[原创]HDU 3389 Game(博弈 Nim 找规律)

2016-08-12 13:42:04 Tabris_ 阅读数：192

https://blog.csdn.net/qq_33184171/article/details/52190898

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Game
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 610 Accepted Submission(s): 426

Problem Description
Bob and Alice are playing a new game. There are n boxes which have been numbered from 1 to n. Each box is either empty or contains several cards. Bob and Alice move the cards in turn. In each turn the corresponding player should choose a non-empty box A and choose another box B that B < A && (A+B)%2=1 && (A+B)%3=0. Then, take an arbitrary number (but not zero) of cards from box A to box B. The last one who can do a legal move wins. Alice is the first player. Please predict who will win the game.

Input
The first line contains an integer T (T<=100) indicating the number of test cases. The first line of each test case contains an integer n (1<=n<=10000). The second line has n integers which will not be bigger than 100. The i-th integer indicates the number of cards in the i-th box.

Output
For each test case, print the case number and the winner’s name in a single line. Follow the format of the sample output.

Sample Input
2
2
1 2
7
1 3 3 2 2 1 2

Sample Output
Case 1: Alice
Case 2: Bob

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1.最后一定会放到 1 3 4这3个盒子里
2.右边最终能移到1 3 4中的哪一个也是能够求的
3.右边的移到左边的步数是偶数个还是奇数个也是可求的 只要经过偶数步数才能到达的 都是必败点

%3 == 1 偶数步骤后到达盒子1

%3 == 2 ji步骤后到达盒子2

%3 == 1 偶数步骤后到达盒子1

%3 == 2 奇数步骤后到达盒子4

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