/*
Euler #26 in Picat.
"""
A unit fraction contains 1 in the numerator. The decimal representation of the
unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be
seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle in
its decimal fraction part.
"""
This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
See also my Picat page: http://www.hakank.org/picat/
*/
main => go.
go => time(euler26). % , time(euler26b).
euler26 =>
MaxLen = 0,
MaxD = 0,
foreach (D in 2..999)
if prime(D) then
Len = get_rep_len(D),
if Len > MaxLen then
MaxLen := Len,
MaxD := D
end
end
end,
println([maxD=MaxD,maxLen=MaxLen]).
euler26b =>
M = [[get_rep_len(D),D]: D in 2..999, prime(D)].sort_down(),
writeln(M[1]).
%
% Get the length of the repeating cycle for 1/n
%
get_rep_len(I) = Len =>
FoundRemainders = [0 : _K in 1..I+1],
Value = 1,
Position = 1,
while (FoundRemainders[Value+1] == 0, Value != 0)
FoundRemainders[Value+1] := Position,
Value := Value*10,
Value := Value mod I,
Position := Position+1
end,
Len = Position-FoundRemainders[Value+1].