Algorithm

Problem Name: beecrowd | 2166

Problem Link: https://www.beecrowd.com.br/judge/en/problems/view/2166

Square Root of 2

 

By M.C. Pinto, UNILA BR Brazil

Timelimit: 1

The method of periodic continued fractions is one of the many ways to calculate the square root of a natural number. This method uses as denominator a repetition for fractions. This repetition can be done by a fixed number of times.

For example, by repeating 2 times the continued fraction to calculate the square root of 2, we have the following equation.

Your task is to calculate the approximate value of square root of 2 given the number N of repetitions.

 

Input

 

The input is a natural number N (0 ≤ N ≤ 100) that indicates the quantity of denominator repetitions in the continued fraction.

 

Output

 

The output is the approximate value of the square root with 10 decimal places.

 

 

 

Input Samples Output Samples

0

1.0000000000

 

 

 

1

1.5000000000

 

 

 

5

1.4142857143

 

Code Examples

#1 Code Example with C Programming

Code - C Programming


#include <stdio.h>

int main(void)
{
    int n;
    double ans=0.0;

    scanf("%i", &n);

    while (n)
    {
        ans+=2.0;
        ans=1.0/ans;
        --n;
    }

    ans+=1.0;

    printf("%.10lf\n", ans);
    return 0;
}
Copy The Code & Try With Live Editor

Output

x
–
+
cmd
1.0000000000

#2 Code Example with C++ Programming

Code - C++ Programming


#include <cmath>
#include <ios>
#include <iostream>

int main(){
    double n, sqrt2 = 1;
    int i, j;
    std::cin >> n;
    for(i = 1,j = 1;i  <  n;i++,j++) {
        sqrt2 += i + j / i; 
        if (i == 2) {
            j --;
        }
    }
    std::cout.precision(10);
    std::cout.setf(std::ios::fixed);
    std::cout << sqrt2 << std::endl;

    return 0;
}
Copy The Code & Try With Live Editor

Output

x
–
+
cmd
1.0000000000

#3 Code Example with Javascript Programming

Code - Javascript Programming


var input = require('fs').readFileSync('/dev/stdin', 'utf8');
var lines = input.split('\n');
var prompt = function(texto) { return lines.shift();};
const repetitions = parseInt(prompt());
var fraction = 0;
var SR2;


for (let i = 0; i  <  repetitions; i++) {
  fraction = 1 / (2 + fraction);
}

SR2 = 1 + fraction;
console.log(SR2.toFixed(10));
Copy The Code & Try With Live Editor

Output

x
–
+
cmd
1.0000000000

#4 Code Example with Python Programming

Code - Python Programming


def r2(n):
    if n == 0:
        return 2
    x = 2+1/r2(n-1)
    return x

n = int(input())
x = r2(n)-1
print('%.10f' % x)
Copy The Code & Try With Live Editor

Output

x
–
+
cmd
1.0000000000
Advertisements

Demonstration

Previous
#2165 Beecrowd Online Judge Solution 2165 Twitting Solution in C, C++, Java, Js and Python
Next
#2167 Beecrowd Online Judge Solution 2167 Engine Failure Solution in C, C++, Java, Js and Python