ETOOBUSY ðŸš€ minimal blogging for the impatient
PWC133  Integer Square Root
TL;DR
Here we are with TASK #1 from The Weekly Challenge #133. Enjoy!
The challenge
You are given a positive integer
$N
.Write a script to calculate the integer square root of the given number.
Please avoid using builtin function. Find out more about it here.
Examples
Input: $N = 10 Output: 3 Input: $N = 27 Output: 5 Input: $N = 85 Output: 9 Input: $N = 101 Output: 10
The questions
Not much to ask for this challenge, as itâ€™s actually the gamification of some study. And I like both studying and games, so I can only thank our host here.
Were it an interview, though, Iâ€™d probably ask this:

how hard should we validate our inputs? Input validation is a good thing, but it might also imply a performance cost which might be avoided by doing proper validation only at the beginning of some data munging. Hence, it might be avoided if the function weâ€™re after will only be used on valid data.

what is the maximum value for the input
$N
? Very big numbers might imply the adoption of specific techniques; moreover itâ€™s good to test with a few values in that ballpark.
The solution
Speaking of validation, Raku basically gives it for free programmer time, so why not?
#!/usr/bin/env raku
use v6;
sub integersquareroot (Int:D $n where * >= 0) {
return $n if $n < 2;
my $x = $n +> 1; # first estimate
my $y = $x + 1; # just to get started with $x < $y
($x, $y) = (($x + ($n / $x).Int) +> 1, $x) while $x < $y;
return $y;
}
sub MAIN (Int:D $n where * >= 0) { put integersquareroot($n) }
I donâ€™t know about the performance hit of using incremental typing here, though.
Looking at the algorithm in C proposed here, itâ€™s easy to spot that
x0
is just a way to memorize the previous value that was calculated.
For this reason, I changed the variablesâ€™ names to reflect it: $x
evolves only in terms of itself, and $y
gets the previous value.
To get the ball rolling, $y
is arbitrarily initialized to be greater
than $x
. This ensures that the while
is triggered at least once,
giving $y
a proper value.
The same algorithm is also implemented in Perl:
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
sub integer_square_root ($n) {
return $n if $n < 2;
my $x = $n >> 1; # first estimate
my $y = $x + 1; # just to get started with $x < $y
($x, $y) = (($x + int($n / $x)) >> 1, $x) while $x < $y;
return $y;
}
say integer_square_root(shift // die "$0 <n>\n");
Here Iâ€™m giving up on input validation and only accounting for the user
forgetting to pass a value on the command line. For the rest, itâ€™s the
same as the Raku version, with due changes in the right places (e.g.
>>
instead of +>
, as well as int
instead of .Int
).
I considered putting a use integer
inside the function, but eventually
decided to avoid it for the explicit int(...)
 at the end of the day,
itâ€™s just one single place where I have to put it, so thereâ€™s little
space for getting this wrong.
I hope itâ€™s everything for this post because Iâ€™m closing it andâ€¦ wishing you to have a nice and safe day!