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 by 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[0] -> arr[1], forms a sorted array {3, 4}.

Input: arr[] = {1, 3, 4, 2}
Output: 3

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[1] ? arr[2] ? … ? arr[N – 2] ? arr[N – 1] where N is the length of the remaining array and the 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, we keep decreasing the 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 <bits/stdc++.h>
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

Javascript

<script>

// Java Script program for above approach

// Function to find the minimum length
// of prefix required to be deleted
function findMinLength( arr)
{

    // Stores index to be returned
    let index = parseInt(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


    // Given arr[]
    let arr=  [ 7, 8, 5, 0, -1,
                 -1, 0, 1, 2, 3, 4 ];
    let n = arr.length;

    // Function call
    document.write(findMinLength(arr));
//contributed by sravan kumar
</script>

Output:

4

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