Created
March 9, 2019 05:08
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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 len(ns, p) | |
l = ns.split(p) | |
l = [''] if (l.nil? || l.empty?) | |
return l.map { |x| x.length } | |
end | |
def len01(ns) | |
return len(ns, /0+/), len(ns, /1+/) | |
end | |
def mx01(ns) | |
l1, l0 = len01(ns) | |
return l1.max, l0.max | |
end | |
def put01(w) | |
ns = dense(w, 0.5) | |
r = (0..1).map { rand(w) }.sort | |
w1 = r[1] - r[0] + 1 | |
s = ('01' * (w1 / 2 + 1))[0...w1] | |
ns[r[0]..r[1]] = s | |
ns1 = '-' * w | |
ns1[r[0]..r[1]] = s | |
ns2 = f2(ns.to_i(2)).to_s(2) | |
return ns, ns2 | |
end | |
def make(w) | |
ns = ns2 = r = nil | |
t = 0 | |
loop \ | |
{ | |
t += 1 | |
ns, ns2 = put01(w) | |
mx1 = mx01(ns2)[0] | |
r = mx1.to_f / w | |
break if (r > 0.45 && r < 0.55) | |
} | |
$stderr.puts([r, t].inspect) | |
return ns | |
end | |
def add(l, mxp, n, x) | |
p = (n % 2).to_s + x['p'] | |
l1m, l0m = mx01(p) | |
return if ([l0m, l1m].max >= 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 len01(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) | |
f = File.open(fn = "gnuplot1.cmd", 'w') | |
f.puts("set palette negative grayscale; unset colorbox;") | |
fmt1(l.map { |x| x.to_s(2).reverse }, f) | |
f.close | |
end | |
x = reverse(100, lambda { |w| make(w) }) | |
p(x['r']) | |
n = x['n'] | |
l = [n] | |
i = 0 | |
while (i < x['p'].length) | |
i += n.even? ? 1 : 2 | |
n = f2(n) | |
l << n | |
end | |
grid(l) |
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