# Sort an array of 0s, 1s and 2s (Simple Counting)

Given an array A[] consisting 0s, 1s and 2s, write a function that sorts A[]. The functions should put all 0s first, then all 1s and all 2s in last.

Examples:

```Input :  {0, 1, 2, 0, 1, 2}
Output : {0, 0, 1, 1, 2, 2}

Input :  {0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1}
Output : {0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2}```

Count the number of 0’s, 1’s and 2’s. After Counting, put all 0’s first, then 1’s and lastly 2’s in the array. We traverse the array two times. Time complexity will be O(n).

## C++

 `// Simple C++ program to sort an array of 0s 1s and 2s.` `#include ` `using` `namespace` `std;`   `void` `sort012(``int``* arr, ``int` `n)` `{` `    ``// Variables to maintain the count of 0's, 1's and 2's` `    ``// in the array` `    ``int` `count0 = 0, count1 = 0, count2 = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(arr[i] == 0)` `            ``count0++;` `        ``if` `(arr[i] == 1)` `            ``count1++;` `        ``if` `(arr[i] == 2)` `            ``count2++;` `    ``}`   `    ``// 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 < n; i++)` `        ``arr[i] = 2;`   `    ``return``;` `}`   `// Prints the array` `void` `printArray(``int``* arr, ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``cout << arr[i] << ``" "``;` `    ``cout << endl;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``sort012(arr, n);` `    ``printArray(arr, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## C

 `// Simple C program to sort an array of 0s 1s and 2s.` `#include `   `void` `sort012(``int``* arr, ``int` `n)` `{` `    ``// Variables to maintain the count of 0's, 1's and 2's` `    ``// in the array` `    ``int` `count0 = 0, count1 = 0, count2 = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(arr[i] == 0)` `            ``count0++;` `        ``if` `(arr[i] == 1)` `            ``count1++;` `        ``if` `(arr[i] == 2)` `            ``count2++;` `    ``}`   `    ``// 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 < n; i++)` `        ``arr[i] = 2;`   `    ``return``;` `}`   `// Prints the array` `void` `printArray(``int``* arr, ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``printf``(``"%d "``, arr[i]);` `    ``printf``(``"\n"``);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``sort012(arr, n);` `    ``printArray(arr, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// Simple Java program to sort an array of 0s 1s and 2s.` `import` `java.lang.*;` `import` `java.util.*;`   `public` `class` `GfG {`   `    ``public` `static` `void` `sort012(``int` `arr[], ``int` `n)` `    ``{` `        ``// Variables to maintain the count of 0's, 1's and` `        ``// 2's in the array` `        ``int` `count0 = ``0``, count1 = ``0``;` `        ``int` `count2 = ``0``;` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``if` `(arr[i] == ``0``)` `                ``count0++;` `            ``if` `(arr[i] == ``1``)` `                ``count1++;` `            ``if` `(arr[i] == ``2``)` `                ``count2++;` `        ``}`   `        ``// 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 < n; i++)` `            ``arr[i] = ``2``;`   `        ``printArray(arr, n);` `    ``}`   `    ``// Prints the array` `    ``public` `static` `void` `printArray(``int` `arr[], ``int` `n)` `    ``{` `        ``for` `(``int` `i = ``0``; i < n; i++)` `            ``System.out.print(arr[i] + ``" "``);` `        ``System.out.println();` `    ``}`   `    ``// Driver function` `    ``public` `static` `void` `main(String args[])` `    ``{`   `        ``int` `arr[] = { ``0``, ``1``, ``1``, ``0``, ``1``, ``2``, ``1``, ``2``, ``0``, ``0``, ``0``, ``1` `};` `        ``int` `n = ``12``;` `        ``sort012(arr, n);` `    ``}` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Python3

