233. Number of Digit One

Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.

Example:

Input: 13
Output: 6
Explanation: Digit 1 occurred in the following numbers: 1, 10, 11, 12, 13.

思路一

class Solution:
    def countDigitOne(self, n):
        """
        :type n: int
        :rtype: int
        """
        k, count = 1, 0
        while k <= n:
            r = n // k  #save previous num
            m = n % k
            print(count)
            count += ((r + 8) // 10) * k + (m + 1 if r % 10 == 1 else 0)
            print(count)
            print('-----')
            k *= 10
        return count

---

思路二

class Solution:
  def countDigitOne(self, n: 'int') -> 'int':
    
    def r(s, k=0):
      n = len(s)
      if n == 1:
        return (s != '0') + (int(s) + 1) * k
      elif s[0] == '0':
        return r(s[1:], k)
      else:
        nines = "9" * (len(s) - 1)
        if s[0] == '1':
          return r(nines, k) + r(s[1:], k + 1)
        else:
          return r(nines, k) * (int(s[0]) - 1) + r(nines, k + 1) + r(s[1:], k)
    
    return r(str(n), 0) if n > 0 else 0