hdu 5742 chess SG函数

最新推荐文章于 2020-12-17 20:03:05 发布

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本文介绍了一种特殊的棋盘游戏，玩家在n×20的棋盘上移动棋子，遵循特定规则。通过分析游戏机制及使用SG函数，找到了先手玩家获胜条件的规律。

Chess

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1908 Accepted Submission(s): 831

Problem Description

Alice and Bob are playing a special chess game on an n × 20 chessboard. There are several chesses on the chessboard. They can move one chess in one turn. If there are no other chesses on the right adjacent block of the moved chess, move the chess to its right adjacent block. Otherwise, skip over these chesses and move to the right adjacent block of them. Two chesses can’t be placed at one block and no chess can be placed out of the chessboard. When someone can’t move any chess during his/her turn, he/she will lose the game. Alice always take the first turn. Both Alice and Bob will play the game with the best strategy. Alice wants to know if she can win the game.

Input

Multiple test cases.

The first line contains an integer

T(T≤100), indicates the number of test cases.

For each test case, the first line contains a single integer

n(n≤1000), the number of lines of chessboard.

Then

n lines, the first integer of ith line is

m(m≤20), indicates the number of chesses on the ith line of the chessboard. Then m integers

pj(1≤pj≤20)followed, the position of each chess.

Output

For each test case, output one line of “YES” if Alice can win the game, “NO” otherwise.

Sample Input

Sample Output

NO
YES

题意：给n堆石子，有两种操作，第一种是选择任意一堆取走一些石子，可以取完这一堆，但不能不取。第二种操作是把某一堆分成三堆石子，每堆石子不能为空。问先手是否必胜。

SG函数，因为数据是1e9，所以打表找一下规律。

#include <bits/stdc++.h>

using namespace std;

int SG[1000];
int sg(int x)
{
    if(SG[x] != -1) return SG[x];
    int vis[150] = {0};
    for(int i = 1;i <= x;i++)     ///正常的nim取石子
        vis[sg(x-i)] = 1;
    for(int i = 1;i <= 100;i++){  ///采用另一种操作，分成三堆
        for(int j = 1;j <= 100;j++){
            for(int k = 1;k <= 100;k++){
                if(i+j+k == x){
                    vis[sg(i)^sg(j)^sg(k)] = 1;
                }
            }
        }
    }
    for(int i = 0;;i++)
        if(!vis[i]) return SG[x] = i;
}

void Init()
{
    memset(SG,-1,sizeof SG);
    SG[0] = 0;
    SG[1] = 1;
    SG[2] = 2;
    sg(100);
    for(int i = 0;i <= 100;i++) printf("%d %d\n",i,SG[i]);
}

int SG_(int x)
{
    if(x%8 == 7) return x+1;
    if(x%8 == 0) return x-1;
    return x;
}

int main()
{
    //Init();  打表找规律
    int T;
    scanf("%d",&T);
    while(T--){
        int n;
        scanf("%d",&n);
        int ans = 0;
        for(int i = 1;i <= n;i++){
            int t;
            scanf("%d",&t);
            ans ^= SG_(t);
        }
        if(ans) puts("First player wins.");
        else    puts("Second player wins.");
    }
    return 0;
}