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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 | |
while (n != 1 && n >= n1) | |
n = n * 3 + 1 if (n % 2 == 1) | |
n /= 2 while (n % 2 == 0) | |
c += 1 | |
end | |
return {'c' => c, 'd' => (0.5 - dense(n1)).abs} | |
end | |
def match(n1, n2) | |
i = 0 | |
i += 1 while (i < n1.size && i < n2.size && n1[i, 1] == n2[i, 1]) | |
return i | |
end | |
def f2(n) | |
n3 = n | |
m1 = nil | |
t = 0 | |
dm = 0 | |
s = nil | |
while (n != 1) | |
n = (n * 3 + 1) / 2 | |
n /= 2 while (n % 2 == 0) | |
n3 = n3 * 3 | |
ns = n.to_s(2) | |
n3s = n3.to_s(2) | |
m = match(ns, n3s) | |
if (!m1.nil? && m != m1) then | |
puts("#{m} != #{m1}") | |
puts(s) | |
raise | |
end | |
nb = (n * 3 + 1) / 2 | |
nb /=2 while (nb % 2 == 0) | |
nbs = nb.to_s(2) | |
n3b = n3 * 3 | |
n3bs = n3b.to_s(2) | |
d = d1 = 20 | |
d1 = m if (m < d1) | |
break if (m > nbs.length || m > n3bs.length) | |
nbs1 = nbs[m - d1...m] | |
nbs2 = nbs[m...m + d] | |
n3bs1 = n3bs[m - d1...m] | |
n3bs2 = n3bs[m...m + d] | |
l = nbs1 + nbs2 | |
r = n3bs1 + n3bs2 | |
m2 = match(l, r) | |
d2 = m2 - d1 | |
s = "m = #{m}\td2 = #{d2}\tt = #{t}\n" | |
s += [ns[0...m], ns[m..-1]].inspect + "\n" | |
s += [n3s[0...m], n3s[m..-1]].inspect + "\n" | |
s += nbs1 + ' ^ ' + nbs2 + "\n" | |
s += n3bs1 + ' ^ ' + n3bs2 + "\n" | |
m1 = m + d2 | |
dm = [[dm.abs, dm], [d2.abs, d2]].max[1] | |
t += 1 | |
# raise if (d2 == nbs2.length || d2 == n3bs2.length) | |
end | |
return t, dm | |
end | |
def long(m) | |
l = [{'n' => 1, 'p' => 0}.merge(f(1))] | |
t = 0 | |
loop \ | |
{ | |
l = l.sort_by { |x| [x['c'], -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)) | |
l << x2 | |
t += 1 | |
return if (t >= 1000) | |
z = l.map { |x| [x['c'], x['n']] }.max | |
return z if (z[0] >= m) | |
} | |
end | |
c = c2 = dm = 0 | |
a = {} | |
loop \ | |
{ | |
begin | |
c1, n = long(100) | |
c2 += 1 | |
end while (n.nil? || a.member?(n)) | |
a[n] = nil | |
t, d = f2(n) | |
# break | |
c += 1 | |
dm = [[dm.abs, dm], [d.abs, d]].max[1] | |
p([c2, c, c1, t, d, dm, a.size.to_f / c2]) | |
} |
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