construct48.rb

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

end

def dense(w, d)
	return '' if (w == 0)
	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 d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d
        
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 seq(n)

	n1 = n
	l = []
	begin
		l << n
		n = f2(n)
	end while (n != 1)
	
	return l
end

def measure(l)
	cm1 = (0...l.size).max_by { |x| l[x] }
	cg = l.index { |x| x < l[0] }
	cg = l.size - 1 if (cg.nil?)
	
	cm = (0..cg).max_by { |x| l[x] }
	c = l.size
	
	{'cg' => cg, 'c' => c, 'cm1' => cm1, 'cm' => cm}
end

def outa(f, l, a = {}, t = '')
	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 ytics nomirror; set y2tics; set title '#{t}'; plot \\")
	k.each { |x| f.puts("'$dat' using (column('#{x}')) with line #{a.fetch(x, '')},\\") }
	f.puts
#	f.puts("reset; pause -1;")

end

def run(w)
	w2 = w / 2
	w1 = rand(w2)
	
	i = rand(w - w1)
	ns = ' ' * w
	ns[i, w1] = '1' * w1
	a = Hash[[(0...w).to_a, [nil] * w].transpose]
	(i...(i + w1)).each { |x| a.delete(x) }
	
	l = a.keys
	w1.times { x = l.delete_at(rand(l.size)); a.delete(x); ns[x, 1] = '0' }

	w3 = w - 2 * w1
	ns2 = dense(w3, 0.5)
	
	a.keys.each_with_index \
	{
		|x, i|
		ns[x, 1] = ns2[i, 1]
	}

	return ns
end

def lsb(ns, b)

	ns = ns.dup
	i = 0
	while (ns.length > 0)
		break if (ns[0, 1] == b)
		ns[0, 1] = ''
	end
	return i

end

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

def avg(l)
	return l.empty? ? 0 : sum(l).to_f / l.size
end

def avgs(l)

        ks = l[0][0].keys
        l1 = []
        l[0].size.times \
        {
                |i|
                l1[i] = Hash[[ks, ks.map { |k| avg(l.map { |x| x[i][k] }) }].transpose]
        }
        return l1

end

def dataset()
	
	w = 500
	l2 = []
	200.times \
	{
		ns = run(w)
		
		mx01 = mx01x(ns)
		l = seq(ns.to_i(2))
		raise if (l[w].nil?)
		a = measure(l)
		a.merge!({'nw2' => l[w].to_s(2).length, 
			'mx01' => mx01, 
			'lsb1' => lsb(ns, '1'),
			'lsb0' => lsb(ns, '0')})
		a['nw2'] /= 10
		a['cg'] *= 10
		a['cm'] *= 10
		l2 << a
	}
	l2.sort_by! { |x| x['mx01'] }
	return l2
end

outa(f = File.open('gnuplot.cmd', 'w'), avgs((1..100).map { dataset() }),
{'c' => 'axes x1y2',
'lsb1' => 'lw 2',
'lsb0' => 'lw 2'})
f.close