Project Euler 题解 #19 Counting Sundays

题目：Counting Sundays

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)?

解题思路

蔡勒公式：一种计算任何一日属一星期中哪一日的算法。

这个公式太牛B了，没看的很明白。

参考下这几个：

蔡勒公式的由来

求某一天是星期几

星期的计算

代码实现

//https://projecteuler.net/problem=19//Counting Sundays#include <cassert>#include <iostream>using namespace std;const char *DayInWeek[] = {"momday", "tuesday", "wednesday", "thursday", "friday", "saturday", "sunday"};//返回值//0:星期一//...//6:星期天int DayOfWeek(int year, int month, int day){assert(year >  0);assert(1 <= month && month <= 12);assert(1 <= day && day <= 31);int dayofweek = 0;if (month == 1 || month == 2){month += 12;year--;}if ((year < 1752) || (year == 1752 && month < 9) || (year == 1752 && month == 9 && day < 3)){dayofweek = (day + 2*month + 3*(month + 1)/5 + year + year/4 + 5)%7;} else{dayofweek = (day + 2*month + 3*(month + 1)/5 + year + year/4 - year/100 + year/400)%7;}return dayofweek;}int _tmain(int argc, _TCHAR* argv[]){cout<<DayInWeek[DayOfWeek(2013, 9, 27)]<<endl;int count = 0;for (int year = 1901; year <= 2000; ++year){for (int month = 1; month <= 12; ++month){if (6 == DayOfWeek(year, month, 1)){++count;}}}cout<<"There are "<<count<<" Sundays fell on the first of the month during the twentieth century"<<endl;system("pause");return 0;}

输出：171

有位读者提出公式1200/7 = 171

可见数学的魅力所在。