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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Sorting Algorithms
A Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
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Introduction to Sorting Techniques – Data Structure and Algorithm Tutorials
Sorting refers to rearrangement of a given array or list of elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of elements in the respective data structure. Why Sorting Algorithms are ImportantThe sorting algorithm is important in Com
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Most Common Sorting Algorithms
Selection Sort
Selection Sort is a comparison-based sorting algorithm. It sorts an array by repeatedly selecting the smallest (or largest) element from the unsorted portion and swapping it with the first unsorted element. This process continues until the entire array is sorted. First we find the smallest element a
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Bubble Sort Algorithm
Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity are quite high. We sort the array using multiple passes. After the fi
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Insertion Sort Algorithm
Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. T
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Merge Sort - Data Structure and Algorithms Tutorials
Merge sort is a popular sorting algorithm known for its efficiency and stability. It follows the divide-and-conquer approach. It works by recursively dividing the input array into two halves, recursively sorting the two halves and finally merging them back together to obtain the sorted array. How do
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Quick Sort
QuickSort is a sorting algorithm based on the Divide and Conquer that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array. It works on the principle of divide and conquer, breaking down the problem into s
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Heap Sort - Data Structures and Algorithms Tutorials
Heap sort is a comparison-based sorting technique based on Binary Heap Data Structure. It can be seen as an optimization over selection sort where we first find the max (or min) element and swap it with the last (or first). We repeat the same process for the remaining elements. In Heap Sort, we use
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Counting Sort - Data Structures and Algorithms Tutorials
Counting Sort is a non-comparison-based sorting algorithm. It is particularly efficient when the range of input values is small compared to the number of elements to be sorted. The basic idea behind Counting Sort is to count the frequency of each distinct element in the input array and use that info
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