Created
August 22, 2009 04:54
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# Project Euler - Problem 14 | |
# http://projecteuler.net/index.php?section=problems&id=14 | |
# | |
# The following iterative sequence is defined for the set of positive | |
# integers: | |
# | |
# n → n/2 (n is even) | |
# n → 3n + 1 (n is odd) | |
# | |
# Using the rule above and starting with 13, we generate the following | |
# sequence: | |
# 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 | |
# | |
# It can be seen that this sequence (starting at 13 and finishing at 1) | |
# contains 10 terms. Although it has not been proved yet (Collatz | |
# Problem), it is thought that all starting numbers finish at 1. | |
# | |
# Which starting number, under one million, produces the longest chain? | |
# | |
# NOTE: Once the chain starts the terms are allowed to go above one | |
# million. | |
@cache = { 1 => 1 } | |
def collatz_no_cache(n) | |
if n.odd? | |
collatz(3 * n + 1) | |
else | |
collatz(n / 2) | |
end | |
end | |
def collatz(n) | |
return @cache[n] if @cache.has_key? n | |
c = collatz_no_cache(n) + 1 | |
@cache[n] = c | |
end | |
max_l, max_n = 0, 0 | |
(1...1_000_000).each do |i| | |
l = collatz(i) | |
if l > max_l | |
max_l = l | |
max_n = i | |
end | |
end | |
puts "Answer: #{max_n}" |
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