Sort an array of 0s, 1s, 2s and 3s

Given an array arr[] of size N consisting of 0, 1, 2, and 3 only, the task is to sort the given array in ascending order.

Example: 

Input: arr[] = {0, 3, 1, 2, 0, 3, 1, 2}
Output: 0 0 1 1 2 2 3 3

Input: arr[] = {0, 1, 3, 1, 0, 1, 3, 2, 1, 2, 0, 3, 0, 0, 1}
Output: 0 0 0 0 0 1 1 1 1 1 2 2 3 3 3

Approach: The given problem can be solved based on the approach discussed in this article. The idea is first to position all the 0s and 3s at the beginning and end of the array, followed by sorting the occurrences of integers 1 and 2. 

Follow the steps below to solve the problem:

• Initialize three variables, say i, mid, and j. Set the values of i and mid as 0 and j as (N – 1).
• Iterate a loop until mid ≤ j and perform the following steps:
  • If the value of arr[mid] is 0, then swap arr[i] and arr[mid] and increment the value of i and mid by 1.
  • Otherwise, if the value of arr[mid] is 3, then swap arr[mid] and arr[j] and decrement j by 1.
  • Otherwise, if the value of arr[i] is either 1 or 2, then increment the value of mid by 1.
• Now to sort the subarray over the range [i, j] by iterating until i ≤ j and perform the following operations:
  • If the value of arr[i] is 2, then swap arr[i] and arr[j] and decrement the value of j by 1.
  • Otherwise, increment the value of i by 1.
• After completing the above steps, print the array arr[] as the resultant sorted array.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to sort the array having
// array element only 0, 1, 2, and 3
void sortArray(int arr[], int N)
{
    int i = 0, j = N - 1, mid = 0;

    // Iterate until mid <= j
    while (mid <= j) {

        // If arr[mid] is 0
        if (arr[mid] == 0) {

            // Swap integers at
            // indices i and mid
            swap(arr[i], arr[mid]);

            // Increment i
            i++;

            // Increment mid
            mid++;
        }

        // Otherwise if the value of
        // arr[mid] is 3
        else if (arr[mid] == 3) {

            // Swap arr[mid] and arr[j]
            swap(arr[mid], arr[j]);

            // Decrement j
            j--;
        }

        // Otherwise if the value of
        // arr[mid] is either 1 or 2
        else if (arr[mid] == 1
                 || arr[mid] == 2) {

            // Increment the value of mid
            mid++;
        }
    }

    // Iterate until i <= j
    while (i <= j) {

        // If arr[i] the value of is 2
        if (arr[i] == 2) {

            // Swap arr[i] and arr[j]
            swap(arr[i], arr[j]);

            // Decrement j
            j--;
        }

        // Otherwise, increment i
        else {
            i++;
        }
    }

    // Print the sorted array arr[]
    for (int i = 0; i < N; i++) {
        cout << arr[i] << " ";
    }
}

// Driver Code
int main()
{
    int arr[] = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = sizeof(arr) / sizeof(arr[0]);
    sortArray(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG{

// Function to sort the array having
// array element only 0, 1, 2, and 3
static void sortArray(int[] arr, int N)
{
    int i = 0, j = N - 1, mid = 0;

    // Iterate until mid <= j
    while (mid <= j)
    {

        // If arr[mid] is 0
        if (arr[mid] == 0)
        {

            // Swap integers at
            // indices i and mid
            int temp = arr[i];
            arr[i] = arr[mid];
            arr[mid] = temp;

            // Increment i
            i++;

            // Increment mid
            mid++;
        }

        // Otherwise if the value of
        // arr[mid] is 3
        else if (arr[mid] == 3)
        {

            // Swap arr[mid] and arr[j]
            int temp = arr[mid];
            arr[mid] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise if the value of
        // arr[mid] is either 1 or 2
        else if (arr[mid] == 1 || arr[mid] == 2)
        {

