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# Minimum elements to be removed from the ends to make the array sorted

• Last Updated : 29 Apr, 2021

Given an array arr[] of length N, the task is to remove the minimum number of elements from the ends of the array to make the array non-decreasing. Elements can only be removed from the left or the right end.

Examples:

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Input: arr[] = {1, 2, 4, 1, 5}
Output:
We can’t make the array sorted after one removal.
But if we remove 2 elements from the right end, the
array becomes {1, 2, 4} which is sorted.
Input: arr[] = {3, 2, 1}
Output:

Approach: A very simple solution to this problem is to find the length of the longest non-decreasing subarray of the given array. Let’s say the length is L. So, the count of elements that need to be removed will be N – L. The length of the longest non-decreasing subarray can be easily found using the approach discussed in this article.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the minimum number``// of elements to be removed from the ends``// of the array to make it sorted``int` `findMin(``int``* arr, ``int` `n)``{` `    ``// To store the final answer``    ``int` `ans = 1;` `    ``// Two pointer loop``    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `j = i + 1;` `        ``// While the array is increasing increment j``        ``while` `(j < n and arr[j] >= arr[j - 1])``            ``j++;` `        ``// Updating the ans``        ``ans = max(ans, j - i);` `        ``// Updating the left pointer``        ``i = j - 1;``    ``}` `    ``// Returning the final answer``    ``return` `n - ans;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 3, 2, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``cout << findMin(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `    ``// Function to return the minimum number``    ``// of elements to be removed from the ends``    ``// of the array to make it sorted``    ``static` `int` `findMin(``int` `arr[], ``int` `n)``    ``{``    ` `        ``// To store the final answer``        ``int` `ans = ``1``;``    ` `        ``// Two pointer loop``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ``int` `j = i + ``1``;``    ` `            ``// While the array is increasing increment j``            ``while` `(j < n && arr[j] >= arr[j - ``1``])``                ``j++;``    ` `            ``// Updating the ans``            ``ans = Math.max(ans, j - i);``    ` `            ``// Updating the left pointer``            ``i = j - ``1``;``        ``}``    ` `        ``// Returning the final answer``        ``return` `n - ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `arr[] = { ``3``, ``2``, ``1` `};``        ``int` `n = arr.length;``        ``System.out.println(findMin(arr, n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the approach` `# Function to return the minimum number``# of elements to be removed from the ends``# of the array to make it sorted``def` `findMin(arr, n):` `    ``# To store the final answer``    ``ans ``=` `1` `    ``# Two pointer loop``    ``for` `i ``in` `range``(n):``        ``j ``=` `i ``+` `1` `        ``# While the array is increasing increment j``        ``while` `(j < n ``and` `arr[j] >``=` `arr[j ``-` `1``]):``            ``j ``+``=` `1` `        ``# Updating the ans``        ``ans ``=` `max``(ans, j ``-` `i)` `        ``# Updating the left pointer``        ``i ``=` `j ``-` `1` `    ``# Returning the final answer``    ``return` `n ``-` `ans` `# Driver code``arr ``=` `[``3``, ``2``, ``1``]``n ``=` `len``(arr)` `print``(findMin(arr, n))` `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``    ` `// Function to return the minimum number``// of elements to be removed from the ends``// of the array to make it sorted``static` `int` `findMin(``int` `[]arr, ``int` `n)``{` `    ``// To store the readonly answer``    ``int` `ans = 1;` `    ``// Two pointer loop``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``int` `j = i + 1;` `        ``// While the array is increasing increment j``        ``while` `(j < n && arr[j] >= arr[j - 1])``            ``j++;` `        ``// Updating the ans``        ``ans = Math.Max(ans, j - i);` `        ``// Updating the left pointer``        ``i = j - 1;``    ``}` `    ``// Returning the readonly answer``    ``return` `n - ans;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 3, 2, 1 };``    ``int` `n = arr.Length;``    ``Console.WriteLine(findMin(arr, n));``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`2`

Time Complexity: O(N )

Auxiliary Space: O(1)

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