S-Nim
Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4091 Accepted Submission(s): 1760
Problem Description
Arthur and his sister Caroll have been playing a game called Nim for some time now. Nim is played as follows:
The starting position has a number of heaps, all containing some, not necessarily equal, number of beads.
The players take turns chosing a heap and removing a positive number of beads from it.
The first player not able to make a move, loses.
Arthur and Caroll really enjoyed playing this simple game until they recently learned an easy way to always be able to find the best move:
Xor the number of beads in the heaps in the current position (i.e. if we have 2, 4 and 7 the xor-sum will be 1 as 2 xor 4 xor 7 = 1).
If the xor-sum is 0, too bad, you will lose.
Otherwise, move such that the xor-sum becomes 0. This is always possible.
It is quite easy to convince oneself that this works. Consider these facts:
The player that takes the last bead wins.
After the winning player's last move the xor-sum will be 0.
The xor-sum will change after every move.
Which means that if you make sure that the xor-sum always is 0 when you have made your move, your opponent will never be able to win, and, thus, you will win.
Understandibly it is no fun to play a game when both players know how to play perfectly (ignorance is bliss). Fourtunately, Arthur and Caroll soon came up with a similar game, S-Nim, that seemed to solve this problem. Each player is now only allowed to remove
a number of beads in some predefined set S, e.g. if we have S =(2, 5) each player is only allowed to remove 2 or 5 beads. Now it is not always possible to make the xor-sum 0 and, thus, the strategy above is useless. Or is it?
your job is to write a program that determines if a position of S-Nim is a losing or a winning position. A position is a winning position if there is at least one move to a losing position. A position is a losing position if there are no moves to a losing position.
This means, as expected, that a position with no legal moves is a losing position.
Input
Input consists of a number of test cases. For each test case: The first line contains a number k (0 < k ≤ 100 describing the size of S, followed by k numbers si (0 < si ≤ 10000) describing S. The second line contains a number m (0 < m ≤ 100) describing the
number of positions to evaluate. The next m lines each contain a number l (0 < l ≤ 100) describing the number of heaps and l numbers hi (0 ≤ hi ≤ 10000) describing the number of beads in the heaps. The last test case is followed by a 0 on a line of its own.
Output
For each position: If the described position is a winning position print a 'W'.If the described position is a losing position print an 'L'. Print a newline after each test case.
Sample Input
2 2 5
3
2 5 12
3 2 4 7
4 2 3 7 12
5 1 2 3 4 5
3
2 5 12
3 2 4 7
4 2 3 7 12
0
Sample Output
LWW
WWL
Source
Norgesmesterskapet 2004
題目：http://acm.hdu.edu.cn/showproblem.php?pid=1536
這也是一道經典SG函數的題目。
有關於SG函數的解，可以戳這個，很詳細→http://blog.csdn.net/lttree/article/details/24886205
這道題題意：
我就按著樣例格式來說吧：
先輸入一個K，表示取數集合的個數。（K為0，則結束）
後面跟k個數,表示取數集合的數（就是每次只能取這幾個數量的物品）
然後會跟一個M,表示有M次詢問。
然後接下來M行，每行先有一個N，表示有多少堆物品。
N後跟著N個數，表示每堆物品數量。
因為，OJ後台的操作，輸入和輸出是分開的（其實就是將你的程序的答案存成一個TXT文件，然後和
標准答案TXT文件進行二進制的比較）
所以，我每個N都直接輸出'L'或者'W‘，
在M行結束時，換行，沒有用數組來存答案。
PS：用scanf比cin快80MS
/************************************************
*************************************************
* Author:Tree *
*From :http://blog.csdn.net/lttree *
* Title : S-Nim *
*Source: hdu 1536 *
* Hint : SG *
*************************************************
*************************************************/
#include
#include
#include
using namespace std;
#define N 10001
int f[N],sg[N];
bool mex[N];
void get_sg(int t,int n)
{
int i,j;
memset(sg,0,sizeof(sg));
for(i=1;i<=n;i++)
{
memset(mex,0,sizeof(mex));
// 對於屬於g(x)後繼的數置1
for( j=1 ;j<=t && f[j]<=i ;j++ )
mex[sg[i-f[j]]]=1;
// 找到最小不屬於該集合的數
for( j=0 ; j<=n ; j++ )
if(!mex[j])
break;
sg[i] = j;
}
}
int main()
{
int k,m,n,i,t,temp;
while( scanf("%d",&k) && k )
{
for(i=1;i<=k;++i)
scanf("%d",&f[i]);
sort(f+1,f+k+1);
get_sg(k,N);
scanf("%d",&m);
while(m--)
{
temp=0;
scanf("%d",&n);
for(i=0;i
