RabbitFarm

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

Part 1

Write a script to generate first 5 Pandigital Numbers in base 10.

Solution

:-initialization(first_5_pandigitals).

pandigital(Pandigitals):-
    Digits = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
    Pandigitals = [A, B, C, D, E, F, G, H, I, J],
    fd_domain([A, B, C, D, E, F, G, H, I, J], Digits),
    A #= 1,
    B #= 0,
    fd_labeling(Pandigitals).

first_5_pandigitals:-
    setof(P, pandigital(P), Pandigitals),
    sort(Pandigitals, [A, B, C, D, E | _ ]),
    print_pandigitals([A, B, C, D, E]).

print_pandigitals([]).
print_pandigitals([H|T]):-
    maplist(number_codes, H, Codes), 
    flatten(Codes, DigitCodes), 
    number_codes(Number, DigitCodes),
    write(Number), nl,
    print_pandigitals(T). 

Sample Run

$ gplc prolog/ch-1.p 
$ prolog/ch-1   
1023456789
1023456798
1023456879
1023456897
1023456978

Notes

Rather than recursively iterate over numbers like in the Perl solution I instead use a bit of constraint programming to generate and test a large number of candidates. I then take only the first five as required. A bit of intuition, based on the definition, reduces the number of candidates generated: the first digit will clearly be a 1, the second a 0.

This runs pretty quickly, yet another testimonial to the design and implementation of GNU Prolog's FD solver. On my 2018 Mac Mini it ran to completion in about second. This is much faster than the brute force Perl solution which takes about 20s on the same machine.

Part 2

You are given 2 positive numbers, $m and $n. Write a script to generate multiplication table and display count of distinct terms.

Solution

:-initialization(main).

table(M, N, K):-
    between(1, M, I),
    between(1, N, J),
    K is I * J.

print_table(M, N, Distinct):-
    findall(K, table(M, N, K), Ks),
    setof(K, table(M, N, K), Distinct),
    print_header(M, N),
    print_seperator(M, N),
    print_rows(M, N, Ks),
    maplist(number_chars, Distinct, DistinctRow), 
    maplist(add_space, DistinctRow, DistinctSpaced),
    flatten(DistinctSpaced, DistinctSpacedFlattened),
    format("~nDistinct Terms: ~S~n", [DistinctSpacedFlattened]),
    length(Distinct, Count),
    format("Count: ~d ~n", [Count]).

print_rows(0, _, _).
print_rows(M, N, Products):-
    length(Row, N),
    append(Rest, Row, Products),
    M0 is M - 1,
    print_rows(M0, N, Rest),
    maplist(number_chars, Row, RowChars), 
    maplist(add_space, RowChars, CharsSpaced),
    flatten(CharsSpaced, CharsSpacedFlattened),
    format(" ~n  ~d | ~S ", [M, CharsSpacedFlattened]).

print_header(_, N):-
    format("  x | ", _),
    print_header(N).    
print_header(0).
print_header(N):-
    N0 is N - 1,
    print_header(N0),
    format("~d ", [N]). 

print_seperator(_, N):-
    format("~n  --+-", _),
    print_seperator(N).
print_seperator(0).
print_seperator(N):-
    N0 is N - 1,
    print_seperator(N0),
    format("~a", ['--']).

add_space(C, CS):-
    flatten(C, F),
    append(F, [' '], FS),
    atom_chars(A, FS),
    atom_chars(A, CS).       

main:-
    print_table(3, 3, _), nl, nl,
    print_table(3, 5, _),
    halt.

Sample Run

$ gplc prolog/ch-2.p
$ prolog/ch-2
  x | 1 2 3 
  --+------- 
  1 | 1 2 3   
  2 | 2 4 6   
  3 | 3 6 9  
Distinct Terms: 1 2 3 4 6 9 
Count: 6 


  x | 1 2 3 4 5 
  --+----------- 
  1 | 1 2 3 4 5   
  2 | 2 4 6 8 10   
  3 | 3 6 9 12 15  
Distinct Terms: 1 2 3 4 5 6 8 9 10 12 15 
Count: 11 

Notes

This was an interesting exercise in formatting output in Prolog! As can be seen, the vast majority of the code here is to format the table in the required way. I haven't ever done all that much with format/2, but it is quite versatile. As far as formatting output goes it provides a solid set of primitives in the spirit of C's printf that allow for us to do whatever we want, albeit with a bit of work.

The actual computation of the value takes no more than the first half dozen or so lines of code in table/3 and print_table/3.

References

Challenge 134

Pandigital Numbers

GNU Prolog format/2