run10.rb

#!/usr/bin/ruby1.8
 
def fs()
	
	lo = [lambda { |n| n * 3 + 1 }, lambda { |n| (n * 3 + 1) / 2 }, 
		lambda { |n| n = (n * 3 + 1) / 2 while (n.odd?); n }]
	le = [lambda { |n| n / 2 }, lambda { |n| n /= 2 while (n.even?); n }]


	l = []
	lo.each \
	{ 
		|o| 
		le.each \
		{ 
			|e| 
			next if (o == lo.last && e == le.last)
			l << lambda \
			{ 
				|n| 
				n = o.call(n) if (n.odd?)
				n = e.call(n) if (n.even?)
				n
			}
		}
	}

	return l
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 = $f.call(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 ** m) | 1 } 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
 
		w2 = w
		if (w == 'r') then
			z = l.sort_by { |x| x['n'] }.reverse[0...100].max_by { |x| x['r'] }
			w2 = 's'
		else
			z = l.max_by { |x| x[w] }
		end
		z.merge!({ 't' => t, 's' => t.to_f / e })
		
                return z if (z[w2] >= m)
		
                return if (t >= e)
        }
 
end

def mx(a, b)
	a.nil? ? b : [a, b].max
end

def mn(a, b)
	a.nil? ? b : [a, b].min
end

def stat(l)
        return 0, 0, 0 if (l.empty?)
        t = t2 = 0
        l.each \
        {
		|x|
		t += x
		t2 += x ** 2
        }
        c = l.size
        a = t.to_f / c
        z = t2.to_f / c - a ** 2
        sd = Math.sqrt(z < 0 ? 0 : z)
        raise if (sd.nan?)
        return a, sd, l.max.to_f
end

def nonmono(l)
	
	mn = nil
	r = nil
	l.each_with_index \
	{
		|d, i|
		d1 = d.abs
		mn = mn(mn, [d1, i])
		r = mx(r, i - mn[1])
	}
	return r

end

def run1(n)
	
	n1s = n.to_s(2).length
	
	l = []
	while (n != 1)
		
		n = $f.call(n)
		l << n
	end
	
	d2 = 0
	l2 = []
	l.each \
	{
		|x|
		d = dense(x) - 0.5
		l2 << d
		break if (d * d2 < 0)
		d2 = d
	}

	cm = (0...l.size).max_by { |j| l[j] }

	l1 = []
	(l2.size...cm).each \
	{
		|j|
		n = l[j]
		ns = n.to_s(2)
		
		m0 = stat(ns.split(/1+/).map { |x| x.length })
		m1 = stat(ns.split(/0+/).map { |x| x.length })

		l1 << ([ns.length, dense(n)] + m0 + m1).flatten
	}
	
	return l1.empty? ? nil : l1
end

def sum(l)
	
	m = l.map { |l2| l2.size - 1 }
	mx = m.max
	l1 = []
	(0..mx).each \
	{
		|x|
		
		t = [0] * l[0][0].size
		l.each \
		{
			|l2|
			i = (x.to_f / mx * (l2.size - 1)).to_i
			l2[i].size.times { |j| t[j] += l2[i][j] }
		}
		puts(t.map { |x| x.to_f / l.size }.join("\t"))
	}
	
end

def test(p, k, m, i, j)
	r = p[k]
	a, b, c = r
	
	return if (c && m >= 1.0)
	
	x = a + m * (b - a)
	z = long(x, k)
	
	return if (z.nil?)
	n = z['n']
	return if ($a.member?(n))
	$a[n] = nil
	
	$stderr.puts([i, j, k, r2(m), r2(x), z['s'], n.to_s(2)].inspect)
	return run1(n)
end

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

p = {'w' => [0, 80, false],
	'p' => [0, 350, false],
	'c' => [0, 550, false],
	'm' => [0, 300, false],
	'cg' => [0, 140, false],
	'cm' => [0, 50, false],
	'r' => [0.0, 1.0, true],
	'z' => [0, 1000, true],
	}

$f = fs()[4]
$a = {}

l = []
i = 0
while (l.size < ARGV[0].to_i)
	l2 = test(p, 'cm', 0.5, i, l.size)
	l << l2 if (!l2.nil?)
	i += 1
end
sum(l)