projecteuler---->problem=19----Counting Sundays

weixin_34067049發表於2015-07-10
Project

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)

翻譯：

現提供你例如以下資訊，只是你可能希望自己印證一下。

  • 1900年1月1日是星期一
  • 除了二月外。四月，六月，九月，十一月，都有30天，其它月份都有31天。

  • 二月在平年有28天，在閏年有29天。
  • 能被4整除的年份是閏年。只是每一個世紀年（??00）必須能被400整除才是閏年。

請問，在20世紀中（從1901年1月1日到2000年12月31日）總共同擁有多少個月份的第一日是星期天？

def f(year,month):
  tmpDay=1
  if month == 1 or month == 2:
      month += 12
      year-=1  
  if ((year<1752) or (year==1752 and month<9) or (year==1752 and month==9 and tmpDay<3)):  
       a = (tmpDay + 2*month + 3*(month+1)/5 + year + year/4 +5) % 7;  
  else:  
       a = (tmpDay + 2*month + 3*(month+1)/5 + year + year/4 - year/100 + year/400)%7
  return a
resu=0
for i in range(1901,2001):
    for j in range(1,13):
       if f(i,j)==1 :
           resu+=1
print resu


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