RabbitFarm

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

Part 1

You are given an array of unique numbers. Write a script to find out all missing numbers in the range 0..$n where $n is the array size.

Solution

missing_number(Numbers, Missing):-
    length(Numbers, NumbersLength),
    between(0, NumbersLength, Missing),
    \+ member(Missing, Numbers). 

Sample Run

$ gprolog --consult-file prolog/ch-1.p
| ?- missing_number([0, 1, 3], Missing).

Missing = 2 ? 

(1 ms) yes
| ?- missing_number([0, 1], Missing).   

Missing = 2

yes
| ?- 

Notes

missing_number/2 will only find one missing number at a time. In the examples that come with the original problem statement there is only ever one missing number. If multiple missing numbers are required backtracking with findall/3 is all you need!

Part 2

You are given an integer, $n > 0. Write a script to determine the number of ways of putting $n pennies in a row of piles of ascending heights from left to right.

Solution

sum(Coins):-
    sum([], Coins, 0).

sum(Coins, Coins, 5). 

sum(Partial, Coins, Sum):-   
    Sum < 5, 
    between(1, 5, X),
    S is Sum + X,
    sum([X | Partial], Coins, S).  

main:-
    findall(Coins, sum(Coins), C),
    maplist(msort, C, CS),
    sort(CS, CoinsSorted),
    write(CoinsSorted), nl,
    halt.  

Sample Run

$ gprolog --consult-file prolog/ch-2.p
| ?- main.
[[1,1,1,1,1],[1,1,1,2],[1,1,3],[1,2,2],[1,4],[2,3],[5]]

Notes

The approach here is the same that I used for the Coins Sum problem from TWC 075. The same as for the Perl solution to the same problem.

References

Challenge 201