traverse17.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 flip(s, n)
	s = s.dup
	s[n, 1] = (s[n, 1].to_i ^ 1).to_s
	return s
end

def delete(s, n)
	s = s.dup
	s[n, 1] = ''
	return s
end

def insert(s, n)
	s0 = s.dup
	s0[n, 0] = '0'
	s1 = s.dup
	s1[n, 0] = '1'
	return s0, s1
end

def edit1(s)
		
	l = []
	s.length.times \
	{
		|n|
		l << flip(s, n)
		l << delete(s, n)
	}

	(s.length + 1).times \
	{
		|n|
		l += insert(s, n)
	}
	return l.select { |x| x[0, 1] != '0' }
end

def sum(l)
	return l.inject { |t, x| t + x }
end

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

def count(ns)
	l1 = seq(ns.to_i(2))
	cg = l1.index { |x| x < l1[0] }
	cg = l1.size if (cg.nil?)
	cm = (0...cg).max_by { |x| l1[x] }

	nw = ns.length
	b = [0, 0]
	l1[nw..cg].each { |x| b[x % 2] += 1 }
	ba = (b[0] - b[1]).abs
	cgnw = cg - nw
	bas = ba.to_f / cgnw * 10
	bas = 0 if (cgnw == 0)

	db = d(l1[cg..-1].map { |x| x % 2 }.join)
	dc = d(l1[nw..-1].map { |x| x % 2 }.join)
	dc = 0 if (dc.nan?)
	
	return {'ns' => ns, 'cm' => cm, 'cg' => cg, 
		'c' => l1.size, 'nw' => nw, 'ba' => ba,
		'cgnw' => cgnw, 'bas' => bas, 
		'dba' => (0.5 - db).abs * 10,
		'dca' => (0.5 - dc).abs * 10}
end

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

	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 += w 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 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 opt(ks)

	l1 = [count('1')]
	seen = {'' => nil, '0' => nil, '1' => nil}
	l = []

	c = 5e3.to_i
	m = 5e3.to_i

	d = c / 2000
	d = 1 if ($d == 0)

	k = 'ba'
	c.times \
	{
		|t|
		$stderr.puts(t) if (t % 100 == 0)
		l2 = l1.map { |x| x[k] }
		
		l2 = order(l1, ks)
		
		i = l2[rand([l2.size, 50].min)]
		
		l3 = l2[m..-1]
		l3 = [] if (l3.nil?)
		x = nil
		
		(l3 | [i]).sort.reverse.each \
		{
			|x1|
			x2 = l1.delete_at(x1)
			x = x2 if (x1 == i)
		}

		
		l << x
		out(x.merge({'t' => t}), 
			{'ns' => nil, 
			'ba' => 'axes x1y2 lw 2',
			'nw' => 'axes x1y2',
			'cgnw' => 'lt 7',
			'bas' => 'axes x1y2',
			'dba' => 'axes x1y2',
			'dca' => 'axes x1y2'}) if (t % d == 0)
		
		
		edit1(x['ns']).each \
		{
			|ns|
			next if (seen.member?(ns))
			l1 << count(ns)
			seen[ns] = nil
		}
	}

end

ks = ['ba']
ks = ['ba', 'nw', 'cm', 'cg', 'c', 'cgnw', 'bas']
ks = ['bas', 'cgnw']
ks = ['cgnw']
ks = ['cgnw', 'dba']
ks = ['dca', 'cg']
opt(ks)