traverse18d.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, fz)
	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] }
	s = l1.map { |x| x.to_s(2) }.join
	
	t0 = s.split('').select { |x| x == '1' }.size
	t1 = s.length - t0
	t = t0 + t1
	t01a = (t1 - t0).abs
	
	z = Kernel.eval(fz)
	
	return {'ns' => ns, 'cm' => cm, 'cg' => cg, 'c' => l1.size, 
		't' => t, 'z' => z, 't0' => t0, 't1' => t1, 'nw' => ns.length}
end

def outa(f1, l, a = {}, t = '')
	f = f1.nil? ? File.open('gnuplot.cmd', 'w') : f1
	f.puts('$dat << eof')
	k = l[0].keys
	
	f.puts(k.join("\t"))
	l.each { |x| f.puts(x.values.join("\t")) }

	f.puts('eof')
	f.puts("set colors classic; set key top left opaque; set title '#{t}'; ")
	f.puts("set ytics nomirror; set y2tics;")
	f.puts("plot \\")
	k.each \
	{ 
		|x| 
		next if (a.member?(x) && a[x].nil?)
		f.puts("'$dat' using (column('#{x}')) with line #{a.fetch(x, '')} lw 2 title '#{x}',\\") 
	}
	f.puts
	f.puts("reset; pause -1;")
	f.flush
	f.close if (f1.nil?)

end

def diff(a, b)
	c = 0
	a.length.times \
	{
		|i|
		c += a[i, 1].to_i ^ b[i, 1].to_i
	}
	return c
end

def traverse(f, fz)
	
	$stderr.puts("\t#{fz}")
	l1 = [count('1', fz)]
	seen = {'' => nil, '0' => nil, '1' => nil}
	l = []

	k = 'z'
	z2 = 0
	1000.times \
	{
		|t|
		$stderr.puts(t) if (t % 100 == 0)
		l2 = l1.map { |x| x[k] }
		
		i = (0...l1.size).min_by { |x| l2[x] }
		x = l1.delete_at(i)
		l << x.merge({'zx' => x['z'] - z2})
		z2 = x['z']
		
		edit1(x['ns']).each \
		{
			|ns|
			next if (seen.member?(ns))
			l1 << count(ns, fz)
			seen[ns] = nil
		}
	}
	outa(f, l, {'ns' => nil, 'zx' => nil}, fz)

end

f = File.open('gnuplot.cmd', 'w')

fs = ["t", 
	"t + t01a", 
	"t - t01a", 
	"t + Math.log(t01a)",
	"t - Math.log(t01a)",
	"t + Math.sqrt(t01a)", 
	"t - Math.sqrt(t01a)",
	"t + t01a ** 2"]

fs.each { |fz| traverse(f, fz) }

f.close