[QUIZ SOLUTION] Happy Numbers (#93) - happy bases

[Daniel Martin]

Here's my solution to find happy bases - note that I don't find any
happy bases (aside from 2 and 4) before I run out of memory, somewhere
near base 1700. It wouldn't surprise me if no other happy bases
exist.

The program checks up to 2*(base-1)*(base-1) for numbers that fall
into an infinite loop (that is not '1' forever) when applying the
digit-square-sum function. This is all that's needed, as it can
easily be shown that any number will eventually get less than that.

There's almost certainly some stuff I could do to be more parsimonious
with memory, chief among them finding a copy of narray that has the
mod! method. (I may revisit this and use a combination of div!, mul!
and sbt! to cut down on temporary arrays) However, this program as it
stands very quickly checks much farther out than I would have thought
necessary if there really were other happy bases out there to be
found.

#!/usr/bin/env ruby
require 'narray'

def dodigsum(base, initial)
tmp = initial / (base ** NArray.to_na([[0],[1],[2]]))
# I would use mod!, but my copy of narray doesn't have mod!
tmp = tmp % base
tmp.mul!(tmp)
initial.fill!(0).add!(tmp.sum(1))
end

def checkbase(base = 10)
base = base.to_i
checklimit = 2*(base-1)*(base-1)
check = NArray.int(checklimit + 1).indgen!
check_initial = check.dup

while true do
dodigsum(base,check)
if check.eq(check_initial).count_true > 2
#Gobs of debugging info
# lp = check.mul!(check.eq(check_initial)).mask(check.ge(2)).min
# puts "#{base} has a loop on #{lp}"
break
end
if check.le(1).count_true > checklimit
puts "#{base} is a happy base"
break
end
end
end

2.upto(3000) { |b|
begin
checkbase(b)
rescue Interrupt
puts "Checking #{b}"
checkbase(b)
rescue Error => e
puts "Bailing on #{b}"
raise e
end
}

__END__

 

[Daniel Martin]

And here's my narray-based solution to find the happiest number under
1_000_000 - it's not the shortest solution I've seen, but it's pretty
fast. It eliminates numbers that end up in loops by setting all
looping numbers to 0.

#!/usr/bin/env ruby
require 'narray'

def dodigsum(initial, base)
ndigits = (Math.log(initial.max)/Math.log(base)).ceil
tmp = initial / (base ** NArray.to_na((0...ndigits).map{|x|[x]}))
tmp = tmp % base
tmp.mul!(tmp)
initial.fill!(0).add!(tmp.sum(1))
end

limit = ARGV[0] || 1_000_000
base = ARGV[1] || 10

limit = limit.to_i
base = base.to_i

check = NArray.int(limit + 1).indgen!
check_initial = check.dup
check_initial[1] = 0
dodigsum(check, base)
checkp = check.dup

onemask = check.eq(1)
# onemask now contains the location of "0 order" happy numbers
order = 0
found_ex = nil
while (check.ge(2).count_true > 0) do
check.mul!(check.ne(check_initial))
check = check[checkp]
newmask = check.eq(1)
order = order + 1
if (not newmask == onemask)
found_ex = [newmask.gt(onemask).where.min, order]
end
onemask = newmask
end
puts "Happiest is #{found_ex[0]}, with happiness order #{found_ex[1]}"
__END__