# Sort a Rotated Sorted Array

You are given a rotated sorted array and your aim is to restore its original sort in place.

Expected to use O(1) extra space and O(n) time complexity.
Examples:

```Input : [3, 4, 1, 2]
Output : [1, 2, 3, 4]

Input : [2, 3, 4, 1]
Output : [1, 2, 3, 4]
```

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

We find the point of rotation. Then we rotate array using reversal algorithm.

``` 1. First find the split point where the sorting breaks.
2. Then call the reverse function in three steps.
- From zero index to split index.
- From split index to end index.
- From zero index to end index.
```

## C++

 `// C++ implementation for restoring original ` `// sort in rotated sorted array ` `#include ` `using` `namespace` `std; ` ` `  `// Function to restore the Original Sort ` `void` `restoreSortedArray(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(arr[i] > arr[i + 1]) { ` ` `  `            ``// In reverse(), the first parameter ` `            ``// is iterator to beginning element ` `            ``// and second parameter is iterator ` `            ``// to last element plus one.    ` `            ``reverse(arr, arr+i+1); ` `            ``reverse(arr + i + 1, arr + n); ` `            ``reverse(arr, arr + n); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to print the Array ` `void` `printArray(``int` `arr[], ``int` `size) ` `{ ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `// Driver function ` `int` `main() ` `{ ` `    ``int` `arr[] = { 3, 4, 5, 1, 2 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``restoreSortedArray(arr, n); ` `    ``printArray(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation for restoring original ` `// sort in rotated sorted array ` `class` `GFG  ` `{ ` ` `  `// Function to restore the Original Sort ` `static` `void` `restoreSortedArray(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``if` `(arr[i] > arr[i + ``1``])  ` `        ``{ ` ` `  `            ``// In reverse(), the first parameter ` `            ``// is iterator to beginning element ` `            ``// and second parameter is iterator ` `            ``// to last element plus one.  ` `            ``reverse(arr,``0``,i); ` `            ``reverse(arr , i + ``1``, n); ` `            ``reverse(arr,``0``, n); ` `        ``} ` `    ``} ` `} ` ` `  `static` `void` `reverse(``int``[] arr, ``int` `i, ``int` `j)  ` `{ ` `    ``int` `temp; ` `    ``while``(i < j) ` `    ``{ ` `        ``temp = arr[i]; ` `        ``arr[i] = arr[j]; ` `        ``arr[j] = temp; ` `        ``i++; ` `        ``j--; ` `    ``} ` `} ` ` `  `// Function to print the Array ` `static` `void` `printArray(``int` `arr[], ``int` `size) ` `{ ` `    ``for` `(``int` `i = ``0``; i < size; i++) ` `        ``System.out.print(arr[i] + ``" "``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``3``, ``4``, ``5``, ``1``, ``2` `}; ` `    ``int` `n = arr.length; ` `    ``restoreSortedArray(arr, n - ``1``); ` `    ``printArray(arr, n); ` `} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

## Python3

 `# Python implementation for restoring original ` `# sort in rotated sorted array ` ` `  `# Function to restore the Original Sort ` `def` `restoreSortedArray(arr, n): ` `    ``for` `i ``in` `range``(n): ` `        ``if` `(arr[i] > arr[i ``+` `1``]): ` `            ``# In reverse(), the first parameter ` `            ``# is iterator to beginning element ` `            ``# and second parameter is iterator ` `            ``# to last element plus one. ` `            ``reverse(arr, ``0``, i); ` `            ``reverse(arr, i ``+` `1``, n); ` `            ``reverse(arr, ``0``, n); ` ` `  `def` `reverse(arr, i, j): ` `    ``while` `(i < j): ` `        ``temp ``=` `arr[i]; ` `        ``arr[i] ``=` `arr[j]; ` `        ``arr[j] ``=` `temp; ` `        ``i ``+``=` `1``; ` `        ``j ``-``=` `1``; ` ` `  `# Function to prthe Array ` `def` `printArray(arr, size): ` `    ``for` `i ``in` `range``(size): ` `        ``print``(arr[i], end``=``""); ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``3``, ``4``, ``5``, ``1``, ``2``]; ` `    ``n ``=` `len``(arr); ` `    ``restoreSortedArray(arr, n ``-` `1``); ` `    ``printArray(arr, n); ` ` `  `# This code is contributed by 29AjayKumar `

