backtrack3.rb

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

end

def dense(w, d)
	w2 = w - 1
	
	a = (0...w2).to_a
	s = '0' * w2
	(1..(d * w - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' }
	return ('1' + s)
	
end

def lenx(ns, p)
	l = ns.split(p)
	l = [] if (l.nil?)
	l.shift if (l[0] == '')
	return l.map { |x| x.length }
end

def len01x(ns)
	return lenx(ns, /0+/), lenx(ns, /1+/)
end

def mx01x(ns)
	l1, l0 = len01x(ns)
	return (l1 + l0).max
end

def add(l, mxp, n, x)

	p = (n % 2).to_s + x['p']
	
	return if (mx01x(p) >= mxp)
	
	
	w = n.to_s(2).length

	l1 = [n] + x['l']

	c = x['c'] + (n.even? ? 1 : 0)
	l << {'n' => n, 
		'p' => p, 
		'w' => n.to_s(2).length,
		'r' => c.to_f / w,
		'l' => l1,
		'c' => c}
end

def back(ns)
	
	mxp = 4
	add(l = [], mxp, ns.to_i(2), {'p' => '', 'l' => [], 'c' => 0})
	
	mx = nil
	k = 'r'
	t = 0
	e = 2
	
	loop \
	{
		return if (l.empty?)
		break if (!mx.nil? && mx[k] >= e)
		
		l.sort_by! { |x| -x[k] }
		mx = [l[0], mx].compact.max_by { |x| x[k] }
		
		x = l.delete_at(rand([l.size, 50].min))
		
		$stderr.puts([t, x[k]].join("\t")) if (t % 100 == 0)
		n = x['n']
	
		add(l, mxp, (n - 1) / 3, x) if ((n - 1) % 3 == 0 && ((n - 1) / 3).odd?)
		add(l, mxp, n * 2, x)
		
		t += 1
	}
	return mx
	
end

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

def out(l, c)
	l.each_with_index \
	{
		|x, j|
		puts([j, x.to_s(2).length, c].join("\t"))
	}
	puts
end

def construct(b)
	
	x = nil
	begin
		ns = dense(100, 0.5)
		ns[49, 50] = b * 50
		
		x = back(ns)

	end while (x.nil?)


	x.delete('l')
	$stderr.puts(x.inspect)
	n = x['n']
	ns = n.to_s(2)
	ns = '1' + ns
	
	ns2 = ns.dup
	ns2[0, 2] = '10'
	
	out(seq(n), 1)
	out(seq(ns.to_i(2)), 2)
	out(seq(ns2.to_i(2)), 3)



end

construct('1')