# Smallest prefix to be deleted such that remaining array can be rearranged to form a sorted array

Given an array arr[] consisting of N integers, the task is to find the minimum length of the prefix needed to be deleted such that the remaining array elements can be rearranged repeatedly selecting the first or the last element one by one to form a sorted array.

Examples:

Input: arr[] = {6, 5, 4, 3, 4}
Output: 3
Explanation:
To make an array sorted according to the given condition, remove the first 3 elements.
After deletion, the array arr[] is modified to {3, 4}.
From the array arr[], selecting the first elements one by one, i.e. arr -> arr, forms a sorted array {3, 4}.

Input: arr[] = {1, 3, 4, 2}
Output: 0
Explanation:
There is no need to delete any prefix.
By selecting array elements in the order arr -> arr -> arr -> arr, forms a sorted array {1, 2, 3, 4}.

Naive Approach: The simplest approach is to delete all possible lengths of the prefix from the given array and for every prefix, check if a sorted array can be formed from the remaining array elements by removal of those prefixes. If found to be true, then print the minimum length of the prefix deleted.

Time Complexity: O(N2)
Auxiliary Space: O(N)

Efficient Approach: The above approach can be optimized by observing that the resultant suffix must be of the form arr ≤ arr ≤ … ≥ arr[N – 2] ≥ arr[N – 1] where N is the length of the remaining array and suffix is of the maximum length. Follow the steps below:

• Initialize a variable index to N – 1.
• Traverse the array from the end and stop at the point where arr[index – 1] ≤ arr[index].
• As the iteration proceeds, keep decrementing answer.
• After completing all the above steps, print the value of the index which is the minimum length of the prefix that must be deleted.

Below is the implementation of the above approach:

## C++

 `// C++ program for above approach`   `#include ` `using` `namespace` `std;`   `// Function to find the minimum length` `// of prefix required to be deleted` `int` `findMinLength(vector<``int``>& arr)` `{` `    ``// Stores index to be returned` `    ``int` `index = (``int``)arr.size() - 1;`   `    ``// Iterate until previous element` `    ``// is <= current index` `    ``while` `(index > 0` `           ``&& arr[index] >= arr[index - 1]) {`   `        ``// Decrementing index` `        ``index--;` `    ``}`   `    ``// Return index` `    ``return` `index;` `}`   `// Driver Code` `int` `main()` `{`   `    ``// Given arr[]` `    ``vector<``int``> arr = { 7, 8, 5, 0, -1,` `                        ``-1, 0, 1, 2, 3, 4 };`   `    ``// Function Call` `    ``cout << findMinLength(arr);`   `    ``return` `0;` `}`

## Java

 `// Java program for above approach ` `import` `java.util.*;` `import` `java.io.*;`   `class` `GFG{` `     `  `// Function to find the minimum length ` `// of prefix required to be deleted ` `static` `int` `findMinLength(``int``[] arr) ` `{ ` `    `  `    ``// Stores index to be returned ` `    ``int` `index = (``int``)arr.length - ``1``; ` `  `  `    ``// Iterate until previous element ` `    ``// is <= current index ` `    ``while` `(index > ``0` `&& arr[index] >= ` `                        ``arr[index - ``1``])` `    ``{ ` `        `  `        ``// Decrementing index ` `        ``index--; ` `    ``} ` `  `  `    ``// Return index ` `    ``return` `index; ` `} `   `// Driver code` `public` `static` `void` `main(String args[]) ` `{ ` `    `  `    ``// Given arr[] ` `    ``int` `arr[]=  { ``7``, ``8``, ``5``, ``0``, -``1``, ` `                 ``-``1``, ``0``, ``1``, ``2``, ``3``, ``4` `};` `    ``int` `n = arr.length;` `    `  `    ``// Function call ` `    ``System.out.println(findMinLength(arr));` `} ` `}`   `// This code is contributed by bikram2001jha`

## Python3

 `# Python3 program for above approach`   `# Function to find the minimum length` `# of prefix required to be deleted` `def` `findMinLength(arr):` `  `  `    ``# Stores index to be returned` `    ``index ``=` `len``(arr) ``-` `1``;`   `    ``# Iterate until previous element` `    ``# is <= current index` `    ``while` `(index > ``0` `and` `arr[index] >``=` `arr[index ``-` `1``]):` `      `  `        ``# Decrementing index` `        ``index ``-``=` `1``;`   `    ``# Return index` `    ``return` `index;`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `  `  `    ``# Given arr` `    ``arr ``=` `[``7``, ``8``, ``5``, ``0``, ``-``1``, ` `           ``-``1``, ``0``, ``1``, ``2``, ``3``, ``4``];` `    ``n ``=` `len``(arr);`   `    ``# Function call` `    ``print``(findMinLength(arr));`   `# This code is contributed by Princi Singh`

## C#

 `// C# program for above approach ` `using` `System;`   `class` `GFG{` `     `  `// Function to find the minimum length ` `// of prefix required to be deleted ` `static` `int` `findMinLength(``int``[] arr) ` `{ ` `    `  `    ``// Stores index to be returned ` `    ``int` `index = (``int``)arr.Length - 1; ` `  `  `    ``// Iterate until previous element ` `    ``// is <= current index ` `    ``while` `(index > 0 && arr[index] >= ` `                        ``arr[index - 1])` `    ``{ ` `        `  `        ``// Decrementing index ` `        ``index--; ` `    ``} ` `    `  `    ``// Return index ` `    ``return` `index; ` `} `   `// Driver code` `public` `static` `void` `Main(String []args) ` `{ ` `    `  `    ``// Given []arr ` `    ``int` `[]arr =  { 7, 8, 5, 0, -1, ` `                  ``-1, 0, 1, 2, 3, 4 };` `                 `  `    ``int` `n = arr.Length;` `    `  `    ``// Function call ` `    ``Console.WriteLine(findMinLength(arr));` `} ` `}`   `// This code is contributed by Amit Katiyar`

Output:

```4

```

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

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