Sorting array elements with set bits equal to K

Given an array of integers and a number K. The task is to sort only those elements of the array whose total set bits are equal to K. Sorting must be done at their relative positions only without affecting any other elements.

Examples:

Input : arr[] = {32, 1, 9, 4, 64, 2}, K = 1 
Output : 1 2 9 4 32 64
All of the elements except 9 has exactly 1 bit set.
So, all elements except 9 are sorted without affecting
the position of 9 in the input array.

Input : arr[] = {2, 15, 12, 1, 3, 9}, K = 2 
Output : 2 15 3 1 9 12


Approach:

  • Initialise two empty vectors.
  • Traverse the array, from left to right and check the set bits of each element.
  • Here, C++ inbuilt function __builtin_popcount() to count setbits.
  • In first vector, insert the index of all elements with set bits equal to K.
  • In second vector, insert the elements with set bits equal to K.
  • Sort the second vector.
  • Now, we have the index of all elements with set bit equals to K in sorted order and also all of the elements with set bit as K in sorted order.
  • So, insert the elements of the second vector into the array at the indices present in first vector one by one.

Below is the implementation of the above approach:

C++

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// C++ program for sorting array elements
// with set bits equal to K
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to sort elements with
// set bits equal to k
void sortWithSetbits(int arr[], int n, int k)
{
    // initialise two vectors
    vector<int> v1, v2;
  
    for (int i = 0; i < n; i++) {
        if (__builtin_popcount(arr[i]) == k) {
  
            // first vector contains indices of
            // required element
            v1.push_back(i);
  
            // second vector contains 
            // required elements
            v2.push_back(arr[i]);
        }
    }
  
    // sorting the elements in second vector
    sort(v2.begin(), v2.end());
  
    // replacing the elements with k set bits
    // with the sorted elements
    for (int i = 0; i < v1.size(); i++)
        arr[v1[i]] = v2[i];
  
    // printing the new sorted array elements
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}
  
// Driver code
int main()
{
    int arr[] = { 14, 255, 1, 7, 13 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int k = 3;
  
    sortWithSetbits(arr, n, k);
  
    return 0;
}

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Python3

# Python 3 program for sorting array
# elements with set bits equal to K

# Function to sort elements with
# set bits equal to k
def sortWithSetbits(arr, n, k):

# initialise two vectors
v1 = []
v2 = []

for i in range(0, n, 1):
if (bin(arr[i]).count(‘1’) == k):

# first vector contains indices
# of required element
v1.append(i)

# second vector contains
# required elements
v2.append(arr[i])

# sorting the elements in second vector
v2.sort(reverse = False)

# replacing the elements with k set
# bits with the sorted elements
for i in range(0, len(v1), 1):
arr[v1[i]] = v2[i]

# printing the new sorted array elements
for i in range(0, n, 1):
print(arr[i], end = ” “)

# Driver code
if __name__ == ‘__main__’:
arr = [14, 255, 1, 7, 13]
n = len(arr)
k = 3

sortWithSetbits(arr, n, k)

# This code is contributed by
# Surendra_Gangwar

Output:

7 255 1 13 14


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