Count Days Spent Together — Python

# Time:  O(1)
# Space: O(1)

# prefix sum
class Solution(object):
    def countDaysTogether(self, arriveAlice, leaveAlice, arriveBob, leaveBob):
        """
        :type arriveAlice: str
        :type leaveAlice: str
        :type arriveBob: str
        :type leaveBob: str
        :rtype: int
        """
        NUMS = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
        prefix = [0]*(len(NUMS)+1)
        for i in xrange(len(NUMS)):
            prefix[i+1] += prefix[i]+NUMS[i]
    
        def day(date):
            return prefix[int(date[:2])-1]+int(date[3:])

        return max(day(min(leaveAlice, leaveBob))-day(max(arriveAlice, arriveBob))+1, 0)