Cutting Game
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 2844 | Accepted: 1036 |
Description
Urej loves to play various types of dull games. He
usually asks other people to play with him. He says that playing those games can
show his extraordinary wit. Recently Urej takes a great interest in a new game,
and Erif Nezorf becomes the victim. To get away from suffering playing such a
dull game, Erif Nezorf requests your help. The game uses a rectangular paper
that consists of W*H grids. Two players cut the paper into two pieces of
rectangular sections in turn. In each turn the player can cut either
horizontally or vertically, keeping every grids unbroken. After N turns the
paper will be broken into N+1 pieces, and in the later turn the players can
choose any piece to cut. If one player cuts out a piece of paper with a single
grid, he wins the game. If these two people are both quite clear, you should
write a problem to tell whether the one who cut first can win or not.
Input
The input contains multiple test cases. Each test
case contains only two integers W and H (2 <= W, H <= 200) in one line,
which are the width and height of the original paper.
Output
For each test case, only one line should be
printed. If the one who cut first can win the game, print "WIN", otherwise,
print "LOSE".
Sample Input
2 2
3 2
4 2
Sample Output
LOSE
LOSE
WIN
Source
POJ
Monthly,CHEN Shixi(xreborner)
sg函数
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <algorithm>
5 #include <set>
6
7 using namespace std;
8
9 const int MAX_N = 205;
10 int dp[MAX_N][MAX_N];
11
12 int grundy(int w, int h) {
13 if(dp[w][h] != -1) return dp[w][h];
14
15 set<int> s;
16 for(int i = 2; w - i >= 2; i++) {
17 s.insert(grundy(i, h) ^ grundy(w - i,h));
18 }
19 for(int i = 2; h - i >= 2; ++i) {
20 s.insert(grundy(w, i) ^ grundy(w, h - i));
21 }
22
23 int res = 0;
24 while(s.count(res)) res++;
25 return dp[w][h] = res;
26 }
27
28 int main()
29 {
30 //freopen("sw.in","r",stdin);
31 int w, h;
32
33 for(int i = 1; i <= 200; ++i) {
34 for(int j = 1; j <= 200; ++j) dp[i][j] = -1;
35 }
36 while(~scanf("%d%d",&w,&h)) {
37 printf("%s\n",grundy(w, h) ? "WIN" : "LOSE");
38 }
39 //cout << "Hello world!" << endl;
40 return 0;
41 }