            // Increment the value of mid
            mid++;
        }
    }

    // Iterate until i <= j
    while (i <= j)
    {

        // If arr[i] the value of is 2
        if (arr[i] == 2)
        {

            // Swap arr[i] and arr[j]
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise, increment i
        else
        {
            i++;
        }
    }

    // Print the sorted array arr[]
    for(int k = 0; k < N; k++)
    {
        System.out.print(arr[k] + " ");
    }
}

// Driver Code
public static void main(String[] args)
{
    int[] arr = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = arr.length;

    sortArray(arr, N);
}
}

// This code is contributed by susmitakundugoaldanga

Python3

# Python3 program for the above approach

# Function to sort the array having
# array element only 0, 1, 2, and 3
def sortArray(arr, N):
    i = 0
    j = N - 1
    mid = 0

    # Iterate until mid <= j
    while (mid <= j):

        # If arr[mid] is 0
        if (arr[mid] == 0):

            # Swap integers at
            # indices i and mid
            arr[i], arr[mid] = arr[mid], arr[i]

            # Increment i
            i += 1

            # Increment mid
            mid += 1

        # Otherwise if the value of
        # arr[mid] is 3
        elif (arr[mid] == 3):

            # Swap arr[mid] and arr[j]
            arr[mid], arr[j] = arr[j], arr[mid]

            # Decrement j
            j -= 1

        # Otherwise if the value of
        # arr[mid] is either 1 or 2
        elif (arr[mid] == 1 or arr[mid] == 2):
            # Increment the value of mid
            mid += 1

    # Iterate until i <= j
    while (i <= j):

        # If arr[i] the value of is 2
        if (arr[i] == 2):

            # Swap arr[i] and arr[j]
            arr[i], arr[j] = arr[j], arr[i]

            # Decrement j
            j -= 1

        # Otherwise, increment i
        else:
            i += 1

    # Print the sorted array arr[]
    for i in range(N):
        print(arr[i], end = " ")

# Driver Code
if __name__ == '__main__':
    arr = [3, 2, 1, 0, 2, 3, 1, 0]
    N = len(arr)
    sortArray(arr, N)

#  This code is contributed by mohit kumar 29.

C#

// C# program for the above approach
using System;

class GFG{

// Function to sort the array having
// array element only 0, 1, 2, and 3
static void sortArray(int[] arr, int N)
{
    int i = 0, j = N - 1, mid = 0;

    // Iterate until mid <= j
    while (mid <= j)
    {

        // If arr[mid] is 0
        if (arr[mid] == 0)
        {

            // Swap integers at
            // indices i and mid
            int temp = arr[i];
            arr[i] = arr[mid];
            arr[mid] = temp;

            // Increment i
            i++;

            // Increment mid
            mid++;
        }

        // Otherwise if the value of
        // arr[mid] is 3
        else if (arr[mid] == 3)
        {

            // Swap arr[mid] and arr[j]
            int temp = arr[mid];
            arr[mid] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise if the value of
        // arr[mid] is either 1 or 2
        else if (arr[mid] == 1 || arr[mid] == 2)
        {

            // Increment the value of mid
            mid++;
        }
    }

    // Iterate until i <= j
    while (i <= j)
    {

        // If arr[i] the value of is 2
        if (arr[i] == 2)
        {

            // Swap arr[i] and arr[j]
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise, increment i
        else
        {
            i++;
        }
    }

    // Print the sorted array arr[]
    for(int k = 0; k < N; k++)
    {
        Console.Write(arr[k] + " ");
    }
}

// Driver Code
public static void Main()
{
    int[] arr = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = arr.Length;

    sortArray(arr, N);
}
}

// This code is contributed by ukasp

Javascript

<script>

// javascript program for the above approach

// Function to sort the array having
// array element only 0, 1, 2, and 3
function sortArray(arr, N)
{
    var i = 0, j = N - 1, mid = 0;

    // Iterate until mid <= j
    while (mid <= j) {

        // If arr[mid] is 0
        if (arr[mid] == 0) {

            // Swap integers at
            // indices i and mid
            var temp = arr[i];
            arr[i] = arr[mid];
            arr[mid] = temp;

