Algorithm


Problem Name: beecrowd | 2159

Problem Link: https://www.beecrowd.com.br/judge/en/problems/view/2159

Approximate Number of Primes

 

By M.C. Pinto, UNILA BR Brazil

Timelimit: 1

Schoenfeld and Rosser published a paper in 1962 describing a minimum and a maximum value to the quantity of prime numbers up to n, for n ≥ 17. This quantity is represented by the function (n) and the inequality is shown below.

Your task is, given a natural number n, to compute the interval's minimum and maximum values to the approximate number of primes up to n.

 

Input

 

The input is a natural number n (17 ≤ n ≤ 109).

 

Output

 

The output is given as two values P and M with 1 decimal place each, such that P < (n) < M according to the given inequality above. These two values have one blank space between them.

 

 

 

Input Samples Output Samples

17

6.0 7.5

 

 

 

50

12.8 16.0

 

 

 

100

21.7 27.3

Code Examples

#1 Code Example with C Programming

Code - C Programming


#include <stdio.h>

int main()
{
    double n, ans1, ans2;
    scanf("%lf", &n);
    ans1 = n/log(n);
    ans2 = (1.25506)*(n/log(n));
    printf("%.1lf %.1lf\n", ans1, ans2);
    return 0;
}
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Input

x
+
cmd
17

Output

x
+
cmd
6.0 7.5

#2 Code Example with C++ Programming

Code - C++ Programming


#include<stdio.h>
#include<math.h>

int main()
{
    int n;
    double a,b;
    while(scanf("%d",&n)!=EOF){
    a=n/log(n);
    b=1.25506*n/log(n);
    printf("%.1lf %.1lf\n",a,b);
    }
    return 0;
}
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Input

x
+
cmd
17

Output

x
+
cmd
6.0 7.5

#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 N = parseInt(prompt());

var P = (N / Math.log(N)).toFixed(1);
var M = ((1.25506 * N) / Math.log(N)).toFixed(1);

console.log(P + " " + M);
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Input

x
+
cmd
17

Output

x
+
cmd
6.0 7.5
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