 # [QUIZ SOLUTION] Happy Numbers (#93)

Modified my first solution to make it thread safe.
Also include the solution for finding happiest between 1 and 1,000,000.

class Integer
def digits(base = 10)
return [self] if self < base
self.divmod(base).inject { |div, mod| div.digits(base) << mod }
end

def happy?(base = 10)
_happy?([], base)
end

protected

def _happy?(happy_list, base)
return false if happy_list.include?(self)
happy_list << self
return happy_list if self == 1
self.digits(base).inject(0) { |n, d| n + d*d }._happy?(happy_list, base)
end
end

# Find happiest between 1 and 1_000_000

···

#
# 1_000_000 is not the happiest. ( [1000000, 1] )
# So, all numbers <= 999_999 after first iteration
# will <= (9**2) * 6 ( = 486 )
#
# Also the rule to determine happy for number
# 123 is the same as 231, 321, 12300, 10230 ... etc
# So, for all 2 digits numbers, we only need to check 55 numbers,
# for all 3 digits numbers, we only need to check 220 numbers ... etc
#
# Here will not use this optimization, because the happiest does not
# so slow ( at least on my PC ) to find it ...

if __FILE__ == \$0

# find all happy numbers ( max happy rank ) between 1 .. (9**2)*6
rate = 1
list = 
max = (9**2) * 6
(1..max).each do |n|
happy = n.happy?
next unless happy
if happy.size == rate
list << n
elsif happy.size > rate
rate = happy.size
list = [n]
end
end

happiest = ((max+1)..1_000_000).each do |n|
break n if list.include?(n.digits.inject(0) { |sum, d| sum + d*d })
end

puts "the happiest number between 1 and 1,000,000 is #{happiest}"
p happiest.happy?
end