Sort an array according to count of set bits
Last Updated : 10 Mar, 2025
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}.
[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.
C++ #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] + " "); Output15 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.
C++ #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] + " "); Output15 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.
C++ #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] + " "); Output15 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.
C++ #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] + " "); Output15 7 5 3 9 6 2 4 32
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