximum sum // by adding numbers with same number of set bits  // count the number of bits // for each element of array function bit_count(n) {     var count = 0;      // Count the number of set bits     while (n) {         count++;          n = n & (n - 1);     }      return count; }  // Function to return the // the maximum sum function maxsum(arr, n) {     var bits = Array(n);      // Calculate the     for (var i = 0; i < n; i++) {         bits[i] = bit_count(arr[i]);     }      // Assuming the number to be     // a maximum of 32 bits     var sum = Array(32).fill(0);      // Add the number to the     // number of set bits     for (var i = 0; i < n; i++) {         sum[bits[i]] += arr[i];     }      var maximum = 0;      // Find the maximum sum     for (var i = 0; i < 32; i++) {          maximum = Math.max(sum[i], maximum);     }      return maximum; }  // Driver code var arr = [2, 3, 8, 5, 6, 7]; var n = arr.length; document.write( maxsum(arr, n));  // This code is contributed by famously. </script>