zlacker

>>jstrie+(OP)

  def digitLength(n):
      dlen = 1
      high = 9
      while n > high:
          dlen += 1
          high = 10*high + 9
      return dlen

>>tzs+ng
One fun enhancement to this is to avoid the n^2 cost it faces with large integers.

    def digit_length(n):
        totlen = 0
        n += not n
        while n > 0:
            klen = 1
            k = 10
            while n > k * k:
                k = k * k
                klen *= 2
            n = n // k
            totlen += klen
        return totlen