题目
You are given the following information, but you may prefer to do some research for yourself.
- 1 Jan 1900 was a Monday.
- Thirty days has September, April, June and November. All the rest have thirty-one, Saving February alone, Which has twenty-eight, rain or shine. And on leap years, twenty-nine.
- A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400. How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
解答
首先需要定义一个函数，给个年份，输出一年中每月的天数：
def get_days(year):
days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
if year % 100 == 0 and year % 400 == 0:
leap = 1
elif year % 100 != 0 and year % 4 == 0:
leap = 1
else:
leap = 0
days[1] += leap
return days
已知起点是1900-01-01是星期一，但我们的起点是1901-01-01，所以需要算一下，这一年过后是星期几，当然要算100年，每一年的1月1号是星期几都得知道，这样才好解题。无非是每月累加起来，模7，然后看月底最后一天是不是周六，因为是的话，则下个月的第一天是周日。就能够计数。
import numpy as np
def solution19():
start = sum(get_days(1900)) % 7
cnt = 0
for year in range(1901, 2001):
x = (np.cumsum(np.array(get_days(1901))) + start) % 7
cnt += np.sum(x == 6)
start = x[-1]
return cnt
