plateau4b.rb

#!/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 delta2(l)
 
        l = (1...l.size).map { |i| l[i] - l[i - 1] }
        y = 0
        l = (1...l.size).map { |i| x = l[i] - l[i - 1]; y += x; [x, y] }
        return l
end
 
def f2(n)
 
 
        l = []
        while (n != 1)
                n = (n * 3 + 1) / 2
                n /= 2 while (n % 2 == 0)
                l << n
        end
        return l
 
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.reverse if (z[0] >= m)
        }
 
end
 
n, = long(100)
l = f2(n)
 
l1 = delta2(l.map { |x| Math.log(x) })
l2 = delta2(l.map { |x| x.to_s(2).length })
 
[l1, l2].transpose.each { |x| puts(x.join("\t")) }