# Find the Minimum length Unsorted Subarray, sorting

#### ByTử vi

Th1 7, 2023

Given an unsorted array arr[0..n-1] of size n, find the minimum length subarray arr[s..e] such that sorting this subarray makes the whole array sorted.
Examples:

1. If the input array is [10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60], your program should be able to find that the subarray lies between indexes 3 and 8.
2. If the input array is [0, 1, 15, 25, 6, 7, 30, 40, 50], your program should be able to find that the subarray lies between indexes 2 and 5.

Approach 1:

1. Find the candidate unsorted subarray
1. Scan from left to right and find the first element which is greater than the next element. Let be the index of such an element. In the above example 1, is 3 (index of 30).
2. Scan from right to left and find the first element (first in right to left order) which is smaller than the next element (next in right to left order). Let be the index of such an element. In the above example 1, e is 7 (index of 31).
2. Check whether sorting the candidate unsorted subarray makes the complete array sorted or not. If not, then include more elements in the subarray.
1. Find the minimum and maximum values in arr[s..e]. Let minimum and maximum values be min and maxmin and max for [30, 25, 40, 32, 31] are 25 and 40 respectively.
2. Find the first element (if there is any) in arr[0..s-1] which is greater than min, change to index of this element. There is no such element in above example 1.
3. Find the last element (if there is any) in arr[e+1..n-1] which is smaller than max, change to index of this element. In the above example 1, e is changed to 8 (index of 35)
3. Print and e.

`// C++ program to find the Minimum length Unsorted Subarray,`

`// sorting which makes the complete array sorted`

C++:

`#include<bits/stdc++.h>`

`using``namespace``std;`

`void``printUnsorted(``int``arr[], ``int``n)`

`{`

`int``s = 0, e = n-1, i, max, min;`

`// step 1(a) of above algo`

`for``(s = 0; s < n-1; s++)`

`{`

`    ``if``(arr[s] > arr[s+1])`

`    ``break``;`

`}`

`if``(s == n-1)`

`{`

`    ``cout << ``"The complete array is sorted"``;`

`    ``return``;`

`}`

`// step 1(b) of above algo`

`for``(e = n - 1; e > 0; e--)`

`{`

`    ``if``(arr[e] < arr[e-1])`

`    ``break``;`

`}`

`// step 2(a) of above algo`

`max = arr[s]; min = arr[s];`

`for``(i = s + 1; i <= e; i++)`

`{`

`    ``if``(arr[i] > max)`

`    ``max = arr[i];`

`    ``if``(arr[i] < min)`

`    ``min = arr[i];`

`}`

`// step 2(b) of above algo`

`for``( i = 0; i < s; i++)`

`{`

`    ``if``(arr[i] > min)`

`    ``{`

`    ``s = i;`

`    ``break``;`

`    ``}    `

`}`

`// step 2(c) of above algo`

`for``( i = n -1; i >= e+1; i--)`

`{`

`    ``if``(arr[i] < max)`

`    ``{`

`    ``e = i;`

`    ``break``;`

`    ``}`

`}`

`// step 3 of above algo`

`cout << ``"The unsorted subarray which"`

`     ``<< ``" makes the given array"``<< endl`

`     ``<< ``"sorted lies between the indices "`

`     ``<< s << ``" and "``<< e;`

`return``;`

`}`

`int``main()`

`{`

`    ``int``arr[] = {10, 12, 20, 30, 25,`

`                 ``40, 32, 31, 35, 50, 60};`

`    ``int``arr_size = ``sizeof``(arr)/``sizeof``(arr[0]);`

`    ``printUnsorted(arr, arr_size);`

`    ``getchar``();`

`    ``return``0;`

`}`

`// This code is contributed`

`// by Akanksha Rai`

Java:

