Sort an array according to count of set bits
Last Updated :
10 Mar, 2025
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Given an array of integers, sort the array (in descending order) according to count of set bits in binary representation of array elements.
Note: For integers having same number of set bits in their binary representation, sort according to their position in the original array i.e., a stable sort.
Examples:
Input: arr[] = [5, 2, 3, 9, 4, 6, 7, 15, 32]
Output: 15 7 5 3 9 6 2 4 32
Explanation: The integers in their binary representation are:
15 -1111
7 -0111
5 -0101
3 -0011
9 -1001
6 -0110
2 -0010
4- -0100
32 -10000
Hence the non-increasing sorted order is: {15}, {7}, {5, 3, 9, 6}, {2, 4, 32}.Input: arr[] = [1, 2, 3, 4, 5, 6]
Output: 3 5 6 1 2 4
Explanation: The integers in their binary representation are:
3 - 0011
5 - 0101
6 - 0110
1 - 0001
2 - 0010
4 - 0100
hence the non-increasing sorted order is {3, 5, 6}, {1, 2, 4}.
Table of Content
[Naive Approach] - Using Insertion Sort - O(n ^ 2) Time and O(n) Space
The idea is to store the set-bit counts of all the integers in the auxiliary array and simultaneously sort both arrays according to the non-increasing order of auxiliary array.
#include <bits/stdc++.h>
using namespace std;
// Function to simultaneously sort both
// arrays using insertion sort
void insertionSort(vector<int> &arr, vector<int> &bitCnt) {
int n = arr.size();
for (int i = 1; i < n; i++) {
int key1 = bitCnt[i];
int key2 = arr[i];
int j = i - 1;
while (j >= 0 && bitCnt[j] < key1) {
bitCnt[j + 1] = bitCnt[j];
arr[j + 1] = arr[j];
j = j - 1;
}
bitCnt[j + 1] = key1;
arr[j + 1] = key2;
}
}
// Function to count set bits in an integer
int countBits(int a) {
int count = 0;
while (a) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
void sortBySetBitCount(vector<int>& arr) {
int n = arr.size();
// Create an array and store
// count of set bits in it.
vector<int> bitCnt(n);
for (int i = 0; i < n; i++)
bitCnt[i] = countBits(arr[i]);
// sort the array
insertionSort(arr, bitCnt);
}
int main() {
vector<int> arr = { 5, 2, 3, 9, 4, 6, 7, 15, 32 };
sortBySetBitCount(arr);
for (int i = 0; i < arr.size(); i++)
cout << arr[i] << " ";
return 0;
}
// Function to simultaneously sort both
// arrays using insertion sort
import java.util.*;
class GfG {
// Function to simultaneously sort both
// arrays using insertion sort
static void insertionSort(int[] arr, int[] bitCnt) {
int n = arr.length;
for (int i = 1; i < n; i++) {
int key1 = bitCnt[i];
int key2 = arr[i];
int j = i - 1;
while (j >= 0 && bitCnt[j] < key1) {
bitCnt[j + 1] = bitCnt[j];
arr[j + 1] = arr[j];
j = j - 1;
}
bitCnt[j + 1] = key1;
arr[j + 1] = key2;
}
}
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static void sortBySetBitCount(int[] arr) {
int n = arr.length;
// Create an array and store
// count of set bits in it.
int[] bitCnt = new int[n];
for (int i = 0; i < n; i++)
bitCnt[i] = countBits(arr[i]);
// sort the array
insertionSort(arr, bitCnt);
}
public static void main(String[] args) {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
sortBySetBitCount(arr);
for (int i = 0; i < arr.length; i++)
System.out.print(arr[i] + " ");
}
}
# Function to simultaneously sort both
# arrays using insertion sort
def insertionSort(arr, bitCnt):
n = len(arr)
for i in range(1, n):
key1 = bitCnt[i]
key2 = arr[i]
j = i - 1
while j >= 0 and bitCnt[j] < key1:
bitCnt[j + 1] = bitCnt[j]
arr[j + 1] = arr[j]
j = j - 1
bitCnt[j + 1] = key1
arr[j + 1] = key2
# Function to count set bits in an integer
def countBits(a):
count = 0
while a:
if a % 2 != 0:
count += 1
a = a // 2
return count
# Function to sort an array according to bit count
def sortBySetBitCount(arr):
n = len(arr)
