# Find the last element after repeatedly removing every second element from either end alternately

Given an array **arr[]** consisting of **N** integers, the task is to find the last remaining array element after removing every second element, starting from the first and last alternately.

**Examples:**

Input:arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Output:8Explanation:Elements in the list are: 1 2 3 4 5 6 7 8 9 10

Starting fromfirstarray element, removing every second element from arr[] = {2.1,4,3,6,5,8,7,10} modifies arr[] to {2, 4, 6, 8, 10}.9,

Starting fromlastarray element, removing every second element from arr[] = {4,2,, 8,6modifies arr[] to {4, 8}.10}

Starting fromfirstarray element, removing every second element from arr[] = {8} modifies arr[] to {8}.4,

Therefore, the last remaining element in the array is8.

Input:arr[] = {2, 3, 5, 6}Output:3

**Naive Approach:** The simplest approach to solve this problem is to remove every second element in the array starting from the first and last indices alternately until the size of the array reduces to **1**. Print the last array element remaining after performing the given operations.

**Time Complexity:** O(N^{2})**Auxiliary Space:** O(1)

**Efficient Approach:** The above approach can also be optimized by an observation in the below illustration for **N = 20**:

The following observations can be made from the above illustration:

- Every time
**N/2**numbers are eliminated. - If the turn direction is from
**left to right**(→), the first element of the sequence changes to**(currentFirstElement + 2**.^{step – 1}) - If the turn direction is from
**right to left**(←) and then remaining numbers in the list are**odd**, the first element of the sequence changes to**(currentFirstElement + 2**.^{step – 1}) - After getting the final value of
**currentFirstElement**from the above steps, print the value as the remaining element in the sequence.

**Steps:**

- Initialize a variable, say
**leftTurn**, to check whether the element is to be deleted from the left or right. - Initialize variables
**remainElements**as**N**,**steps**as**1**, and**head**as**1**, to store the remaining element in the sequence, a number of steps performed, and the first element of the sequence. - Iterate until
**remainElements**is greater than**1**:- if the value of
**leftTurn**is**true**, then update the**head**as**(head + 2**. Otherwise, if the^{step – 1})**remainElement**is odd, then update the**head**as**(head + 2**.^{step – 1}) - Update the value of
**remainElement**as**remainElement/2**. - Update the
**steps**as**2 * steps**. - Toggle the
**leftTurn**to remove elements from the right.

- if the value of
- After completing the above steps, print the value at the index
**(head – 1)**as the remaining element.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the last element` `// remaining in the array after` `// performing the given operations` `void` `printLastElement(` `int` `arr[], ` `int` `N)` `{` ` ` `// Checks if traversal is from` ` ` `// left to right or vice versa` ` ` `bool` `leftTurn = ` `true` `;` ` ` `// Store the elements currently` ` ` `// present in the array` ` ` `int` `remainElements = N;` ` ` `// Store the distance between 2` ` ` `// consecutive array elements` ` ` `int` `step = 1;` ` ` `// Store the first element` ` ` `// of the remaining array` ` ` `int` `head = 1;` ` ` `// Iterate while elements` ` ` `// are greater than 1` ` ` `while` `(remainElements > 1) {` ` ` `// If left to right turn` ` ` `if` `(leftTurn) {` ` ` `// Update head` ` ` `head = head + step;` ` ` `}` ` ` `// Otherwise, check if the` ` ` `// remaining elements are odd` ` ` `else` `{` ` ` `// If true, update head` ` ` `if` `(remainElements % 2 == 1)` ` ` `head = head + step;` ` ` `}` ` ` `// Eleminate half of the array elements` ` ` `remainElements = remainElements / 2;` ` ` `// Double the steps after each turn` ` ` `step = step * 2;` ` ` `// Alter the turn` ` ` `leftTurn = !leftTurn;` ` ` `}` ` ` `// Print the remaining element` ` ` `cout << arr[head - 1];` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `arr[] = { 2, 3, 5, 6 };` ` ` `int` `N = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `printLastElement(arr, N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.lang.*;` `class` `GFG{` `// Function to find the last element` `// remaining in the array after` `// performing the given operations` `public` `static` `void` `printLastElement(` `int` `arr[], ` `int` `N)` `{` ` ` ` ` `// Checks if traversal is from` ` ` `// left to right or vice versa` ` ` `boolean` `leftTurn = ` `true` `;` ` ` `// Store the elements currently` ` ` `// present in the array` ` ` `int` `remainElements = N;` ` ` `// Store the distance between 2` ` ` `// consecutive array elements` ` ` `int` `step = ` `1` `;` ` ` `// Store the first element` ` ` `// of the remaining array` ` ` `int` `head = ` `1` `;` ` ` `// Iterate while elements` ` ` `// are greater than 1` ` ` `while` `(remainElements > ` `1` `)` ` ` `{` ` ` `// If left to right turn` ` ` `if` `(leftTurn)` ` ` `{` ` ` `// Update head` ` ` `head = head + step;` ` ` `}` ` ` `// Otherwise, check if the` ` ` `// remaining elements are odd` ` ` `else` ` ` `{` ` ` `// If true, update head` ` ` `if` `(remainElements % ` `2` `== ` `1` `)` ` ` `head = head + step;` ` ` `}` ` ` `// Eleminate half of the array elements` ` ` `remainElements = remainElements / ` `2` `;` ` ` `// Double the steps after each turn` ` ` `step = step * ` `2` `;` ` ` `// Alter the turn` ` ` `leftTurn = !leftTurn;` ` ` `}` ` ` `// Print the remaining element` ` ` `System.out.print( arr[head - ` `1` `]);` `}` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `[] arr = { ` `2` `, ` `3` `, ` `5` `, ` `6` `};` ` ` `int` `N = arr.length;` ` ` ` ` `printLastElement(arr, N);` `}` `}` `// This code is contributed by SoumikMondal` |

