RabbitFarm

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

Part 1

You are given a list of integers, @list. Write a script to find the total pairs in the sorted list where 2 consecutive elements has the max gap. If the list contains less then 2 elements then return 0.

Solution

largest_gap(Numbers, LargestGap):-
    largest_gap(Numbers, -1, LargestGap).  
largest_gap([], LargestGap, LargestGap).  
largest_gap([_|[]], LargestGap, LargestGap).  
largest_gap([A, B|Numbers], Gap, LargestGap):-
    G is B - A,
    (G > Gap, largest_gap([B|Numbers], G, LargestGap));
    largest_gap([B|Numbers], Gap, LargestGap).

gap_pairs(Numbers, GapPairs):-
    length(Numbers, L),
    L =< 2,
    GapPairs = 0.
gap_pairs(Numbers, GapPairs):-
    length(Numbers, L),
    L > 2, 
    largest_gap(Numbers, LargestGap),
    gap_pairs(Numbers, LargestGap, 0, GapPairs).
gap_pairs([], _, GapPairs, GapPairs).
gap_pairs([_|[]], _, GapPairs, GapPairs).
gap_pairs([A, B|Numbers], LargestGap, Pairs, GapPairs):-
    LargestGap #= B - A,
    succ(Pairs, P),
    gap_pairs([B|Numbers], LargestGap, P, GapPairs).
gap_pairs([A, B|Numbers], LargestGap, Pairs, GapPairs):-
    LargestGap #\= B - A,
    gap_pairs([B|Numbers], LargestGap, Pairs, GapPairs). 

Sample Run

$ gprolog --consult-file prolog/ch-1.p
| ?- gap_pairs([3], Pairs).

Pairs = 0 ? 

(1 ms) yes
| ?- gap_pairs([2, 5, 8, 1], Pairs).

Pairs = 2 ? 

yes
| ?- 

Notes

At first glance this code may look more complex than it really is. All we are doing is , first, computing the largest gap between any two adjacent numbers. Then, second, seeing which pairs have exactly this gap.

Part 2

You are given an integer $n > 0. Write a script to print the count of primes less than $n.

Solution

primes_under_n(N, NumberPrimes):-
    findall(Prime, (between(2, N, I), fd_prime(I), Prime = I), Primes),
    length(Primes, NumberPrimes).  

Sample Run

$ gprolog --consult-file prolog/ch-2.p
| ?- primes_under_n(10, Primes).

Primes = 4

yes
| ?- primes_under_n(15, Primes).

Primes = 6

yes
| ?- primes_under_n(1, Primes). 

Primes = 0

yes
| ?- primes_under_n(25, Primes).

Primes = 9

yes

Notes

This solution is short and sweet! No reason or the writeup to be longer than the code itself, right?

References

Challenge 198