            // Increment i
            i++;

            // Increment mid
            mid++;
        }

        // Otherwise if the value of
        // arr[mid] is 3
        else if (arr[mid] == 3) {

            var temp = arr[mid];
            arr[mid] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise if the value of
        // arr[mid] is either 1 or 2
        else if (arr[mid] == 1
                 || arr[mid] == 2) {

            // Increment the value of mid
            mid++;
        }
    }

    // Iterate until i <= j
    while (i <= j) {

        // If arr[i] the value of is 2
        if (arr[i] == 2) {

            // Swap arr[i] and arr[j]
            var temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;

            // Decrement j
            j--;
        }

        // Otherwise, increment i
        else {
            i++;
        }
    }

    // Print the sorted array arr[]
    for (i = 0; i < N; i++) {
        document.write(arr[i] + " ");
    }
}

// Driver Code
    var arr = [3, 2, 1, 0, 2, 3, 1, 0];
    var N = arr.length;
    sortArray(arr, N);

</script>

Output

0 0 1 1 2 2 3 3 

Time Complexity: O(N)
Auxiliary Space: O(1)

Another Approach(by simply counting 0,1,2 and 3):
We simply traverse the full array and count the occurrence of 0,1,2 and 3’s.
After traversing the whole array we modify out array and set 0,1,2 and 3’s to correct positions.
Below is the implementation of the above approach:

C++

// C++ Program for the above approach
#include<bits/stdc++.h>
using namespace std;

// function to sor the array having
// array element only 0,1,2 and 3
void sortArray(int arr[], int N){
    int count0 = 0;
    int count1 = 0;
    int count2 = 0;
    int count3 = 0;
    for(int i = 0; i<N; i++){
        if(arr[i] == 0) count0++;
        else if(arr[i] == 1) count1++;
        else if(arr[i] == 2) count2++;
        else count3++;
    }
    // Putting the 0's in the array in starting.
    for (int i = 0; i < count0; i++)
        arr[i] = 0;

    // Putting the 1's in the array after the 0's.
    for (int i = count0; i < (count0 + count1); i++)
        arr[i] = 1;

    // Putting the 2's in the array after the 1's
    for (int i = (count0 + count1); i < (count0 + count1 + count2); i++)
        arr[i] = 2;

    // Putting the 3's in the array after the 2's
    for (int i = (count0 + count1 + count2); i < N; i++)
        arr[i] = 3;

    // print the sorted array
    for(int i = 0; i<N; i++){
        cout<<arr[i]<<" ";
    }
}

// Driver Code
int main()
{
    int arr[] = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = sizeof(arr) / sizeof(arr[0]);
    sortArray(arr, N);

    return 0;
}

// THIS CODE IS CONTRIBUTED BY YASH AGARWAL(YASHAGARWAL2852002)

Java

import java.util.Arrays;

class Main
{

  // function to sor the array having
  // array element only 0,1,2 and 3
  static void sortArray(int[] arr, int N) {
    int count0 = 0;
    int count1 = 0;
    int count2 = 0;
    int count3 = 0;
    for(int i = 0; i < N; i++) {
      if(arr[i] == 0) count0++;
      else if(arr[i] == 1) count1++;
      else if(arr[i] == 2) count2++;
      else count3++;
    }

    // Putting the 0's in the array in starting.
    for (int i = 0; i < count0; i++)
      arr[i] = 0;

    // Putting the 1's in the array after the 0's.
    for (int i = count0; i < (count0 + count1); i++)
      arr[i] = 1;

    // Putting the 2's in the array after the 1's
    for (int i = (count0 + count1); i < (count0 + count1 + count2); i++)
      arr[i] = 2;

    // Putting the 3's in the array after the 2's
    for (int i = (count0 + count1 + count2); i < N; i++)
      arr[i] = 3;

    // print the sorted array
    System.out.println(Arrays.toString(arr));
  }

  // Driver Code
  public static void main(String[] args) {
    int arr[] = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = arr.length;
    sortArray(arr, N);
  }
}

