Created
August 14, 2016 15:35
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def f1(n) | |
n = (n * 3 + 1) / 2 while (n % 2 == 1) | |
n /= 2 while (n % 2 == 0) | |
return n | |
end | |
def seq2(n) | |
l = [n] | |
n1 = n | |
begin | |
l << (n = f1(n)) | |
end while (n >= n1 && n != 1) | |
return l | |
end | |
def d(s) | |
c = s.split('').select { |x| x == '1' }.size | |
d = s.empty? ? 0 : c.to_f / s.length | |
return (0.5 - d).abs, d | |
end | |
def r(x) | |
return sprintf("%.3f", x).to_f | |
end | |
def mnmx(l) | |
return l.min, l.max | |
end | |
def stat(l) | |
return if (l.empty?) | |
t = t2 = 0 | |
l.each \ | |
{ | |
|x| | |
t += x | |
t2 += x ** 2 | |
} | |
c = l.size | |
a = t.to_f / c | |
z = t2.to_f / c - a ** 2 | |
sd = Math.sqrt(z < 0 ? 0 : z) | |
return l.size, a, sd, l.max, l.min | |
end | |
def mx(n) | |
l = seq2(n) | |
d1, d = d(n.to_s(2)) | |
ls = l.size | |
return {'ls' => ls, 'd' => d} | |
end | |
def three(n, p) | |
p2 = p + 1 | |
n2 = n | (1 << p2) | |
x = {'n' => n, 'p' =>p}.merge(mx(n)) | |
x2 = x.merge('p' => p2) | |
x3 = {'n' => n2, 'p' => p2}.merge(mx(n2)) | |
return [x2, x3] | |
end | |
def hard(c) | |
l1 = [] | |
l2 = three(1, 0) | |
a = [] | |
c.times \ | |
{ | |
|n| | |
$stderr.puts(n) if (n % 100 == 0) | |
b = {} | |
l2.each_with_index \ | |
{ | |
|x, i| | |
ls = x['ls'] | |
b[ls] = b.fetch(ls, []) + [x.merge({'i' => i})] | |
} | |
j = (2..a.size).find { |i| a[i].nil? || a[i] < 50 } | |
j = a.size if (j.nil?) | |
k = b.keys.sort.find { |i| i >= j } | |
k = b.keys.min if (k.nil?) | |
x = b[k][rand(b[k].size)] | |
i = x['i'] | |
x = l2.delete_at(i) | |
l1 << x | |
l2 += three(x['n'], x['p']) | |
ls = x['ls'] | |
a[ls] = 0 if (a[ls].nil?) | |
a[ls] += 1 | |
# p([j, k, b.keys.sort, a]) | |
# p(a) | |
} | |
return l1 | |
end | |
l = hard(20000) | |
b = {} | |
l.each_with_index \ | |
{ | |
|x, i| | |
ls = x['ls'] | |
b[ls] = b.fetch(ls, []) + [x.merge({'i' => i})] | |
} | |
b.sort.each \ | |
{ | |
|k, l| | |
l1 = l.map { |x| x['d'] } | |
puts([k, stat(l1)].join("\t")) | |
} | |
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