# Create an array and store
# count of set bits in it.
bitCnt = [0] * n
for i in range(n):
bitCnt[i] = countBits(arr[i])
# sort the array
insertionSort(arr, bitCnt)
if __name__ == "__main__":
arr = [5, 2, 3, 9, 4, 6, 7, 15, 32]
sortBySetBitCount(arr)
for i in range(len(arr)):
print(arr[i], end=" ")
// Function to simultaneously sort both
// arrays using insertion sort
using System;
using System.Collections.Generic;
class GfG {
// Function to simultaneously sort both
// arrays using insertion sort
static void insertionSort(int[] arr, int[] bitCnt) {
int n = arr.Length;
for (int i = 1; i < n; i++) {
int key1 = bitCnt[i];
int key2 = arr[i];
int j = i - 1;
while (j >= 0 && bitCnt[j] < key1) {
bitCnt[j + 1] = bitCnt[j];
arr[j + 1] = arr[j];
j = j - 1;
}
bitCnt[j + 1] = key1;
arr[j + 1] = key2;
}
}
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static void sortBySetBitCount(int[] arr) {
int n = arr.Length;
// Create an array and store
// count of set bits in it.
int[] bitCnt = new int[n];
for (int i = 0; i < n; i++)
bitCnt[i] = countBits(arr[i]);
// sort the array
insertionSort(arr, bitCnt);
}
static void Main() {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
sortBySetBitCount(arr);
for (int i = 0; i < arr.Length; i++)
Console.Write(arr[i] + " ");
}
}
// Function to simultaneously sort both
// arrays using insertion sort
function insertionSort(arr, bitCnt) {
let n = arr.length;
for (let i = 1; i < n; i++) {
let key1 = bitCnt[i];
let key2 = arr[i];
let j = i - 1;
while (j >= 0 && bitCnt[j] < key1) {
bitCnt[j + 1] = bitCnt[j];
arr[j + 1] = arr[j];
j = j - 1;
}
bitCnt[j + 1] = key1;
arr[j + 1] = key2;
}
}
// Function to count set bits in an integer
function countBits(a) {
let count = 0;
while (a) {
if (a % 2 !== 0)
count += 1;
a = Math.floor(a / 2);
}
return count;
}
// Function to sort an array according to bit count
function sortBySetBitCount(arr) {
let n = arr.length;
// Create an array and store
// count of set bits in it.
let bitCnt = new Array(n).fill(0);
for (let i = 0; i < n; i++)
bitCnt[i] = countBits(arr[i]);
// sort the array
insertionSort(arr, bitCnt);
}
let arr = [5, 2, 3, 9, 4, 6, 7, 15, 32];
sortBySetBitCount(arr);
for (let i = 0; i < arr.length; i++)
process.stdout.write(arr[i] + " ");
Output
15 7 5 3 9 6 2 4 32
[Better Approach] - Using Inbuilt Sort Function - O(n * log n) Time and O(1) Space
The idea is to use the inbuilt sort function and custom comparator to sort the array according to set-bit count.