## Python3

`# Python3 program for the above approach` `# Function to find the last element` `# remaining in the array after` `# performing the given operations` `def` `printLastElement(arr, N):` ` ` `# Checks if traversal is from` ` ` `# left to right or vice versa` ` ` `leftTurn ` `=` `True` ` ` `# Store the elements currently` ` ` `# present in the array` ` ` `remainElements ` `=` `N` ` ` `# Store the distance between 2` ` ` `# consecutive array elements` ` ` `step ` `=` `1` ` ` `# Store the first element` ` ` `# of the remaining array` ` ` `head ` `=` `1` ` ` `# Iterate while elements` ` ` `# are greater than 1` ` ` `while` `(remainElements > ` `1` `):` ` ` `# If left to right turn` ` ` `if` `(leftTurn):` ` ` `# Update head` ` ` `head ` `=` `head ` `+` `step` ` ` `# Otherwise, check if the` ` ` `# remaining elements are odd` ` ` `else` `:` ` ` `# If true, update head` ` ` `if` `(remainElements ` `%` `2` `=` `=` `1` `):` ` ` `head ` `=` `head ` `+` `step` ` ` `# Eleminate half of the array elements` ` ` `remainElements ` `=` `remainElements ` `/` `/` `2` ` ` `# Double the steps after each turn` ` ` `step ` `=` `step ` `*` `2` ` ` `# Alter the turn` ` ` `leftTurn ` `=` `not` `leftTurn` ` ` `# Print the remaining element` ` ` `print` `(arr[head ` `-` `1` `])` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `arr ` `=` `[ ` `2` `, ` `3` `, ` `5` `, ` `6` `]` ` ` `N ` `=` `len` `(arr)` ` ` `printLastElement(arr, N)` `# This code is contributed by ukasp` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to find the last element` `// remaining in the array after` `// performing the given operations` `function` `printLastElement(arr, N)` `{` ` ` ` ` `// Checks if traversal is from` ` ` `// left to right or vice versa` ` ` `var` `leftTurn = ` `true` `;` ` ` `// Store the elements currently` ` ` `// present in the array` ` ` `var` `remainElements = N;` ` ` `// Store the distance between 2` ` ` `// consecutive array elements` ` ` `var` `step = 1;` ` ` `// Store the first element` ` ` `// of the remaining array` ` ` `var` `head = 1;` ` ` `// Iterate while elements` ` ` `// are greater than 1` ` ` `while` `(remainElements > 1)` ` ` `{` ` ` `// If left to right turn` ` ` `if` `(leftTurn)` ` ` `{` ` ` `// Update head` ` ` `head = head + step;` ` ` `}` ` ` `// Otherwise, check if the` ` ` `// remaining elements are odd` ` ` `else` ` ` `{` ` ` `// If true, update head` ` ` `if` `(remainElements % 2 == 1)` ` ` `head = head + step;` ` ` `}` ` ` `// Eleminate half of the array elements` ` ` `remainElements = remainElements / 2;` ` ` `// Double the steps after each turn` ` ` `step = step * 2;` ` ` `// Alter the turn` ` ` `leftTurn = !leftTurn;` ` ` `}` ` ` `// Print the remaining element` ` ` `document.write(arr[head - 1]);` `}` `// Driver code` `var` `arr = [ 2, 3, 5, 6 ];` `var` `N = arr.length;` ` ` `printLastElement(arr, N);` `// This code is contributed by Ankita saini` `</script>` |

## C#

`// C# program for the above approach` `using` `System;` `public` `class` `GFG{` ` ` ` ` `// Function to find the last element` `// remaining in the array after` `// performing the given operations` `public` `static` `void` `printLastElement(` `int` `[] arr, ` `int` `N)` `{` ` ` ` ` `// Checks if traversal is from` ` ` `// left to right or vice versa` ` ` `bool` `leftTurn = ` `true` `;` ` ` ` ` `// Store the elements currently` ` ` `// present in the array` ` ` `int` `remainElements = N;` ` ` ` ` `// Store the distance between 2` ` ` `// consecutive array elements` ` ` `int` `step = 1;` ` ` ` ` `// Store the first element` ` ` `// of the remaining array` ` ` `int` `head = 1;` ` ` ` ` `// Iterate while elements` ` ` `// are greater than 1` ` ` `while` `(remainElements > 1)` ` ` `{` ` ` ` ` `// If left to right turn` ` ` `if` `(leftTurn)` ` ` `{` ` ` ` ` `// Update head` ` ` `head = head + step;` ` ` `}` ` ` ` ` `// Otherwise, check if the` ` ` `// remaining elements are odd` ` ` `else` ` ` `{` ` ` ` ` `// If true, update head` ` ` `if` `(remainElements % 2 == 1)` ` ` `head = head + step;` ` ` `}` ` ` ` ` `// Eleminate half of the array elements` ` ` `remainElements = remainElements / 2;` ` ` ` ` `// Double the steps after each turn` ` ` `step = step * 2;` ` ` ` ` `// Alter the turn` ` ` `leftTurn = !leftTurn;` ` ` `}` ` ` ` ` `// Print the remaining element` ` ` `Console.Write( arr[head - 1]);` `}` ` ` `// Driver code` ` ` ` ` `static` `public` `void` `Main (){` ` ` `int` `[] arr = { 2, 3, 5, 6 };` ` ` `int` `N = arr.Length;` ` ` ` ` `printLastElement(arr, N);` ` ` `}` ` ` `}` `// This code is contributed by avanitrachhadiya2155` |

**Output:**

3

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