# Sort an array with swapping only with a special element is allowed

Given an array of length n + 1, containing elements 1 through n and a space, Requires the use of a given swap (index i, index j) function to sort the array, You can only swap the gap and a number, in the end, put the gap at the end.
There will be a number 999 in array as gap or space.
Examples:

Input  : arr = {1, 5, 4, 999, 3, 2}
Output : arr = {1, 2, 3, 4, 5, 999}
We need to sort only by moving

Input  : arr = {1, 5, 4, 3, 2, 8, 7, 999, 6}
Output : arr = {1, 2, 3, 4, 5, 6, 7, 8, 999}

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We follow a recursive approach to solve this problem. As we can only swap numbers with the space. First of all we find the index of space. If the index is start of array, then move this space to the second last index by swapping with each number in it’s right.
If space is neither start of array nor last element of array and element before it greater than the element next to space then do following.

Step 1: Swap space and element next to space
In case of {3, 999, 2} make it {3, 2, 999}

Step 2 : Swap space and greater element
eg-convert {3, 2, 999} to {999, 2, 3}

Otherwise, elements next to index are sorted and swap it with the previous element. Again call the sort function with size of array decreased by 1 and index of space – 1 as we will get one sorted element each time.

## C++

 // CPP program to sort an array by moving one // space around. #include using namespace std;    // n is total number of elements. // index is index of 999 or space. // k is number of elements yet to be sorted. void sortRec(int arr[], int index, int k, int n) {     // print the sorted array when loop reaches     // the base case     if (k == 0) {         for (int i = 1; i < n; i++)             cout << arr[i] << " ";         cout << 999;         return;     }        // else if k>0 and space is at 0th index swap     // each number with space and store index at     // second last index     else if (k > 0 && index == 0) {         index = n - 2;         for (int i = 1; i <= index; i++) {             arr[i - 1] = arr[i];         }         arr[index] = 999;     }        // if space is neither start of array nor last     // element of array and element before it greater     // than/ the element next to space     if (index - 1 >= 0 && index + 1 < n &&         arr[index - 1] > arr[index + 1]) {            // first swap space and element next to space         // in case of {3, 999, 2} make it {3, 2, 999}         swap(arr[index], arr[index + 1]);            // than swap space and greater element         // convert {3, 2, 999} to {999, 2, 3}         swap(arr[index - 1], arr[index + 1]);     }        else         swap(arr[index], arr[index - 1]);        sortRec(arr, index - 1, k - 1, n); }    // Wrapper over sortRec. void sort(int arr[], int n) {     // Find index of space (or 999)     int index = -1;     for (int i = 0; i < n; i++) {         if (arr[i] == 999) {             index = i;             break;         }     }        // Invalid input     if (index == -1)         return;        sortRec(arr, index, n, n); }       // driver program int main() {     int arr[] = { 3, 2, 999, 1 };     int n = sizeof(arr) / sizeof(arr[0]);     sort(arr, n);     return 0; }

## Java

 // Java program to sort an array by moving one  // space around.     class GFG {    // n is total number of elements.  // index is index of 999 or space.  // k is number of elements yet to be sorted.  static void sortRec(int arr[], int index, int k, int n)  {      // print the sorted array when loop reaches      // the base case      if (k == 0)     {          for (int i = 1; i < n; i++)                          System.out.print(arr[i] + " ");                  System.out.println(999);          return;      }         // else if k>0 and space is at 0th index swap      // each number with space and store index at      // second last index      else if (k > 0 && index == 0)     {          index = n - 2;          for (int i = 1; i <= index; i++)         {              arr[i - 1] = arr[i];          }          arr[index] = 999;      }         // if space is neither start of array nor last      // element of array and element before it greater      // than/ the element next to space      if (index - 1 >= 0 && index + 1 < n &&      arr[index - 1] > arr[index + 1])     {             // first swap space and element next to space          // in case of {3, 999, 2} make it {3, 2, 999}          swap(arr,index, index + 1);             // than swap space and greater element          // convert {3, 2, 999} to {999, 2, 3}          swap(arr,index - 1, index + 1);      }         else         swap(arr,index, index - 1);         sortRec(arr, index - 1, k - 1, n);  }     static int[] swap(int []arr, int i, int j) {     int temp = arr[i];     arr[i] = arr[j];     arr[j] = temp;     return arr; }    // Wrapper over sortRec.  static void sort(int arr[], int n)  {      // Find index of space (or 999)      int index = -1;      for (int i = 0; i < n; i++)     {          if (arr[i] == 999)         {              index = i;              break;          }      }         // Invalid input      if (index == -1)          return;         sortRec(arr, index, n, n);  }        // Driver code  public static void main(String[] args) {     int arr[] = { 3, 2, 999, 1 };      int n = arr.length;      sort(arr, n);  } }    // This code contributed by Rajput-Ji

## C#

 // C# program to sort an array by moving one  // space around.  using System;    class GFG  {     // n is total number of elements.  // index is index of 999 or space.  // k is number of elements yet to be sorted.  static void sortRec(int []arr, int index, int k, int n)  {      // print the sorted array when loop reaches      // the base case      if (k == 0)      {          for (int i = 1; i < n; i++)                          Console.Write(arr[i] + " ");                  Console.WriteLine(999);          return;      }         // else if k>0 and space is at 0th index swap      // each number with space and store index at      // second last index      else if (k > 0 && index == 0)      {          index = n - 2;          for (int i = 1; i <= index; i++)          {              arr[i - 1] = arr[i];          }          arr[index] = 999;      }         // if space is neither start of array nor last      // element of array and element before it greater      // than/ the element next to space      if (index - 1 >= 0 && index + 1 < n &&      arr[index - 1] > arr[index + 1])      {             // first swap space and element next to space          // in case of {3, 999, 2} make it {3, 2, 999}          swap(arr,index, index + 1);             // than swap space and greater element          // convert {3, 2, 999} to {999, 2, 3}          swap(arr,index - 1, index + 1);      }         else         swap(arr,index, index - 1);         sortRec(arr, index - 1, k - 1, n);  }     static int[] swap(int []arr, int i, int j)  {      int temp = arr[i];      arr[i] = arr[j];      arr[j] = temp;      return arr;  }     // Wrapper over sortRec.  static void sort(int []arr, int n)  {      // Find index of space (or 999)      int index = -1;      for (int i = 0; i < n; i++)      {          if (arr[i] == 999)          {              index = i;              break;          }      }         // Invalid input      if (index == -1)          return;         sortRec(arr, index, n, n);  }        // Driver code  public static void Main(String[] args)  {      int []arr = { 3, 2, 999, 1 };      int n = arr.Length;      sort(arr, n);  }  }     // This code has been contributed by 29AjayKumar

Output:

1 2 3 999

Time Complexity- O(n2)

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