#include <bits/stdc++.h>
using namespace std;
// Function to count set bits in an integer
int countBits(int a) {
int count = 0;
while (a) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// custom comparator of std::sort
bool cmp(int a, int b) {
int count1 = countBits(a);
int count2 = countBits(b);
// this takes care of the stability of sorting algorithm too
if (count1 <= count2)
return false;
return true;
}
// Function to sort an array according to bit count
void sortBySetBitCount(vector<int>& arr) {
stable_sort(arr.begin(), arr.end(), cmp);
}
int main() {
vector<int> arr = { 5, 2, 3, 9, 4, 6, 7, 15, 32 };
sortBySetBitCount(arr);
for (int i = 0; i < arr.size(); i++)
cout << arr[i] << " ";
return 0;
}
// Function to count set bits in an integer
import java.util.*;
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
// using stable sort
static int[] sortBySetBitCount(int[] arr) {
int n = arr.length;
Integer[] arrObj = new Integer[n];
for (int i = 0; i < n; i++) {
arrObj[i] = arr[i];
}
Arrays.sort(arrObj, new Comparator<Integer>() {
public int compare(Integer a, Integer b) {
int c1 = countBits(a);
int c2 = countBits(b);
if(c1 == c2)
return 0;
return c1 < c2 ? 1 : -1;
}
});
int[] ans = new int[n];
for (int i = 0; i < n; i++) {
ans[i] = arrObj[i];
}
return ans;
}
public static void main(String[] args) {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
int[] ans = sortBySetBitCount(arr);
for (int i = 0; i < ans.length; i++)
System.out.print(ans[i] + " ");
}
}
# Function to count set bits in an integer
def countBits(a):
count = 0
while a:
if a % 2 != 0:
count += 1
a //= 2
return count
# Function to sort an array according to bit count
# using stable sort
def sortBySetBitCount(arr):
arr.sort(key=lambda x: -countBits(x))
return arr
if __name__ == "__main__":
arr = [5, 2, 3, 9, 4, 6, 7, 15, 32]
sortBySetBitCount(arr)
for i in range(len(arr)):
print(arr[i], end=" ")
// Function to count set bits in an integer
using System;
using System.Linq;
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
// using stable sort
static int[] sortBySetBitCount(int[] arr) {
int n = arr.Length;
var sorted = arr.Select((x, i) => new { Value = x, Index = i })
.OrderByDescending(item => countBits(item.Value))
.ThenBy(item => item.Index)
.Select(item => item.Value)
.ToArray();
return sorted;
}
static void Main() {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
int[] ans = sortBySetBitCount(arr);
for (int i = 0; i < ans.Length; i++)
Console.Write(ans[i] + " ");
}
}
// Function to count set bits in an integer
function countBits(a) {
let count = 0;
while (a) {
if (a % 2 !== 0)
count += 1;
a = Math.floor(a / 2);
}
return count;
}
// Function to sort an array according to bit count
// using stable sort
function sortBySetBitCount(arr) {
arr.sort((a, b) => {
let c1 = countBits(a);
let c2 = countBits(b);
if (c1 === c2)
return 0;
return c1 < c2 ? 1 : -1;
});
return arr;
}
let arr = [5, 2, 3, 9, 4, 6, 7, 15, 32];
sortBySetBitCount(arr);
for (let i = 0; i < arr.length; i++)
process.stdout.write(arr[i] + " ");
Output
15 7 5 3 9 6 2 4 32
[Expected Approach] - Using Counting Sort - O(n) Time and O(n) Space
The idea is to use counting sort to arrange the elements in descending order of count of set-bits. For any integer, assuming the minimum and maximum set-bits can be 1 and 31 respectively, create an array count[][] of size 32, where each element count[i] stores the elements of given array with count of their set bits equal to i. After inserting all the elements, traverse count[][] in reverse order, and store the elements at each index in the given array.
#include <bits/stdc++.h>
using namespace std;
// Function to count set bits in an integer
int countBits(int a) {
int count = 0;
while (a) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
void sortBySetBitCount(vector<int>& arr) {
int n = arr.size();
// Create a 2d array to map array elements
// to their corresponding set bit count
vector<vector<int>> count(32);
// insert elements in the 2d array
for (int i=0; i<n; i++) {
int setBit = countBits(arr[i]);
count[setBit].push_back(arr[i]);
}
// to track the index of sorted array
int j = 0;
// Traverse through all bit counts
for (int i = 31; i >= 0; i--) {
// Traverse through all elements
// of current bit count
for(int k = 0; k < count[i].size(); k++) {
arr[j++] = count[i][k];
}
}
}
int main() {
