hdu1524 A Chess Game 有向无环图---sg

A Chess Game

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 916    Accepted Submission(s): 415

Problem Description

Let's design a new chess game. There are N positions to hold M chesses in this game. Multiple chesses can be located in the same position. The positions are constituted as a topological graph, i.e. there are directed edges connecting some positions, and no cycle exists. Two players you and I move chesses alternately. In each turn the player should move only one chess from the current position to one of its out-positions along an edge. The game does not end, until one of the players cannot move chess any more. If you cannot move any chess in your turn, you lose. Otherwise, if the misfortune falls on me... I will disturb the chesses and play it again.

Do you want to challenge me? Just write your program to show your qualification!

Input

Input contains multiple test cases. Each test case starts with a number N (1 <= N <= 1000) in one line. Then the following N lines describe the out-positions of each position. Each line starts with an integer Xi that is the number of out-positions for the position i. Then Xi integers following specify the out-positions. Positions are indexed from 0 to N-1. Then multiple queries follow. Each query occupies only one line. The line starts with a number M (1 <= M <= 10), and then come M integers, which are the initial positions of chesses. A line with number 0 ends the test case.

Output

There is one line for each query, which contains a string "WIN" or "LOSE". "WIN" means that the player taking the first turn can win the game according to a clever strategy; otherwise "LOSE" should be printed.

Sample Input

   
   
   
   

    
    
    
    4
2 1 2
0
1 3
0
1 0
2 0 2
0

4
1 1
1 2
0
0
2 0 1
2 1 1
3 0 1 3
0
   
   
   
   

Sample Output

   
   
   
   

    
    
    
    WIN
WIN
WIN
LOSE
WIN
   
   
   
   

Source

PKU Monthly

Recommend

LL

 

在一个有向无环图上给定几颗棋子的初始位置，问谁有必胜策略。

求出每个点的sg值。异或。

#include<iostream>
#include<cstdlib>
#include<stdio.h>
#include<memory.h>
using namespace std;
int mat[1010][1010];
int n;
int sg[1010];
int dfs(int d)
{
    if(sg[d]!=-1) return sg[d];
    bool g[1010]={0};
    for(int i=0;i<n;i++)
    {
        if(mat[d][i]==1)
        {
            g[dfs(i)]=1;
        }
    }
    for(int i=0;;i++)
    if(g[i]==0) return sg[d]=i;
}
int main()
{
    int m,x,y,q;
    while(scanf("%d",&n)!=EOF)
    {
        memset(mat,-1,sizeof(mat));
        memset(sg,-1,sizeof(sg));
        for(int i=0;i<n;i++)
        {
            scanf("%d",&x);
            if(x==0)  sg[i]=0;
            while(x--)
            {
                scanf("%d",&y);
                mat[i][y]=1;
            }
        }
        scanf("%d",&m);
        while(1)
        {
            if(m==0) break;
            int ans=0;
            for(int i=0;i<m;i++)
            {
                scanf("%d",&q);
                if(sg[q]!=-1) ans^=sg[q];
                else
                ans^=dfs(q);
            }
            if(ans!=0) puts("WIN");
            else puts("LOSE");
            scanf("%d",&m);
        }
    }
}