/*
Euler 55 in Picat.
http://projecteuler.net/problem=55
"""
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337
That is, 349 took three iterations to arrive at a palindrome.
Although no one has proved it yet, it is thought that some numbers, like 196,
never produce a palindrome. A number that never forms a palindrome through the reverse
and add process is called a Lychrel number. Due to the theoretical nature of these
numbers, and for the purpose of this problem, we shall assume that a number is Lychrel
until proven otherwise. In addition you are given that for every number below ten-thousand,
it will either
(i) become a palindrome in less than fifty iterations, or,
(ii) no one, with all the computing power that exists, has managed so far
to map it to a palindrome. In fact, 10677 is the first number to be shown to require
over fifty iterations before producing a palindrome: 4668731596684224866951378664
(53 iterations, 28-digits).
Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first
example is 4994.
How many Lychrel numbers are there below ten-thousand?
NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical
nature of Lychrel numbers.
"""
This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
See also my Picat page: http://www.hakank.org/picat/
*/
main => go.
go =>
Limit = 50,
Count = 0,
foreach(N in 1..9999,lychrel(N,Limit))
Count := Count + 1
end,
println(count=Count),
nl.
go2 =>
Limit = 50,
Lychrel = [],
foreach(N in 1..9999, lychrel(N,Limit))
Lychrel := Lychrel ++ [N]
end,
println(Lychrel),
nl.
go3 =>
Limit = 1000,
Lychrel = [],
foreach(N in 1..9999, lychrel(N,Limit))
Lychrel := Lychrel ++ [N]
end,
println(Lychrel),
println(Lychrel.length),
nl.
lychrel(N, Limit) =>
Count = 0,
Found = 0,
while (Found == 0, Count <= Limit)
Count := Count + 1,
N := reverse_and_add(N),
if palindromic(N) then
Found := 1
end
end,
Found == 0.
table
reverse_and_add(N) = M =>
L = number_chars(N),
L2 = reverse(L),
M := N + parse_term(L2).
table
palindromic(N) =>
L=number_chars(N),
L=reverse(L).