db.rb

def f1(n)
	n = (n * 3 + 1) / 2 while (n.odd?)
	n /= 2 while (n.even?)
	return n
end

def dense(n)
 
        s = n.to_s(2)
        c = 0
        s.length.times \
        {
                |i|
                c += s[i, 1].to_i
        }
        return c.to_f / s.length
 
end

def widthdiff(x, y)
        x.to_s(2).length - y.to_s(2).length
 
end

def widthratio(x, y)
        x.to_s(2).length.to_f / y.to_s(2).length
end

def f(n, w)
 
        n1 = n
        c = 0
	l = [n]
	cg = nil
	
        while (n != 1)
		n = f1(n)

		l << n
                c += 1
	
		cg = c if (cg.nil? && n < n1)

		break if (!cg.nil? && w != 'c')
        end
	cm = (0...l.size).max_by { |x| l[x] }
	
        return {'cm' => cm,
		'cg' => cg.nil? ? 0 : cg, 
		'm' => l[cm].to_s(2).length,
		'w' => widthdiff(l[cm], n1),
		'r' => widthratio(l[cm], n1),
		'c' => l.size,
		'd' => (0.5 - dense(n1)).abs}
 
end

def long(m, w)
 
	return {'n' => rand(2 ** (s = m * 1000)) | 1, 's' => s } if (w == 'z')
		
        l = [{'n' => 1, 'p' => 0}.merge(f(1, w))]
        t = 0
	e = 2000
	
        loop \
        {
                l = l.sort_by { |x| [x[w], -x['d']] }.reverse
 
                x = l.delete_at(rand([l.size, 20].min))
 
                p2 = x['p'] + 1
                n2 = x['n'] + 2 ** p2
 
 
                x1 = x.dup
                x1['p'] = p2
                l << x1
 
                x2 = {'n' => n2, 'p' => p2}.merge(f(n2, w))
                l << x2
                t += 1
 
		if (w == 'r') then
			z = l.sort_by { |x| x['n'] }.reverse[0...100].max_by { |x| x['r'] }
		else
			z = l.max_by { |x| x[w] }
		end
		z.merge!({ 't' => t, 's' => t.to_f / e })
		
                return z if (z['s'] >= m)
        }
 
end

def test(k, m)
	
	if ($x['c'][k].nil?) then
		$x['c'][k] = 0
		$x['x'] += 1
		$x['a'][k] = {}
	end
	
	begin
		z = long(m, k)
		z['x'] = k
		
		$x['c'][k] += 1
		
		n = z['n']
	end while ($x['a'][k].member?(n))
	
	$x['a'][k][n] = nil
	
	$stderr.puts([$x['c'][k], $x['a'][k].size, k, z['s'], n.to_s(2)].inspect)
	$f.puts(z)
	$f.flush
end

def r2(x)
	sprintf("%.2f", x).to_f
end

def range(k)
	
	c = 100
	c.times { |i| test(k, i.to_f / c) }
end

p = ['w', 'p', 'c', 'm', 'cg', 'cm', 'r', 'z']

$x = {'a' => {}, 'c' => {}, 'x' => -1}


# test('w', 0.5); exit
# range('w'); exit

$f = File.open('db.txt', 'w')

p.each { |k| range(k) }

$x['c'].keys.each { |k| $stderr.puts("#{k}\t#{$x['a'][k].size}") }