Created
August 20, 2015 16:57
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#!/usr/bin/ruby1.8 | |
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 f(n) | |
n1 = n | |
c = 0 | |
m = 0 | |
while (n != 1 && n >= n1) | |
n = (n * 3 + 1) / 2 while (n.odd?) | |
n /= 2 while (n.even?) | |
m = [m, n].max | |
c += 1 | |
end | |
return {'w' => widthdiff(m, n1), | |
'c' => c, | |
'd' => (0.5 - dense(n1)).abs, | |
'm' => m} | |
end | |
def long(m) | |
l = [{'n' => 1, 'p' => 0}.merge(f(1))] | |
w = 'w' | |
loop \ | |
{ | |
l = l.sort_by { |x| [x[w], x['d']] }.reverse | |
break if (l[0][w] >= m) | |
x = l.delete_at(rand([l.size, 10].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)) | |
l << x2 | |
raise if (l.size >= 1000) | |
} | |
l = l.sort_by { |x| -x[w] } | |
return l.first, l.size | |
end | |
def widthdiff(x, y) | |
x.to_s(2).length - y.to_s(2).length | |
end | |
def run() | |
x, c = long(ARGV[0].to_i) | |
n = x['n'] | |
l = [] | |
while (n != 1) | |
c1 = c0 = 0 | |
while (n.odd?) | |
n = (n * 3 + 1) / 2 | |
c1 += 1 | |
end | |
while (n.even?) | |
n /= 2 | |
c0 += 1 | |
end | |
ns = n.to_s(2) | |
puts([ns.length, c0, c1].join("\t")) | |
end | |
end | |
run() | |
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