vector<int> arr = { 5, 2, 3, 9, 4, 6, 7, 15, 32 };
sortBySetBitCount(arr);
for (int i = 0; i < arr.size(); i++)
cout << arr[i] << " ";
return 0;
}
// Function to count set bits in an integer
import java.util.*;
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static void sortBySetBitCount(int[] arr) {
int n = arr.length;
// Create a 2d array to map array elements
// to their corresponding set bit count
ArrayList<ArrayList<Integer>> count = new ArrayList<>();
for (int i = 0; i < 32; i++) {
count.add(new ArrayList<>());
}
// insert elements in the 2d array
for (int i = 0; i < n; i++) {
int setBit = countBits(arr[i]);
count.get(setBit).add(arr[i]);
}
// to track the index of sorted array
int j = 0;
// Traverse through all bit counts
for (int i = 31; i >= 0; i--) {
// Traverse through all elements
// of current bit count
ArrayList<Integer> curr = count.get(i);
for (int k = 0; k < curr.size(); k++) {
arr[j++] = curr.get(k);
}
}
}
public static void main(String[] args) {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
sortBySetBitCount(arr);
for (int i = 0; i < arr.length; i++)
System.out.print(arr[i] + " ");
}
}
# Function to count set bits in an integer
def countBits(a):
count = 0
while a:
if a % 2 != 0:
count += 1
a = a // 2
return count
# Function to sort an array according to bit count
def sortBySetBitCount(arr):
n = len(arr)
# Create a 2d array to map array elements
# to their corresponding set bit count
count = [[] for _ in range(32)]
# insert elements in the 2d array
for i in range(n):
setBit = countBits(arr[i])
count[setBit].append(arr[i])
# to track the index of sorted array
j = 0
# Traverse through all bit counts
for i in range(31, -1, -1):
# Traverse through all elements
# of current bit count
for k in range(len(count[i])):
arr[j] = count[i][k]
j += 1
# Driver Code
if __name__ == "__main__":
arr = [5, 2, 3, 9, 4, 6, 7, 15, 32]
sortBySetBitCount(arr)
for i in range(len(arr)):
print(arr[i], end=" ")
// Function to count set bits in an integer
using System;
using System.Collections.Generic;
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static void sortBySetBitCount(int[] arr) {
int n = arr.Length;
// Create a 2d array to map array elements
// to their corresponding set bit count
List<List<int>> count = new List<List<int>>();
for (int i = 0; i < 32; i++) {
count.Add(new List<int>());
}
// insert elements in the 2d array
for (int i = 0; i < n; i++) {
int setBit = countBits(arr[i]);
count[setBit].Add(arr[i]);
}
// to track the index of sorted array
int j = 0;
// Traverse through all bit counts
for (int i = 31; i >= 0; i--) {
// Traverse through all elements
// of current bit count
for (int k = 0; k < count[i].Count; k++) {
arr[j++] = count[i][k];
}
}
}
static void Main() {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
sortBySetBitCount(arr);
for (int i = 0; i < arr.Length; i++)
Console.Write(arr[i] + " ");
}
}
// Function to count set bits in an integer
function countBits(a) {
let count = 0;
while (a) {
if (a % 2 !== 0)
count += 1;
a = Math.floor(a / 2);
}
return count;
}
// Function to sort an array according to bit count
function sortBySetBitCount(arr) {
let n = arr.length;
// Create a 2d array to map array elements
// to their corresponding set bit count
let count = [];
for (let i = 0; i < 32; i++) {
count.push([]);
}
// insert elements in the 2d array
for (let i = 0; i < n; i++) {
let setBit = countBits(arr[i]);
count[setBit].push(arr[i]);
}
// to track the index of sorted array
let j = 0;
// Traverse through all bit counts
for (let i = 31; i >= 0; i--) {
// Traverse through all elements
// of current bit count
for (let k = 0; k < count[i].length; k++) {
arr[j++] = count[i][k];
}
}
}
let arr = [5, 2, 3, 9, 4, 6, 7, 15, 32];
sortBySetBitCount(arr);
for (let i = 0; i < arr.length; i++)
process.stdout.write(arr[i] + " ");
Output
15 7 5 3 9 6 2 4 32
[Alternate Approach] - Using Multimap - O(n * log n) Time and O(n) Space
The idea is store the elements corresponding to negative (to ensure elements are sorted in descending order) of their count of set-bits in a multimap.
- Create a MultiMap whose key values will be the negative of the number of set-bits of the element.
- Traverse the array and do following for each element:
- Count the number set-bits of this element. Let it be 'setBitCount'
- count.insert({(-1) * setBitCount, element})
- Traverse 'count' and print the second elements.
