Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 65536 KB
Adam and Eve enter this year's ACM International Collegiate Programming Contest.
Last night, they played the Calendar Game, in celebration of this contest. This game
consists of the dates from January 1, 1900 to November 4, 2001, the contest day. The
game starts by randomly choosing a date from this interval. Then, the players, Adam
and Eve, make moves in their turn with Adam moving first: Adam, Eve, Adam, Eve, etc.
There is only one rule for moves and it is simple: from a current date, a player in
his/her turn can move either to the next calendar date or the same day of the next
month. When the next month does not have the same day, the player moves only to the
next calendar date. For example, from December 19, 1924, you can move either to
December 20, 1924, the next calendar date, or January 19, 1925, the same day of the
next month. From January 31 2001, however, you can move only to February 1, 2001,
because February 31, 2001 is invalid.
A player wins the game when he/she exactly reaches the date of November 4, 2001. If a player moves to a date after November 4, 2001, he/she looses the game.
Write a program that decides whether, given an initial date, Adam, the first mover, has a winning strategy.
For this game, you need to identify leap years, where February has 29 days. In the Gregorian calendar, leap years occur in years exactly divisible by four. So, 1993, 1994, and 1995 are not leap years, while 1992 and 1996 are leap years. Additionally, the years ending with 00 are leap years only if they are divisible by 400. So, 1700, 1800, 1900, 2100, and 2200 are not leap years, while 1600, 2000, and 2400 are leap years.