coreBugZJ

此 blog 已棄。

POJ 2975 Nim

/*
2

POJ 2975 Nim
3

----問題描述：
6

Nim is a 2-player game featuring several piles of stones. Players alternate turns, and on his/her turn, a player’s move consists of removing one or more stones from any single pile. Play ends when all the stones have been removed, at which point the last player to have moved is declared the winner. Given a position in Nim, your task is to determine how many winning moves there are in that position.
8

A position in Nim is called “losing” if the first player to move from that position would lose if both sides played perfectly. A “winning move,” then, is a move that leaves the game in a losing position. There is a famous theorem that classifies all losing positions. Suppose a Nim position contains n piles having k1, k2, …, kn stones respectively; in such a position, there are k1 + k2 + … + kn possible moves. We write each ki in binary (base 2). Then, the Nim position is losing if and only if, among all the ki’s, there are an even number of 1’s in each digit position. In other words, the Nim position is losing if and only if the xor of the ki’s is 0.
10

Consider the position with three piles given by k1 = 7, k2 = 11, and k3 = 13. In binary, these values are as follows:
12

0111
14

1011
15

1101
16

There are an odd number of 1’s among the rightmost digits, so this position is not losing. However, suppose k3 were changed to be 12. Then, there would be exactly two 1’s in each digit position, and thus, the Nim position would become losing. Since a winning move is any move that leaves the game in a losing position, it follows that removing one stone from the third pile is a winning move when k1 = 7, k2 = 11, and k3 = 13. In fact, there are exactly three winning moves from this position: namely removing one stone from any of the three piles.
18

----輸入：
21

The input test file will contain multiple test cases, each of which begins with a line indicating the number of piles, 1 ≤ n ≤ 1000. On the next line, there are n positive integers, 1 ≤ ki ≤ 1, 000, 000, 000, indicating the number of stones in each pile. The end-of-file is marked by a test case with n = 0 and should not be processed.
23

----輸出：
26

For each test case, write a single line with an integer indicating the number of winning moves from the given Nim position.
28

----樣例輸入：
31

3
33

7 11 13
34

2
35

1000000000 1000000000
36

0
37

----樣例輸出：
40

3
42

0
43

----分析：
46

經典 Nim 博弈。
48

*/
51

#include <iostream>
54

#include <cstdio>
55

using namespace std;
57

const int N = 1009;
59

int n, k[ N ];
60

int main() {
62

int i, s, c;
63

while ( (1 == scanf( "%d", &n )) && (0 < n) ) {
64

s = 0;
65

for ( i = 0; i < n; ++i ) {
66

scanf( "%d", k + i );
67

s = (s ^ k[ i ]);
68

}
69

if ( 0 == s ) {
70

puts( "0" );
71

continue;
72

}
73

c = 0;
74

for ( i = 0; i < n; ++i ) {
75

if ( (s ^ k[ i ]) <= k[ i ] ) {
76

++c;
77

}
78

}
79

printf( "%d\n", c );
80

}
81

return 0;
82

}
83

posted on 2012-06-04 16:01 coreBugZJ 閱讀(1012) 評論(0) 編輯收藏引用所屬分類: ACM 、Algorithm 、Mathematics 、課內作業

只有注冊用戶登錄后才能發表評論。


相關文章: 微軟2014實習生及秋令營技術類職位在線測試 TopCoder SRM 593 DIV2 第三題生成全排列的非回溯方法（TopCoder SRM 591 DIV 2） A* 算法求解八數碼問題，POJ 1077 Eight POJ 1067 取石子游戲 POJ 2068 Nim POJ 2975 Nim POJ 3696 The Luckiest number POJ 3604 Professor Ben EOJ 1117 剩余定理

網站導航: 博客園 IT新聞 BlogJava 博問 Chat2DB 管理

青青草原综合久久大伊人导航_色综合久久天天综合_日日噜噜夜夜狠狠久久丁香五月_热久久这里只有精品

coreBugZJ

My Links

Blog Stats

常用鏈接

留言簿(10)

隨筆分類(458)

隨筆檔案(268)

相冊

ACM

AI

LaTeX

安全

編程語言

好有道理

技術

開源

科學

數學

圖形圖像

文化

問題（練習＆有趣）

資源

最新隨筆

搜索

最新評論

閱讀排行榜

評論排行榜

POJ 2975 Nim