Program for Area Of Square after N-th fold

A square is a flat shape, in one plane, defined by four points at the four corners. A square has four sides all of equal length, and four corners, all right angles (90 degree angles). A square is a kind of rectangle. 
Given a square of side and number of folds . The task is to find the area of square after F-th fold.
The folding of square is as follows: 

1. In 1st folding, fold the square from left to right side in the form a triangle.
2. In 2nd folding, fold the square from up to down side.
3. In 3rd folding, again fold the square from left to right side.

Examples:

Input : N = 4, F = 2
Output : 2
Explanation: 
Initially square side is 4 x 4
After 1st folding, square side becomes 4 x 2
After 2nd folding, square side becomes 2 x 2
Thus area equals 2 x 2 = 4.

Input : N = 100, F = 6
Output : 156.25

Approach: 

• Initially calculate the area of the square before folding.
• After each folding, the area of square reduces by half. That is, area = area/2.
• So, we finally divide the area of square by pow(2, F)

Below is the implementation of above approach:

C++

// CPP program to find
// the area of the square
#include <bits/stdc++.h>
using namespace std;

// Function to calculate area of square after
// given number of folds
double areaSquare(double side, double fold)
{
    double area = side * side;

    return area * 1.0 / pow(2, fold);
}

// Driver Code
int main()
{
    double side = 4, fold = 2;

    cout << areaSquare(side, fold);

    return 0;
}

Java

// Java program to find the area of the square
class GFG
{

    // Function to calculate area of square
    // after given number of folds
    static double areaSquare(double side,
                            double fold)
    {
        double area = side * side;

        return area * 1.0 / Math.pow(2, fold);
    }

    // Driver Code
    public static void main(String []args)
    {
        double side = 4, fold = 2;

        System.out.println(areaSquare(side, fold));
    }
}

// This code is contributed
// by aishwarya.27

Python3

# Python3 program to find the area
# of the square

# Function to calculate area of
# square after given number of folds
def areaSquare(side, fold) :
        area = side * side
        ans = area / pow(2, fold)
        return ans

# Driver Code
if __name__ == "__main__" :

    side = 4
    fold = 2
    print(areaSquare(side, fold))

# This code is contributed by Ryuga

C#

// C# program to find the area of the square
using System;

class GFG
{

// Function to calculate area of square
// after given number of folds
static double areaSquare(double side,
                         double fold)
{
    double area = side * side;

    return area * 1.0 / Math.Pow(2, fold);
}

// Driver Code
public static void Main()
{
    double side = 4, fold = 2;

    Console.Write(areaSquare(side, fold));
}
}

// This code is contributed
// by Akanksha Rai

PHP

<?php
// PHP program to find the area of the square

// Function to calculate area of square
// after given number of folds
function areaSquare($side, $fold)
{
    $area = $side * $side;

    return $area * 1.0 / pow(2, $fold);
}

// Driver Code
$side = 4;
$fold = 2;
echo areaSquare($side, $fold);

// This code is contributed by ajit
?>

Javascript

<script>
// Javascript program to find
// the area of the square

// Function to calculate area of square after
// given number of folds
function areaSquare( side,  fold)
{
    var area = side * side;

    return (area * 1.0 )/ (Math.pow(2, fold));
}

// Driver Code
var side = 4, fold = 2;

    document.write(areaSquare(side, fold));

// This code is contributed by akshitsaxenaa09.
</script>

Output:

4

Time complexity : O(logn) 
Auxiliary Space : O(1)