#+title: Challenge 133
#+date: 2021-10-04
#+html_link_up: ../
#+export_file_name: index
#+options: toc:nil
#+setupfile: ~/.emacs.d/org-templates/level-2.org

* Task 1 - Integer Square Root

You are given a positive integer ~$N~.

Write a script to calculate the integer square root of the given number.

Please avoid using built-in function. Find out more about it [[https://en.wikipedia.org/wiki/Integer_square_root][here]].

#+begin_src
Input: $N = 10
Output: 3

Input: $N = 27
Output: 5

Input: $N = 85
Output: 9

Input: $N = 101
Output: 10
#+end_src

** Raku

- Program: [[file:raku/ch-1.raku]]

Initial estimate is set to ~$n +> 1~, then we loop infinitely until
previous 2 estimates are equal.

#+begin_src raku
my $x = $n +> 1;
loop {
    given ($x + ($n / $x)) / 2 {
        last if $x == $_;
        $x = $_;
    }
}
put $x;
#+end_src

** C

- Program: [[file:c/ch-1.c]]

~argv~ holds the input & ~argc~ holds the number of inputs. The input should
be a single integer so ~argc~ should be equal to 2. After checking for
that, we check if valid value was passed.

Loop until previous 2 estimates are equal.

#+begin_src c
double x = num >> 1;
for (;;) {
    double x_next = (x + (num / x)) / 2;
    if (x == x_next)
        break;
    x = x_next;
 }
printf("%f\n", x);
#+end_src