C Programming – HackerRank Solution | 2. CALCULATING π |

Write a Modular C Programming code to solve CALCULATING π hacker rank, So why calculate π? Because it’s easy and computers are good for exhaustive calculations.

In 1966 Donald G. Fink published a book entitled “Computers and the Human Mind”, which introduced the idea of artificial intelligence as it related to computers. One of the first problems he introduced to illustrate the utility of computers was the calculation of π. He posed the question as to why compute π to 100,000 decimal places when 30 decimal places suffice to calculate the circumference of the known universe? This estimate of 30 decimal places was made by astronomer Simon Newcomb (1835-1909). In 2006, Arndt & Haenel estimated that “39 digits of π are sufficient to calculate the volume of the universe to the nearest atom”.

So why calculate π? Because it’s easy and computers are good for exhaustive calculations.

Fink used a series of the following form:

π = 4/1 – 4/3 + 4/5 – 4/7 + 4/9 – 4/11 + 4/13…

Then goes on the say that using this formula to derive 100,000 decimal places of π would require 10to power of 100,000 terms. So many in fact that “shortcuts must be used even with a fast computer”. It was 1966, and computers were slow, and used punch cards!

He postulates that a speed-up comes by way of simple averaging.

Here’s a summary:

• sum of the first 98 terms = 3.131388 (too low)

• sum of the first 99 terms = 3.151693 (too high)

• sum of the first 100 terms = 3.131593 (too low)

• average of 98 and 99 term sums = 3.141541 (still too low)

• average of the 99 and 100 terms = 3.141643 (still too high)

• average of the two averages = 3.141592 (nearby value of π)

image

TASK:

Based on N terms, determine the average of the two averages i.e. ACCURATE VALUE OF π.

Input Format

N indicates the number of terms for series.

Constraints

100 <= N <=1000

For N = 150, the sum of the first 148 terms, sum of the first 149 terms, sum of the first 150 terms, and so on…

Output Format

Calculated accurate value of π.

Sample Input 0

100

Sample Output 0

Pi value = 3.141592

Sample Input 1

10

Sample Output 1

Not permitted to calculate

Refer : C Programming HackerRank all solutions for Loops | Arrays | strings

 

 

CODE:

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

void calculate(int n);
float pi_value_single(int n);
int main() {
    
    int n;
    scanf("%d",&n);
    if(n>=100 && n<=1000)
    {
     calculate(n);
    }
    else
    {
        printf("Not permitted to calculate");
    }
}
void calculate(int n)
{
    float pi_1,pi_2,pi_0,pi_avg_1,pi_avg_2,pi;
    int n1,n2;
    n1=n-1;
    n2=n-2;
    pi_0=pi_value_single(n);
    pi_1=pi_value_single(n1);
    pi_2=pi_value_single(n2);
    pi_avg_1=(pi_1+pi_2)/2;
    pi_avg_2=(pi_0+pi_1)/2;
    pi=(pi_avg_1+pi_avg_2)/2;
    printf("Pi value = %lf",pi);
}
float pi_value_single(int n)
{
    float i,j=1;
    float sum=0;
     for(i=1;i<=n;i++)
 {
   sum=sum+((4/j)*pow(-1,i-1)); 
     j=j+2;
 }
    return sum;
}

OUTPUT

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Input (stdin)

100
Your Output (stdout)

Pi value = 3.141592
Expected Output

Pi value = 3.141592

 

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