## C#

 `// C# implementation for restoring original ` `// sort in rotated sorted array ` `using` `System; ` `     `  `class` `GFG  ` `{ ` ` `  `// Function to restore the Original Sort ` `static` `void` `restoreSortedArray(``int` `[]arr, ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``if` `(arr[i] > arr[i + 1])  ` `        ``{ ` ` `  `            ``// In reverse(), the first parameter ` `            ``// is iterator to beginning element ` `            ``// and second parameter is iterator ` `            ``// to last element plus one.  ` `            ``reverse(arr,0,i); ` `            ``reverse(arr , i + 1, n); ` `            ``reverse(arr,0, n); ` `        ``} ` `    ``} ` `} ` ` `  `static` `void` `reverse(``int``[] arr, ``int` `i, ``int` `j)  ` `{ ` `    ``int` `temp; ` `    ``while``(i < j) ` `    ``{ ` `        ``temp = arr[i]; ` `        ``arr[i] = arr[j]; ` `        ``arr[j] = temp; ` `        ``i++; ` `        ``j--; ` `    ``} ` `} ` ` `  `// Function to print the Array ` `static` `void` `printArray(``int` `[]arr, ``int` `size) ` `{ ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``Console.Write(arr[i] + ``" "``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int``[] arr = { 3, 4, 5, 1, 2 }; ` `    ``int` `n = arr.Length; ` `    ``restoreSortedArray(arr, n - 1); ` `    ``printArray(arr, n); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```1 2 3 4 5
```

We can binary search to find the rotation point as discussed here .

Efficient code approach using binary search:

1. First find the index of minimum element (split index) in the array using binary search
2. Then call the reverse function in three steps.
• From zero index to split index.
• From split index to end index.
• From zero index to end index.

## C++

 `// C++ implementation for restoring original  ` `// sort in rotated sorted array using binary search  ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Function to find start index of array ` `int` `findStartIndexOfArray(``int` `arr[], ``int` `low,``int` `high) ` `{ ` `    ``if` `(low>high) ` `    ``{ ` `        ``return` `-1; ` `    ``} ` ` `  `    ``if` `(low == high) ` `    ``{ ` `        ``return` `low; ` `    ``} ` ` `  `    ``int` `mid = low + (high-low)/2; ` `    ``if``(arr[mid] > arr[mid+1]) ` `        ``return` `mid+1; ` ` `  `    ``if``(arr[mid-1] > arr[mid]) ` `        ``return` `mid; ` ` `  `    ``if``(arr[low] > arr[mid]) ` `        ``return` `findStartIndexOfArray(arr, low, mid-1); ` `    ``else` `        ``return` `findStartIndexOfArray(arr, mid+1, high); ` `} ` ` `  `// Function to restore the Original Sort ` `void` `restoreSortedArray(``int` `arr[], ``int` `n) ` `{ ` `    ``// array is already sorted ` `    ``if` `(arr[0] < arr[n-1]) ` `        ``return``; ` `     `  `    ``int` `start = findStartIndexOfArray(arr, 0, n-1); ` `    ``// In reverse(), the first parameter ` `    ``// is iterator to beginning element ` `    ``// and second parameter is iterator ` `    ``// to last element plus one. ` `    ``reverse(arr, arr + start); ` `    ``reverse(arr + start, arr + n); ` `    ``reverse(arr, arr + n); ` `     `  `} ` ` `  `// Function to print the Array ` `void` `printArray(``int` `arr[], ``int` `size) ` `{ ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `// Driver function ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 4, 5}; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``restoreSortedArray(arr, n); ` `    ``printArray(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation for restoring original  ` `// sort in rotated sorted array using binary search  ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to find start index of array  ` `    ``static` `int` `findStartIndexOfArray(``int` `arr[],  ` `                            ``int` `low, ``int` `high) ` `    ``{ ` `        ``if` `(low > high)  ` `        ``{ ` `            ``return` `-``1``; ` `        ``} ` ` `  `        ``if` `(low == high) ` `        ``{ ` `            ``return` `low; ` `        ``} ` ` `  `        ``int` `mid = low + (high - low) / ``2``; ` `        ``if` `(arr[mid] > arr[mid + ``1``]) ` `        ``{ ` `            ``return` `mid + ``1``; ` `        ``} ` ` `  `        ``if` `(arr[mid - ``1``] > arr[mid])  ` `        ``{ ` `            ``return` `mid; ` `        ``} ` ` `  `        ``if` `(arr[low] > arr[mid]) ` `        ``{ ` `            ``return` `findStartIndexOfArray(arr, low, mid - ``1``); ` `        ``}  ` `        ``else` `        ``{ ` `            ``return` `findStartIndexOfArray(arr, mid + ``1``, high); ` `        ``} ` `    ``} ` ` `  `    ``// Function to restore the Original Sort  ` `    ``static` `void` `restoreSortedArray(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// array is already sorted  ` `        ``if` `(arr[``0``] < arr[n - ``1``])  ` `        ``{ ` `            ``return``; ` `        ``} ` ` `  `        ``int` `start = findStartIndexOfArray(arr, ``0``, n - ``1``); ` `         `  `        ``// In reverse(), the first parameter  ` `        ``// is iterator to beginning element  ` `        ``// and second parameter is iterator  ` `        ``// to last element plus one.  ` `        ``Arrays.sort(arr, ``0``, start); ` `        ``Arrays.sort(arr, start, n); ` `        ``Arrays.sort(arr); ` ` `  `    ``} ` ` `  `    ``// Function to print the Array  ` `    ``static` `void` `printArray(``int` `arr[], ``int` `size)  ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < size; i++)  ` `        ``{ ` `            ``System.out.print(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `arr[] = {``1``, ``2``, ``3``, ``4``, ``5``}; ` `        ``int` `n = arr.length; ` `        ``restoreSortedArray(arr, n); ` `        ``printArray(arr, n); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

## Python3

 `# Python3 implementation for restoring original  ` `# sort in rotated sorted array using binary search  ` ` `  `# Function to find start index of array ` `def` `findStartIndexOfArray(arr, low, high): ` `    ``if` `(low > high): ` `        ``return` `-``1``; ` `     `  `    ``if` `(low ``=``=` `high): ` `        ``return` `low; ` `     `  `    ``mid ``=` `low ``+` `(high ``-` `low) ``/` `2``; ` `    ``if` `(arr[mid] > arr[mid ``+` `1``]): ` `        ``return` `mid ``+` `1``; ` `     `  `    ``if` `(arr[mid ``-` `1``] > arr[mid]): ` `        ``return` `mid; ` `     `  `    ``if` `(arr[low] > arr[mid]): ` `        ``return` `findStartIndexOfArray(arr, low, mid ``-` `1``); ` `    ``else``: ` `        ``return` `findStartIndexOfArray(arr, mid ``+` `1``, high); ` ` `  `# Function to restore the Original Sort ` `def` `restoreSortedArray(arr, n): ` ` `  `    ``# array is already sorted ` `    ``if` `(arr[``0``] < arr[n ``-` `1``]): ` `        ``return``; ` `     `  `    ``start ``=` `findStartIndexOfArray(arr, ``0``, n ``-` `1``); ` ` `  `    ``# In reverse(), the first parameter ` `    ``# is iterator to beginning element ` `    ``# and second parameter is iterator ` `    ``# to last element plus one. ` `    ``reverse(arr, ``0``, start); ` `    ``reverse(arr, start, n); ` `    ``reverse(arr); ` ` `  `# Function to prthe Array ` `def` `printArray(arr, size): ` `    ``for` `i ``in` `range``(size): ` `        ``print``(arr[i], end``=``""); ` `     `  `def` `reverse(arr, i, j): ` `    ``while` `(i < j): ` `        ``temp ``=` `arr[i]; ` `        ``arr[i] ``=` `arr[j]; ` `        ``arr[j] ``=` `temp; ` `        ``i ``+``=` `1``; ` `        ``j ``-``=` `1``; ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5` `]; ` `    ``n ``=` `len``(arr); ` `    ``restoreSortedArray(arr, n); ` `    ``printArray(arr, n); ` ` `  `# This code is contributed by PrinciRaj1992 `

## C#

 `// C# implementation for restoring original  ` `// sort in rotated sorted array using binary search  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to find start index of array  ` `    ``static` `int` `findStartIndexOfArray(``int` `[]arr,  ` `                            ``int` `low, ``int` `high) ` `    ``{ ` `        ``if` `(low > high)  ` `        ``{ ` `            ``return` `-1; ` `        ``} ` ` `  `        ``if` `(low == high) ` `        ``{ ` `            ``return` `low; ` `        ``} ` ` `  `        ``int` `mid = low + (high - low) / 2; ` `        ``if` `(arr[mid] > arr[mid + 1]) ` `        ``{ ` `            ``return` `mid + 1; ` `        ``} ` ` `  `        ``if` `(arr[mid - 1] > arr[mid])  ` `        ``{ ` `            ``return` `mid; ` `        ``} ` ` `  `        ``if` `(arr[low] > arr[mid]) ` `        ``{ ` `            ``return` `findStartIndexOfArray(arr, low, mid - 1); ` `        ``}  ` `        ``else` `        ``{ ` `            ``return` `findStartIndexOfArray(arr, mid + 1, high); ` `        ``} ` `    ``} ` ` `  `    ``// Function to restore the Original Sort  ` `    ``static` `void` `restoreSortedArray(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``// array is already sorted  ` `        ``if` `(arr[0] < arr[n - 1])  ` `        ``{ ` `            ``return``; ` `        ``} ` ` `  `        ``int` `start = findStartIndexOfArray(arr, 0, n - 1); ` `         `  `        ``// In reverse(), the first parameter  ` `        ``// is iterator to beginning element  ` `        ``// and second parameter is iterator  ` `        ``// to last element plus one.  ` `        ``Array.Sort(arr, 0, start); ` `        ``Array.Sort(arr, start, n); ` `        ``Array.Sort(arr); ` ` `  `    ``} ` ` `  `    ``// Function to print the Array  ` `    ``static` `void` `printArray(``int` `[]arr, ``int` `size)  ` `    ``{ ` `        ``for` `(``int` `i = 0; i < size; i++)  ` `        ``{ ` `            ``Console.Write(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `[]arr = {1, 2, 3, 4, 5}; ` `        ``int` `n = arr.Length; ` `        ``restoreSortedArray(arr, n); ` `        ``printArray(arr, n); ` `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

```1 2 3 4 5
```

This article is contributed by Kshitiz Gupta.If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.