Python3

# Python Program for the above approach
# function to sort the array having
# array elements only 0,1,2 and 3
def sortArray(arr, N):
    count0 = 0
    count1 = 0
    count2 = 0
    count3 = 0
    for i in range(N):
        if(arr[i] == 0):
            count0 += 1
        elif(arr[i] == 1):
            count1 += 1
        elif(arr[i] == 2):
            count2 += 1
        else:
            count3 += 1

    # Putting the 0's in the array in starting.
    for i in range(count0):
        arr[i] = 0

    # Putting the 1's in the array after the 0's.
    for i in range(count0, count0+count1):
        arr[i] = 1

    # Putting the 2's in the array after the 1's
    for i in range(count0+count1, count0+count1+count2):
        arr[i] = 2

    # Putting the 3's in the array after the 2's
    for i in range(count0+count1+count2, N):
        arr[i] = 3

    # print the sorted array
    for i in range(N):
        print(arr[i], end=" ")


# driver code to test above function
arr = [3, 2, 1, 0, 2, 3, 1, 0]
N = len(arr)
sortArray(arr, N)

Javascript

// JavaScript Program for the above approach
// function to sort the array having
// array elements only 0,1,2 and 3
function sortArray(arr, N){
    let count0 = 0;
    let count1 = 0;
    let count2 = 0;
    let count3 = 0;
    for(let i = 0; i<N; i++){
        if(arr[i] == 0) count0++;
        else if(arr[i] == 1) count1++;
        else if(arr[i] == 2) count2++;
        else count3++;
    }
    // Putting the 0's in the array in starting.
    for (let i = 0; i < count0; i++)
        arr[i] = 0;

    // Putting the 1's in the array after the 0's.
    for (let i = count0; i < (count0 + count1); i++)
        arr[i] = 1;

    // Putting the 2's in the array after the 1's
    for (let i = (count0 + count1); i < (count0 + count1 + count2); i++)
        arr[i] = 2;

    // Putting the 3's in the array after the 2's
    for (let i = (count0 + count1 + count2); i < N; i++)
        arr[i] = 3;
    // print the sorted array
    for(let i = 0; i<N; i++){
        console.log(arr[i] + " ");
    }
}

// driver code to test above function
let arr = [3, 2, 1, 0, 2, 3, 1, 0];
let N = arr.length;
sortArray(arr, N);

// THIS CODE IS CONTRIBUTED BY KIRTI AGARWAL(KIRTIAGARWAL23121999)

C#

using System;

class MainClass
{
// function to sort the array having
// array element only 0, 1, 2, and 3
static void SortArray(int[] arr, int N)
{
int count0 = 0;
int count1 = 0;
int count2 = 0;
int count3 = 0;
    // count the occurrence of each element in the array
    for (int i = 0; i < N; i++)
    {
        if (arr[i] == 0)
            count0++;
        else if (arr[i] == 1)
            count1++;
        else if (arr[i] == 2)
            count2++;
        else
            count3++;
    }

    // Put the 0's in the array at the beginning.
    for (int i = 0; i < count0; i++)
        arr[i] = 0;

    // Put the 1's in the array after the 0's.
    for (int i = count0; i < (count0 + count1); i++)
        arr[i] = 1;

    // Put the 2's in the array after the 1's.
    for (int i = (count0 + count1); i < (count0 + count1 + count2); i++)
        arr[i] = 2;

    // Put the 3's in the array after the 2's.
    for (int i = (count0 + count1 + count2); i < N; i++)
        arr[i] = 3;

    // print the sorted array
    Console.WriteLine(string.Join(", ", arr));
}

static void Main(string[] args)
{
    int[] arr = { 3, 2, 1, 0, 2, 3, 1, 0 };
    int N = arr.Length;
    SortArray(arr, N);
}
}

Output

0 0 1 1 2 2 3 3 

Time Complexity: O(N)
Auxiliary Space: O(1)