# RabbitFarm

### 2022-05-15

#### Happily Computing Prime Palindrome Numbers

The examples used here are from the weekly challenge problem statement and demonstrate the working solution.

## Part 1

Write a script to find all prime numbers less than 1000, which are also palindromes in base 10.

### Solution

``````
use strict;
use warnings;
use Math::Primality qw/is_prime/;

sub palindrome_primes_under{
my(\$n) = shift;
my @palindrome_primes;
{
\$n--;
unshift @palindrome_primes, \$n if(is_prime(\$n) && join("", reverse(split(//, \$n))) == \$n);
redo if \$n > 1;
}
return @palindrome_primes;
}

MAIN:{
print join(", ", palindrome_primes_under(1000));
}
``````

### Sample Run

``````
\$ perl perl/ch-1.pl
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929
``````

### Notes

I have become incorrigible in my use of `redo`! The novelty just hasn't worn off I suppose. There is nothing really wrong with it, of course, it's just not particularly modern convention what with it's vaguely `goto` like behavior. Anyway, there's not a whole lot to cover here. All the real work is done in the one line which tests both primality and, uh, palindromedary.

## Part 2

Write a script to find the first 8 Happy Numbers in base 10.

### Solution

``````
use strict;
use warnings;
use boolean;
use constant N => 8;

sub happy{
my \$n = shift;
my @seen;
my \$pdi = sub{
my \$n = shift;
my \$total = 0;
{
\$total += (\$n % 10)**2;
\$n = int(\$n / 10);
redo if \$n > 0;
}
return \$total;
};
{
push @seen, \$n;
\$n = \$pdi->(\$n);
redo if \$n > 1 && (grep {\$_ == \$n} @seen) == 0;
}
return boolean(\$n == 1);
}

MAIN:{
my \$i = 0;
my @happy;
{
\$i++;
push @happy, \$i if happy(\$i);
redo if @happy < N;
}
print join(", ", @happy) . "\n";
}
``````

### Sample Run

``````
\$ perl perl/ch-2.pl
1, 7, 10, 13, 19, 23, 28, 31
``````

### Notes

This solution has even more `redo`, huzzah! Again, fairly straightforward bit of code which follows the definitions. The happiness check is done using a perfect digit invariant (PDI) function, here rendered as an anonymous inner subroutine. A good chance here when looking at this code to remind ourselves that `\$n` inside that anonymous subroutine is in a different scope and does not effect the outer `\$n`!

## References

Challenge 164

posted at: 23:58 by: Adam Russell | path: /perl | permanent link to this entry

#### The Weekly Challenge 164 (Prolog Solutions)

The examples used here are from the weekly challenge problem statement and demonstrate the working solution.

## Part 1

Write a script to find all prime numbers less than 1000, which are also palindromes in base 10.

### Solution

``````
:-initialization(main).

palindrome(X):-
fd_labeling(X),
number_codes(X, C),
reverse(C, CR),
number_codes(X, CR).

palindrome_primes(N, PalindromePrimes, NumberPrimes):-
fd_labeling(NumberPrimes),
length(Primes, NumberPrimes),
fd_domain(Primes, 1, N),
fd_all_different(Primes),
maplist(palindrome, Primes),
maplist(fd_prime, Primes),
fd_labeling(Primes),
PalindromePrimes = Primes.

palindrome_primes(N, Primes):-
NP is N // 2,
fd_domain(NumberPrimes, 1, NP),
fd_maximize(palindrome_primes(N, Primes, NumberPrimes), NumberPrimes).

palindrome_prime(N, Prime):-
between(1, N, Prime),
palindrome(Prime),
fd_prime(Prime).

pp(_, _) --> [].
pp(N, Seen) --> [X], {palindrome_prime(N, X), \+ member(X, Seen)}, pp(N, [X|Seen]).

main:-
findall(Prime, palindrome_prime(1000, Prime), PalindromePrimes),
write(PalindromePrimes), nl.
``````

### Sample Run

``````
\$ gprolog --consult-file prolog/ch-1.p
[2,3,5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919,929]
| ?- phrase(pp(1000, []), PalindromePrimes).

PalindromePrimes = [] ? ;

PalindromePrimes =  ? ;

PalindromePrimes = [2,3] ? ;

PalindromePrimes = [2,3,5] ? ;

PalindromePrimes = [2,3,5,7] ? ;

PalindromePrimes = [2,3,5,7,11] ? ;

PalindromePrimes = [2,3,5,7,11,101] ? ;

PalindromePrimes = [2,3,5,7,11,101,131] ? ;

PalindromePrimes = [2,3,5,7,11,101,131,151] ? ;

PalindromePrimes = [2,3,5,7,11,101,131,151,181] ? ;

PalindromePrimes = [2,3,5,7,11,101,131,151,181,191] ? ;

PalindromePrimes = [2,3,5,7,11,101,131,151,181,191,313] ?
.
.
.
``````

### Notes

I experimented with a few different ways to generate Palindrome Primes. The quickest and most efficient way is what is used in `main/0`. Now, suppose we wanted to reason about lists of such numbers versus just generating them there is also a DCG option as shown which will generate or validate all possible lists of Palindrome Primes. Finally, there is the extremely inefficient method using constraints to maximize the size of the list of Palindrome Primes under 1000. This works! Now, does it work "well"? Absolutely not! This is not a very good method for performing the task and is many orders of magnitude slower than the other two. I will admit to an odd satisfaction to getting this unusual approach work, however.

## Part 2

Given a list of numbers, generate the skip summations.

### Solution

``````
:-initialization(main).

pdi(0, Total, Total).
pdi(N, Total_, Total):-
N_ is N // 10,
Total__ is Total_ + round(mod(N, 10) ** 2),
pdi(N_, Total__, Total).
pdi(N, Total):-
pdi(N, 0, Total).

happy(1, _).
happy(N, Seen):-
\+ member(N, Seen),
pdi(N, Total),!,
N_ is Total,
happy(N_, [N|Seen]).
happy(N):-
happy(N, []).

happy(_) --> [].
happy(Seen) --> [X], {between(1, 100, X), \+ member(X, Seen), happy(X)}, happy([X|Seen]).

main:-
length(Happy, 8),
phrase(happy([]), Happy),
write(Happy), nl.
``````

### Sample Run

``````
\$ gprolog --consult-file prolog/ch-2.p
[1,7,10,13,19,23,28,31]
``````

### Notes

As with the code in the first part I also implemented this as a DCG. Here a DCG is more practical since we are asked specifically to generate a list of the first 8 Happy Numbers. This is more of a "list reasoning" task than how the Palindrome Prime question was asked.

## References

Challenge 164

posted at: 23:58 by: Adam Russell | path: /prolog | permanent link to this entry