construct159.rb

def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

end

def seq(n)

	n1 = n
	l = [n1]
	while (n != 1)
		n = f2(n)
		l << n
	end 
	
	return l
end

def adj(ns)

	ns1 = ns.dup
	ns1[0, 1] = '10'
	
	ns2 = ns.dup
	ns2[0, 1] = '11'
	
	return ns1, ns2
end

def expand()
	l = [{'ns' => '1'}]

	20.times \
	{
		|i|
		l2 = []
		l.each \
		{
			|x|
			adj(x['ns']).each \
			{
				|x|
				
				n = x.to_i(2)
				l1 = seq(n)
				cg = l1.index { |x| x < l1[0] }
				cg = l1.size if (cg.nil?)
				l2 << {'ns' => x, 'l' => l1, 'cg' => cg, 'l1' => l1[i...cg]} if (cg >= x.length)
			}
		}
		l = l2
		$stderr.puts(l.map { |x| x['cg'] }.max)
	}
	return l
end

def out(a, fn)
	f = File.open(fn, 'w')
	f.puts('$dat << eof')

	a.sort_by { |k, v| v}.each { |k, v| f.puts([-k[0], k[1], Math.log(v)].join("\t")) }
	f.puts('eof')
	f.puts('plot $dat using 1:2:3 with point pt 5 linecolor palette')
	f.close
	$stderr.puts([fn, a.size].inspect)
end

l = expand()
$stderr.puts(l.size)


a = {}
a2 = {}

l.each_with_index \
{
	|x2, j|
	c = c2 = 0
	
	x2['l1'].reverse.each_with_index \
	{
		|x, i|
		c += [-1, 1][x % 2]
		c2 += [-1, 3][x % 2]
		a[[i, c]] = a.fetch([i, c], 0) + 1
		a2[[i, c2]] = a2.fetch([i, c2], 0) + 1
	}
}

out(a, 'gnuplot.cmd')
out(a2, 'gnuplot2.cmd')