Reduce Array to Single Element with Given Operation in C++

Given an integer variable Number as input. Let us consider an array containing elements in the range 1 to Number in sorted order. If we perform an operation on an array such that at each step the elements at odd positions are removed. Then the goal is to perform this operation N number of times till only a single element is left. Print that element at the end.

Note-: The positioning of elements is such that the array at index 0 is at 1st position and so on.

Test Cases for Number of elements in array

Input Number=1, output = 1

Input Number=2, output = 2

Input Number=3, output = 2

Input Number=4, output = 4

Input Number=5, output = 4

Input Number=6, output = 4

Input Number=7, output = 4

......

Input Number=12, output = 8

Input Number=20, output = 16

Based on the above observation, for the range of numbers between 2ⁱ to 2ⁱ⁺¹-1 output will be 2ⁱ.

Examples

Input −Number=7

Output − The single element after reduction operation is : 4

Explanation − First element is at position 1 and so on.

The array will be [ 1 2 3 4 5 6 7 ]

After 1st Operation: [ 2 4 6 ]

After 2nd Operation: [ 4 ]

Input − Number=18

Output − The single element after reduction operation is : 4

Explanation − First element is at position 1 and so on.

The array will be [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ]

After 1st Operation: [ 2 4 6 8 10 12 14 16 18]

After 2nd Operation: [ 2 8 12 16 ]

After 3rd Operation: [ 8 16 ]

After 4th operation [ 16 ]

Approach used in the below program is as follows

In this approach we will use a while loop to calculate the end result based on the above formula. Take initial value as 2 and traverse till 2*result <= input number and double the value at each iteration.

• Take the input variable Number

• Function getsingleElement(long num) takes the input number and prints the result based on the above formula.

• Take a variable result.

• Initialize result with 2.

• Traverse using while loop till result*2<=num.

• Double result inside will.

• As soon as the while loop ends we will get the desired value.

• Return result.

• Print the result inside main.

Example

#include<bits/stdc++.h>
using namespace std;
long getsingleElement(long num){
   long result;
   result=2;
   while(result*2 <= num){
      result=result*2;
   }
   return result;
}
int main(){
   int Number = 20;
   cout<<"The single element after reduction operation is : "<<getsingleElement(Number) ;
   return 0;
}

Output

If we run the above code it will generate the following Output

The single element after reduction operation is : 16