`import``java.io.*;`

`class``Main`

`{`

`    ``static``void``printUnsorted(``int``arr[], ``int``n)`

`    ``{`

`      ``int``s = ``0``, e = n-``1``, i, max, min;  `

`      ``// step 1(a) of above algo`

`      ``for``(s = ``0``; s < n-``1``; s++)`

`      ``{`

`        ``if``(arr[s] > arr[s+``1``])`

`          ``break``;`

`      ``}`

`      ``if``(s == n-``1``)`

`      ``{`

`        ``System.out.println(``"The complete array is sorted"``);`

`        ``return``;`

`      ``}`

`      ``// step 1(b) of above algo`

`      ``for``(e = n - ``1``; e > ``0``; e--)`

`      ``{`

`        ``if``(arr[e] < arr[e-``1``])`

`          ``break``;`

`      ``}`

`      ``// step 2(a) of above algo`

`      ``max = arr[s]; min = arr[s];`

`      ``for``(i = s + ``1``; i <= e; i++)`

`      ``{`

`        ``if``(arr[i] > max)`

`          ``max = arr[i];`

`        ``if``(arr[i] < min)`

`          ``min = arr[i];`

`      ``}`

`      ``// step 2(b) of above algo`

`      ``for``( i = ``0``; i < s; i++)`

`      ``{`

`        ``if``(arr[i] > min)`

`        ``{ `

`          ``s = i;`

`          ``break``;`

`        ``}     `

`      ``}`

`      ``// step 2(c) of above algo`

`      ``for``( i = n -``1``; i >= e+``1``; i--)`

`      ``{`

`        ``if``(arr[i] < max)`

`        ``{`

`          ``e = i;`

`          ``break``;`

`        ``}`

`      ``} `

`      ``// step 3 of above algo`

`      ``System.out.println(``" The unsorted subarray which"``+`

`                         ``" makes the given array sorted lies"``+`

`                       ``"  between the indices "``+s+``" and "``+e);`

`      ``return``;`

`    ``}`

`    ``public``static``void``main(String args[])`

`    ``{`

`      ``int``arr[] = {``10``, ``12``, ``20``, ``30``, ``25``, ``40``, ``32``, ``31``, ``35``, ``50``, ``60``};`

`      ``int``arr_size = arr.length;`

`      ``printUnsorted(arr, arr_size);`

`    ``}`

`}`

PHP:

`<?php`

`// PHP program to find the Minimum length Unsorted Subarray,`

`// sorting which makes the complete array sorted`

`function``printUnsorted(&``\$arr``, ``\$n``)`

`{`

`    ``\$s``= 0;`

`    ``\$e``= ``\$n``- 1;`

`    ``// step 1(a) of above algo`

`    ``for``(``\$s``= 0; ``\$s``< ``\$n``- 1; ``\$s``++)`

`    ``{`

`        ``if``(``\$arr``[``\$s``] > ``\$arr``[``\$s``+ 1])`

`        ``break``;`

`    ``}`

`    ``if``(``\$s``== ``\$n``- 1)`

`    ``{`

`        ``echo``"The complete array is sorted"``;`

`        ``return``;`

`    ``}`

`    ``// step 1(b) of above algo`

`    ``for``(``\$e``= ``\$n``- 1; ``\$e``> 0; ``\$e``--)`

`    ``{`

`        ``if``(``\$arr``[``\$e``] < ``\$arr``[``\$e``- 1])`

`        ``break``;`

`    ``}`

`    ``// step 2(a) of above algo`

`    ``\$max``= ``\$arr``[``\$s``];`

`    ``\$min``= ``\$arr``[``\$s``];`

`    ``for``(``\$i``= ``\$s``+ 1; ``\$i``<= ``\$e``; ``\$i``++)`

`    ``{`

`        ``if``(``\$arr``[``\$i``] > ``\$max``)`

`            ``\$max``= ``\$arr``[``\$i``];`

`        ``if``(``\$arr``[``\$i``] < ``\$min``)`

`            ``\$min``= ``\$arr``[``\$i``];`

`    ``}`

`    ``// step 2(b) of above algo`

`    ``for``( ``\$i``= 0; ``\$i``< ``\$s``; ``\$i``++)`

`    ``{`

`        ``if``(``\$arr``[``\$i``] > ``\$min``)`

`        ``{`

`            ``\$s``= ``\$i``;`

`            ``break``;`

`        ``}    `

`    ``}`

`    ``// step 2(c) of above algo`

`    ``for``( ``\$i``= ``\$n``- 1; ``\$i``>= ``\$e``+ 1; ``\$i``--)`

`    ``{`

`        ``if``(``\$arr``[``\$i``] < ``\$max``)`

`        ``{`

`            ``\$e``= ``\$i``;`

`            ``break``;`

`        ``}`

`    ``}`

`    ``// step 3 of above algo`

`    ``echo``" The unsorted subarray which makes "``.`

`                     ``"the given array "``. ``"\n"``.`

`            ``" sorted lies between the indees "``.`

`                              ``\$s``. ``" and "``. ``\$e``;`

`    ``return``;`

`}`

`// Driver code`

`\$arr``= ``array``(10, 12, 20, 30, 25, 40,`

`             ``32, 31, 35, 50, 60);`

`\$arr_size``= sizeof(``\$arr``);`

`printUnsorted(``\$arr``, ``\$arr_size``);`

`// This code is contributed`

`// by ChitraNayal`

`?>`

Output:

```The unsorted subarray which makes the given array
sorted lies between the indices 3 and 8```

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

Please write comments if you find the above code/algorithm incorrect, or find better ways to solve the same problem.