bitwise39b.rb

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

end

def d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d
        
end

def keys(ks2)

	ksmn = ks2.select { |x| x.end_with?('-') }
	
	ksmx = ks2 - ksmn
	
	ksmn.each { |x| x.replace(x.chop) }
	
	x = {'ks' => ksmn + ksmx, 'ksmx' => ksmx, 'ksmn' => ksmn}
	
	$stderr.puts(x.inspect)

	return x
	
end

def order(l, ks2)
	l2 = (0...l.size).map { {} }

	$k = keys(ks2) if ($k.nil?)
	
	$k['ks'].each \
	{
		|k|
		
		l1 = (0...l.size).map { |x| {k => l[x][k], 'i' => x} }

		s = $k['ksmx'].member?(k) ? -1 : 1
		
		l1.sort_by! { |x| s * x[k] }

		(0...l1.size).each { |x| l2[l1[x]['i']][k] = x }
	}
	l2.each { |x| x['z'] = x.values.inject(0) { |t, x| t + x } }
	
	return (0...l2.size).sort_by { |x| l2[x]['z'] }
end

def out(a, a2 = {}, t = nil, ct = "(column('t')):")

	fn = $fn.nil? ? 'out.txt' : $fn
	k = a.keys
	
	if ($f1.nil?) then
		$f1 = File.open(fn, 'w')
		$f1.puts(k.join("\t")) 
		
		f2 = File.open('gnuplot.cmd', 'w')
		st = t.nil? ? 'unset title; ' : "set title '#{t}'; "
		f2.puts("set ytics nomirror; set y2tics; set colors classic; set key top left box opaque; #{st}; plot \\")
		(a.keys - ['t']).each \
		{
			|x|
			next if (a2.member?(x) && a2[x].nil?)
			m = a2.fetch(x, '')
			m += ' with line' if (!m.include?('with'))
			f2.puts("'#{fn}' using #{ct}(column('#{x}')) title '#{x}' #{m}, \\")
		}
		f2.puts
		f2.close
	end
	$f1.puts(a.values_at(*k).join("\t"))
	$f1.flush
end

def remove(a, ks)
	a = a.dup
	ks.each { |x| a.delete(x) }
	return a
end

def seq(n)

	n1 = n
	l = []
	begin
		l << n
		n = f2(n)
	end while (n != 1)
	
	return l
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 mx(l2)
	return l2.empty? ? 0 : l2.map { |x| len01x(x.to_s(2)) }.flatten.max
end

def count(ns)

	nw = ns.length

	l = seq(ns.to_i(2))
	cm1 = (0...l.size).max_by { |x| l[x] }
	cg = l.index { |x| x < l[0] }
	cg = l.size if (cg.nil?)
	
	cm = (0...cg).max_by { |x| l[x] }

	c = l.size
		
	mxl = mx(l[0..cm])
	mxr = mx(l[cm..cg])
	
	return {
		'nw' => nw, 
		'cm' => cm,
		'cm1' => cm1,
		'cg' => cg,
		'c' => c,
		'mxl' => mxl,
		'mxr' => mxr,
		'mxrl' => mxr - mxl,
		'l' => l,
		'ns' => ns, 
		'n' => ns.to_i(2)
		}
end

def fmt(x)
	return remove(x, ['l'])
end

def axes2(x2)
	return x2.inject({}) { |h, x| h.merge({x => 'axes x1y2' }) }
	
end

def add(l, ns, x2)
	
	$t = 0 if ($t.nil?)
	$t += 1
	
	x = count(ns).merge({'t' => $t})
	l << x
	
	x = fmt(x)
	
	out(remove(x, ['ns']), x2) if ($t % $d == 0)
		
	$stderr.puts(x.inspect) if ($t % 200 == 0) 

end

def adj(ns)

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

def opt(ks, c, x2)

	$d = c / 2000
	
	add(l = [], '1', x2)

	(c / 2).times \
	{
		l1 = order(l, ks)

		i = l1[rand([l1.size, 50].min)]
		
		x = l.delete_at(i)

		ns1, ns2 = adj(x['ns'])
		
		add(l, ns1, x2)
		add(l, ns2, x2)
		
	}

	return l[order(l, ks)[0]]
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 stat(l)
	return 0, 0, 0 if (l.empty?)
	
	t = l.inject { |a, x| a + x }
	t2 = l.inject { |a, x| a + 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
end

def stat2(l, n, m)
	return Hash[[["#{m}a#{n}", "#{m}sd#{n}", "#{m}mx#{n}"], stat(l)].transpose]
end

def stat3(x, t)
	l1, l0 = len01x(x)
	return stat2(l1, "1", t).merge(stat2(l0, "0", t))
end

def hist(l, f)
	h = {}
	l.each \
	{
		|x|
		h[x] = h.fetch(x, 0) + 1
	}
	$c = 0 if ($c.nil?)
	h.sort.each \
	{
		|x|
		f.puts([x, $c].join("\t"))
	}
	f.puts
	$c += 1
end

def dissect(x, f)
	l1, l0 = len01x(x)

	hist(l1, f)
	hist(l0, f)
end

def review()
	l = File.open('out.txt').readlines
	c = l[0].split.index('n')
	l2 = l[1..-1].map { |ln| ln.split[c].to_i }
	
	f = File.open('out2.txt', 'w')
	
	l2[-1..-1].each \
	{
		|x|
		

		l = seq(x)
		cm1 = (0...l.size).max_by { |x| l[x] }
		cg = l.index { |x| x < l[0] }
		cg = l.size if (cg.nil?)
		
		cm = (0...cg).max_by { |x| l[x] }

		l2 = l.map { |x| x.to_s(2) }
		
		w = [cm, cg - cm].min
		$stderr.puts([cm, cg, w].inspect)
		
		ll = l2[0..w].join
		lr = l2[cm..(cm + w)].join
		dissect(ll, f)
		dissect(lr, f)

	}
	f.close
	
	exit
end

review() if (File.exist?('out.txt'))

ks = ['nw', 'cm', 'cg', 'c', 'mxl-', 'mxr-']

x2 = axes2(['mxl', 'mxr', 'mxrl'])
x2['mxrl'] += ' with impulse'
x2['n'] = nil

x = opt(ks, 1e4.to_i, x2)
$stderr.puts(fmt(x).inspect)