backtrack.rb

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

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 lenz(ns, p)
	l = ns.split(p)
	l = [''] if (l.nil? || l.empty?)
	return l.map { |x| x.length }
end

def len01z(ns)
	return len(ns, /0+/), len(ns, /1+/)
end

def mx01z(ns)
	l1, l0 = len01(ns)
	return l1.max, l0.max
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 add(l, mxp, n, x)

	p = (n % 2).to_s + x['p']
	
#	l1m, l0m = mx01(p)
#	return if ([l0m, l1m].max >= mxp)
	
	return if (mx01x(p) >= mxp)
	
	
	w = n.to_s(2).length

	l1 = [n] + x['l']

	c = x['c'] + (n.even? ? 1 : 0)
	l << {'n' => n, 
		'p' => p, 
		'w' => n.to_s(2).length,
		'r' => c.to_f / w,
		'l' => l1,
		'c' => c}
end

def back(ns)
	
	mxp = 4
	add(l = [], mxp, ns.to_i(2), {'p' => '', 'l' => [], 'c' => 0})
	
	mx = nil
	k = 'r'
	t = 0
	e = 2
	
	loop \
	{
		return if (l.empty?)
		break if (!mx.nil? && mx[k] >= e)
		
		l.sort_by! { |x| -x[k] }
		mx = [l[0], mx].compact.max_by { |x| x[k] }
		
		x = l.delete_at(rand([l.size, 50].min))
		
		puts([t, x[k]].join("\t")) if (t % 100 == 0)
		n = x['n']
	
		add(l, mxp, (n - 1) / 3, x) if ((n - 1) % 3 == 0 && ((n - 1) / 3).odd?)
		add(l, mxp, n * 2, x)
		
		t += 1
	}
	return mx
	
end

def reverse(w, mk)
	t = 0
	x = nil
	loop \
	{
		t += 1
		ns = mk.call(w)
		x = back(ns)
		break if (!x.nil?)
	}
#	$stderr.puts([t, x].inspect)
	return x
end

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

def e(ns)
	return len01x(ns).flatten.size.to_f / ns.length
end

def fmt1(l, f)

	w = l.max_by { |x| x.length }.length
	
	f.puts("set colors classic; set ytics nomirror; set y2tics; set key top right opaque;\\")
	f.puts("plot \\")
	f.puts("[0:#{l.size - 1}][0:#{w}] '-' matrix using 2:1:3 with image title '', \\")
	f.puts("'-' using 1 with line title 'e' axes x1y2 lw 3, \\")
	f.puts("'-' using (column('d')) with line axes x1y2 lw 3 ")
	l1 = []
	l.each_with_index \
	{
		|z, i|
		
		l1 << [d(z), e(z)]
		c = w - z.length
		z[z.length...w] = '0' * c
		
		f.puts(z.split('').join(' '))
	}
	f.puts("eof")
	f.puts("eof")
	l1.each { |x| f.puts(x[1]) }
	f.puts("eof")
	f.puts("d")
	l1.each { |x| f.puts(x[0]) }
	f.puts("eof")
	
	
end

def grid(l, b)
	
	f = File.open(fn = "gnuplot#{b}.cmd", 'w')
	f.puts("set palette negative grayscale; unset colorbox;")
	
	fmt1(l.map { |x| x.to_s(2).reverse }, f)
	f.close

end

def adj(x, m, n, s2, p2, p, x3)
	s2.replace(p[0...x] + (x3 % 2).to_s)
	m = (s2[x, 1] == p[x, 1])
	n = p2.reverse.to_i(2)
	p2[x, 1] = m ? '11' : '01'
	return m, n, x3
end

def terras121(p)
	
	p2 = ['01', '11'][p[0, 1].to_i]
	n = 1
	n3 = 0
	m = p2 == '11'
	x3 = (p2.reverse.to_i(2)) >> 1

	(1...p.length).each \
	{
		|x|

		if (!m)
			ns = n.to_s(2)
			ns[0, 1] = ''
			m1 = x3 - 3**n3
			n1 = f2(m1)
		end

		n3 = p[0...x].split('').select { |z| z == '1' }.size
		
		s2 = ''
		m, n, x3 = adj(x, m, n, s2, p2, p, m ? (f2(x3) + 3**n3) : (n1 + 3**n3))
	}

	n = p2.reverse.to_i(2)

	return n
end

def seq(n)
	l = [n]
	while (n != 1)
		n = f2(n)
		l << n
	end
	return l
	
end

def construct(b)
	
	x = nil
	begin
		ns = dense(100, 0.5)
		ns[49, 50] = b * 50
		ns2 = terras121(ns).to_s(2)
		
		x = back(ns2)

	end while (x.nil?)


	x.delete('l')
	p(x)
	l = seq(x['n'])

	return l
end

['0', '1'].each { |x| grid(construct(x), x) }