Find the last remaining element after repeated removal of an element from pairs of increasing adjacent array elements

• Last Updated : 01 Apr, 2021

Given an array arr[] consisting of N integers, the task is to print the last remaining array element after repeatedly selecting pairs of increasing adjacent elements (arr[i], arr[i + 1]) and removing any of the elements in the pair. If it is not possible to reduce the array to a single element, then print “Not Possible”.

Examples:

Input: arr[] = {3, 1, 2, 4}
Output: 4
Explanation:
Step 1: Choose a pair (1, 2) and remove 2 from it. Now the array becomes [3, 1, 4].
Step 2: Choose pair (1, 4) and remove 1 from it. Now the array becomes [3, 4].
Step 3: Choose pair (3, 4) and remove 3 from it. Now the array becomes .
Hence, the remaining element is 4.

Input: arr[] = {2, 3, 1}
Output: Not Possible

Approach: The given problem can be solved by observing the fact that if the first array element is less than the last array element, then all the elements between them can be removed by performing the given operations. Therefore, simply check if arr < arr[N – 1] or not. If found to be true, print either the first or last array element. Otherwise, print -1.

Below is the implementation of the above approach:

C++14

 // C++ program for the above approach#include using namespace std; // Function to print the last remaining// array element after after performing// given operationsvoid canArrayBeReduced(int arr[], int N){    // If size of the array is 1    if (N == 1) {        cout << arr;        return;    }     // Check for the condition    if (arr < arr[N - 1]) {        cout << arr[N - 1];    }     // If condition is not satisfied    else        cout << "Not Possible";} // Driver Codeint main(){    int arr[] = { 6, 5, 2, 4, 1, 3, 7 };    int N = sizeof(arr) / sizeof(arr);     // Function Call    canArrayBeReduced(arr, N);     return 0;}

Java

 // Java program for the above approachimport java.io.*;class GFG{   // Function to print the last remaining  // array element after after performing  // given operations  static void canArrayBeReduced(int[] arr, int N)  {     // If size of the array is 1    if (N == 1)    {      System.out.print(arr);      return;    }     // Check for the condition    if (arr < arr[N - 1])    {      System.out.print(arr[N - 1]);    }     // If condition is not satisfied    else      System.out.print("Not Possible");  }   // Driver Code  public static void main(String[] args)  {    int[] arr = { 6, 5, 2, 4, 1, 3, 7 };    int N = arr.length;     // Function Call    canArrayBeReduced(arr, N);  }} // This code is contributed by Dharanendra L V.

Python3

 # Python 3 program for the above approach # Function to print the last remaining# array element after after performing# given operationsdef canArrayBeReduced(arr,  N):     # If size of the array is 1    if (N == 1):        print(arr)        return     # Check for the condition    if (arr < arr[N - 1]):        print(arr[N - 1])     # If condition is not satisfied    else:        print("Not Possible")  # Driver Codeif __name__ == "__main__":     arr = [6, 5, 2, 4, 1, 3, 7]    N = len(arr)     # Function Call    canArrayBeReduced(arr, N)     # This code is contributed by chitranayal.

C#

 // C# program for the above approachusing System; public class GFG {   // Function to print the last remaining  // array element after after performing  // given operations  static void canArrayBeReduced(int[] arr, int N)  {     // If size of the array is 1    if (N == 1)    {      Console.Write(arr);      return;    }     // Check for the condition    if (arr < arr[N - 1])    {      Console.Write(arr[N - 1]);    }     // If condition is not satisfied    else      Console.Write("Not Possible");  }   // Driver Code  static public void Main()  {    int[] arr = { 6, 5, 2, 4, 1, 3, 7 };    int N = arr.Length;     // Function Call    canArrayBeReduced(arr, N);  }} // This code is contributed by Dharanendra L V.

Javascript


Output:
7

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

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