题解 | #选牛比赛#

#
# 代码中的类名、方法名、参数名已经指定，请勿修改，直接返回方法规定的值即可
#
#
# @param digits string字符串一维数组
# @param n int整型
# @return int整型
#
class Solution:
    def countEligibleCows(self, digits: List[str], n: int) -> int:
        # write code here
        digit = [int(d) for d in digits]
        limit = [int(d) for d in str(n)]
        if len(limit) == 1: return sum(d<=limit[0] for d in digit)
        q = len(digit)
        num = q*(q**(len(limit)-1)-1)//(q-1)    # a0 * (q^(n-1)-1)/(q-1)
        for i in range(len(limit)):
            opt = sum(d<limit[i] for d in digit)
            num += opt * q*(q**(len(limit)-i-1)-1)//(q-1)
            if limit[i] not in digit: break
        return num