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Maximum sum by adding numbers with same number of set bits

  • Difficulty Level : Easy
  • Last Updated : 21 May, 2021

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;
}

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#




// 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>
Output: 
14

 

Time Complexity: O(N * 32) 
Auxiliary Space: O(N)
 

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