 `# Python C++ program to sort an array of 0s` `# 1s and 2s.` `import` `math`   `def` `sort012(arr, n):`   `    ``# Variables to maintain the count of 0's, ` `    ``# 1's and 2's in the array` `    ``count0 ``=` `0` `    ``count1 ``=` `0` `    ``count2 ``=` `0` `    ``for` `i ``in` `range``(``0``,n):` `        ``if` `(arr[i] ``=``=` `0``):` `            ``count0``=``count0``+``1` `        ``if` `(arr[i] ``=``=` `1``):` `            ``count1``=``count1``+``1` `        ``if` `(arr[i] ``=``=` `2``):` `            ``count2``=``count2``+``1` `    `    `    ``# Putting the 0's in the array in starting.` `    ``for` `i ``in` `range``(``0``,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),n) :` `        ``arr[i] ``=` `2` `    `  `    ``return`     `# Prints the array` `def` `printArray( arr,  n):`   `    ``for` `i ``in` `range``(``0``,n):` `        ``print``( arr[i] , end``=``" "``)` `    ``print``()`     `# Driver code` `arr ``=` `[ ``0``, ``1``, ``1``, ``0``, ``1``, ``2``, ``1``, ``2``, ``0``, ``0``, ``0``, ``1` `]` `n ``=` `len``(arr)` `sort012(arr, n)` `printArray(arr, n)`   `# This code is contributed by Gitanjali.`

## C#

 `// Simple C# program` `// to sort an array of 0s` `// 1s and 2s.` `using` `System;`   `public` `class` `GfG{`   `    ``public` `static` `void` `sort012(``int` `[]arr, ``int` `n)` `    ``{` `        ``// Variables to maintain` `        ``// the count of 0's, ` `        ``// 1's and 2's in the array` `        ``int` `count0 = 0, count1 = 0;` `        ``int` `count2 = 0;` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``if` `(arr[i] == 0)` `                ``count0++;` `            ``if` `(arr[i] == 1)` `                ``count1++;` `            ``if` `(arr[i] == 2)` `                ``count2++;` `        ``}` `    `  `        ``// 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 < n; i++) ` `            ``arr[i] = 2;` `    `  `        ``printArray(arr, n);` `    ``}` `    `  `    ``// Prints the array` `    ``public` `static` `void` `printArray(``int` `[]arr, ``int` `n)` `    ``{` `        ``for` `(``int` `i = 0; i < n; i++)` `            ``Console.Write(arr[i] + ``" "``);` `        ``Console.WriteLine();` `    ``}` `    `  `    ``// Driver function ` `    ``public` `static` `void` `Main()` `    ``{` `    `  `        ``int` `[]arr = { 0, 1, 1, 0, 1, 2, 1,` `                    ``2, 0, 0, 0, 1 };` `        ``int` `n = 12;` `        ``sort012(arr, n);` `    ``}` `}`   `// This code is contributed by vt_m`

## Javascript

 ``

Output

`0 0 0 0 0 1 1 1 1 1 2 2 `

Time Complexity: O(n)

Auxiliary Space: O(1)
Problems with the above solution.:

1. It requires two traversals of array.
2. This solution may not work if values are a part of the structure. For example, consider a situation where 0 represents Computer Science Stream, 1 represents Electronics and 2 represents Mechanical. We have a list of student objects (or structures) and we want to sort them. We cannot use the above sort as we simply put 0s, 1s, and 2s one by one.

