Created
February 11, 2016 21:59
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def f1(n) | |
n = (n * 3 + 1) / 2 while (n.odd?) | |
n /= 2 while (n.even?) | |
return n | |
end | |
def dense(n) | |
s = n.to_s(2) | |
c = 0 | |
s.length.times \ | |
{ | |
|i| | |
c += s[i, 1].to_i | |
} | |
return c.to_f / s.length | |
end | |
def widthdiff(x, y) | |
x.to_s(2).length - y.to_s(2).length | |
end | |
def widthratio(x, y) | |
x.to_s(2).length.to_f / y.to_s(2).length | |
end | |
def f(n, w) | |
n1 = n | |
c = 0 | |
l = [n] | |
cg = nil | |
while (n != 1) | |
n = f1(n) | |
l << n | |
c += 1 | |
cg = c if (cg.nil? && n < n1) | |
break if (!cg.nil? && w != 'c') | |
end | |
cm = (0...l.size).max_by { |x| l[x] } | |
return {'cm' => cm, | |
'cg' => cg.nil? ? 0 : cg, | |
'm' => l[cm].to_s(2).length, | |
'w' => widthdiff(l[cm], n1), | |
'r' => widthratio(l[cm], n1), | |
'c' => l.size, | |
'd' => (0.5 - dense(n1)).abs} | |
end | |
def long(m, w) | |
return {'n' => rand(2 ** (s = m * 1000)) | 1, 's' => s } if (w == 'z') | |
l = [{'n' => 1, 'p' => 0}.merge(f(1, w))] | |
t = 0 | |
e = 2000 | |
loop \ | |
{ | |
l = l.sort_by { |x| [x[w], -x['d']] }.reverse | |
x = l.delete_at(rand([l.size, 20].min)) | |
p2 = x['p'] + 1 | |
n2 = x['n'] + 2 ** p2 | |
x1 = x.dup | |
x1['p'] = p2 | |
l << x1 | |
x2 = {'n' => n2, 'p' => p2}.merge(f(n2, w)) | |
l << x2 | |
t += 1 | |
if (w == 'r') then | |
z = l.sort_by { |x| x['n'] }.reverse[0...100].max_by { |x| x['r'] } | |
else | |
z = l.max_by { |x| x[w] } | |
end | |
z.merge!({ 't' => t, 's' => t.to_f / e }) | |
return z if (z['s'] >= m) | |
} | |
end | |
def adv1(n) | |
l = [n] | |
n1 = n | |
while (n != 1) | |
n = f1(n) | |
break if (n < n1) | |
l << n | |
end | |
return l | |
end | |
def nonmono(l) | |
return nil if (l.empty?) | |
mn = nil | |
r = nil | |
l.each_with_index \ | |
{ | |
|d, i| | |
mn = [mn, [d, i]].compact.min | |
r = [r, [i - mn[1], mn[1], i]].compact.max | |
} | |
return r[0] | |
end | |
def smooth(l) | |
m = l.map { |x| x.size }.max - 1 | |
l2 = [] | |
(0..m).each \ | |
{ | |
|x| | |
t = 0 | |
l.each \ | |
{ | |
|l1| | |
t += l1[(x.to_f / m * (l1.size - 1)).to_i] | |
} | |
l2 << t | |
} | |
return l2 | |
end | |
def track(n, c, z) | |
l1 = [] | |
l2 = [] | |
1000.times \ | |
{ | |
l = adv1(n).map { |x| x.to_s(2).length } | |
n += 2 | |
x1 = l[0] | |
l.map! { |x| x - x1 } | |
m = (0...l.size).max_by { |x| l[x] } | |
mx = l[m] | |
next if (mx == 0) | |
l.map! { |x| x.to_f / mx } | |
next if ([m, l.size - m].min < 5) | |
l1 << l[0..m] | |
l2 << l[m..-1] | |
} | |
return if (l1.empty? || l2.empty?) | |
x1 = nonmono(smooth(l1).map { |x| - x}) | |
x2 = nonmono(smooth(l2)) | |
puts([c, (c * 2) + z, x1, x2, l1.size, l2.size].join("\t")) | |
end | |
def test(k, m) | |
if ($x['c'][k].nil?) then | |
$x['c'][k] = 0 | |
$x['x'] += 1 | |
$x['a'][k] = {} | |
puts | |
end | |
z = long(m, k) | |
$x['c'][k] += 1 | |
n = z['n'] | |
return if ($x['a'][k].member?(n)) | |
$x['a'][k][n] = nil | |
$stderr.puts([$x['c'][k], $x['a'][k].size, k, z['s'], n.to_s(2)].inspect) | |
track(n, $x['x'], m) | |
$stdout.flush | |
end | |
def r2(x) | |
sprintf("%.2f", x).to_f | |
end | |
p = ['w', 'p', 'c', 'm', 'cg', 'cm', 'r', 'z'] | |
$x = {'a' => {}, 'c' => {}, 'x' => -1} | |
#test('w', 0.5); exit | |
c = 100 | |
p.each { |k| c.times { |i| test(k, i.to_f / c) } } | |
$x['c'].keys.each { |k| $stderr.puts("#{k}\t#{$x['c'][k]}") } | |
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