#include <bits/stdc++.h>
using namespace std;
// Function to count set bits in an integer
int countBits(int a) {
int count = 0;
while (a) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
void sortBySetBitCount(vector<int>& arr) {
int n = arr.size();
// to map the elements to their
// corresponding set bit count
multimap<int, int> count;
// Iterate over all values and
// insert into multimap
for( int i = 0 ; i < n ; i++ ) {
count.insert({(-1) * countBits(arr[i]), arr[i]});
}
int j = 0;
// Iterate over all values and
// insert into the array
for(auto i: count) {
arr[j++] = i.second;
}
}
int main() {
vector<int> arr = { 5, 2, 3, 9, 4, 6, 7, 15, 32 };
sortBySetBitCount(arr);
for (int i = 0; i < arr.size(); i++)
cout << arr[i] << " ";
return 0;
}
// Function to count set bits in an integer
import java.util.*;
class Pair {
int val;
int idx;
Pair(int val, int idx) {
this.val = val;
this.idx = idx;
}
}
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static int[] sortBySetBitCount(int[] arr) {
int n = arr.length;
Pair[] pairs = new Pair[n];
for (int i = 0; i < n; i++) {
pairs[i] = new Pair(arr[i], i);
}
Arrays.sort(pairs, new Comparator<Pair>() {
public int compare(Pair p1, Pair p2) {
int c1 = countBits(p1.val);
int c2 = countBits(p2.val);
if (c1 == c2)
return Integer.compare(p1.idx, p2.idx);
return Integer.compare(c2, c1);
}
});
int[] ans = new int[n];
for (int i = 0; i < n; i++) {
ans[i] = pairs[i].val;
}
return ans;
}
public static void main(String[] args) {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
int[] ans = sortBySetBitCount(arr);
for (int i = 0; i < ans.length; i++)
System.out.print(ans[i] + " ");
}
}
# Function to count set bits in an integer
def countBits(a):
count = 0
while a:
if a % 2 != 0:
count += 1
a //= 2
return count
# Function to sort an array according to bit count
def sortBySetBitCount(arr):
n = len(arr)
# Create an array of (index, value) pairs
paired = list(enumerate(arr))
# Stable sort: first by descending countBits, then by original index
paired.sort(key=lambda x: (-countBits(x[1]), x[0]))
ans = [x[1] for x in paired]
return ans
if __name__ == "__main__":
arr = [5, 2, 3, 9, 4, 6, 7, 15, 32]
ans = sortBySetBitCount(arr)
for i in range(len(ans)):
print(ans[i], end=" ")
// Function to count set bits in an integer
using System;
using System.Linq;
using System.Collections.Generic;
class GfG {
// Function to count set bits in an integer
static int countBits(int a) {
int count = 0;
while (a != 0) {
if (a % 2 != 0)
count += 1;
a = a / 2;
}
return count;
}
// Function to sort an array according to bit count
static int[] sortBySetBitCount(int[] arr) {
int n = arr.Length;
var paired = arr.Select((val, idx) => new { val, idx });
var sorted = paired.OrderByDescending(x => countBits(x.val))
.ThenBy(x => x.idx)
.Select(x => x.val)
.ToArray();
return sorted;
}
static void Main() {
int[] arr = {5, 2, 3, 9, 4, 6, 7, 15, 32};
int[] ans = sortBySetBitCount(arr);
for (int i = 0; i < ans.Length; i++)
Console.Write(ans[i] + " ");
}
}
// Function to count set bits in an integer
function countBits(a) {
let count = 0;
while (a) {
if (a % 2 !== 0)
count += 1;
a = Math.floor(a / 2);
}
return count;
}
// Function to sort an array according to bit count
function sortBySetBitCount(arr) {
let n = arr.length;
// Create an array of pairs [index, value]
let paired = arr.map((val, idx) => [idx, val]);
// Stable sort: first by descending countBits, then by original index
paired.sort((a, b) => {
let c1 = countBits(a[1]);
let c2 = countBits(b[1]);
if (c1 === c2)
return a[0] - b[0];
return c2 - c1;
});
let ans = paired.map(x => x[1]);
return ans;
}
let arr = [5, 2, 3, 9, 4, 6, 7, 15, 32];
let ans = sortBySetBitCount(arr);
for (let i = 0; i < ans.length; i++)
process.stdout.write(ans[i] + " ");
Output
15 7 5 3 9 6 2 4 32