Another Approach:

## C++

 `// C++ program ` `#include ` `using` `namespace` `std;` `// Example` `//` `// input = [0, 1, 2, 2, 0, 0]` `// output = [0, 0, 0, 1, 2, 2]`   `int` `main() {` `    `  `    ``vector<``int``> inputArray={0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1};` `    ``vector<``int``> outputArray;` `    ``int` `indexOfOne = 0;` `    ``for``(``int` `item: inputArray)` `    ``{` `        ``if``(item==2)` `        ``{   outputArray.push_back(item);` `        ``}` `        ``else` `if``(item==1)` `        ``{   outputArray.insert(outputArray.begin() + indexOfOne, item);` `            ``indexOfOne+=1;` `        ``}` `        ``else` `if``(item==0)` `        ``{   outputArray.insert(outputArray.begin(), item);` `            ``indexOfOne+=1;` `        ``}` `        ``else` `        ``{   cout<<``" wrong value - Aborting "``;` `            ``continue``;` `        ``}` `    ``}` `    `  `    ``for``(``int` `i=0;i

## Java

 `import` `java.util.ArrayList;` `import` `java.util.List;`   `// Example` `//` `// input = [0, 1, 2, 2, 0, 0]` `// output = [0, 0, 0, 1, 2, 2]` `class` `GFG {` `    ``static` `int``[] inputArray = { ``0``, ``1``, ``1``, ``0``, ``1``, ``2``, ``1``, ``2``, ``0``, ``0``, ``0``, ``1` `};` `    ``static` `List outputArray = ``new` `ArrayList<>();` `    ``static` `int` `indexOfOne = ``0``;`   `    ``static` `void` `print() {` `        ``for` `(``int` `item : inputArray)` `            ``if` `(item == ``2``)` `                ``outputArray.add(item);` `            ``else` `if` `(item == ``1``) {` `                ``outputArray.add(indexOfOne, item);` `                ``indexOfOne += ``1``;` `            ``} ``else` `if` `(item == ``0``) {` `                ``outputArray.add(``0``, item);` `                ``indexOfOne += ``1``;` `            ``} ``else` `{` `                ``System.out.println(``" wrong value - Aborting "``);` `                ``continue``;` `            ``}` `    ``}`   `    ``public` `static` `void` `main(String[] args) {` `        ``print();` `        ``for` `(``int` `item : outputArray)` `            ``System.out.print(item+``", "``);` `    ``}` `}` `// This code is contributed by Amit Katiyar`

## Python3

 `# Example` `#` `# input = [0, 1, 2, 2, 0, 0]` `# output = [0, 0, 0, 1, 2, 2]`   `inputArray ``=` `[``0``, ``1``, ``1``, ``0``, ``1``, ``2``, ``1``, ``2``, ``0``, ``0``, ``0``, ``1``]` `outputArray ``=` `[]` `indexOfOne ``=` `0` `for` `item ``in` `inputArray:` `    ``if` `item ``=``=` `2``:` `        ``outputArray.append(item)` `    ``elif` `item ``=``=` `1``:` `        ``outputArray.insert(indexOfOne, item)` `        ``indexOfOne ``+``=` `1` `    ``elif` `item ``=``=` `0``:` `        ``outputArray.insert(``0``, item)` `        ``indexOfOne ``+``=` `1` `    ``else``:` `        ``print``(``" wrong value - Aborting "``)` `        ``continue` `print``(outputArray)`

## C#

 `using` `System;` `using` `System.Collections.Generic;`   `// Example` `//` `// input = [0, 1, 2, 2, 0, 0]` `// output = [0, 0, 0, 1, 2, 2]`   `class` `GFG{` `    `  `static` `int``[] inputArray = { 0, 1, 1, 0, 1, 2, ` `                            ``1, 2, 0, 0, 0, 1 };` `static` `List<``int``> outputArray = ``new` `List<``int``>();` `static` `int` `indexOfOne = 0;`   `static` `void` `print() ` `{` `    ``foreach` `(``int` `item ``in` `inputArray)` `        ``if` `(item == 2)` `            ``outputArray.Add(item);` `        ``else` `if` `(item == 1) ` `        ``{` `            ``outputArray.Insert(indexOfOne, item);` `            ``indexOfOne += 1;` `        ``}` `        ``else` `if` `(item == 0) ` `        ``{` `            ``outputArray.Insert(0, item);` `            ``indexOfOne += 1;` `        ``} ` `        ``else` `        ``{` `            ``Console.WriteLine(``" wrong value - Aborting "``);` `            ``continue``;` `        ``}` `}`   `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `    ``print();` `    ``foreach``(``int` `item ``in` `outputArray)` `        ``Console.Write(item + ``", "``);` `}` `}`   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, `

Time Complexity: O(n)

Auxiliary Space: O(1)

Optimal Solution that handles above issues :
Sort an array of 0s, 1s and 2s (Dutch National Flag Algorithm)

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