Game of Cards Gym - 101128G (SG函数)

Posted 2021-11-27 jiaaaaaaaqi

Problem G: Game of Cards

\[ Time Limit: 1 s \quad Memory Limit: 256 MiB \]

题意

题意就是给出\(n\)堆扑克牌，然后给出一个\(m\)，每次一个人的操作方法是从一堆扑克牌上面选出\(0-m\)张牌拿开，然后此时顶上牌的点数是\(x\)，在拿开\(x\)张牌，最后不能操作的人输。

思路

就是一个裸的\(sg\)函数，用dfs比较好写，然后直接模拟就可以了。

/***************************************************************
    > File Name    : G.cpp
    > Author       : Jiaaaaaaaqi
    > Created Time : 2019年05月06日 星期一 18时04分27秒
 ***************************************************************/

#include <map>
#include <set>
#include <list>
#include <ctime>
#include <cmath>
#include <stack>
#include <queue>
#include <cfloat>
#include <string>
#include <vector>
#include <cstdio>
#include <bitset>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define  lowbit(x)  x & (-x)
#define  mes(a, b)  memset(a, b, sizeof a)
#define  fi         first
#define  se         second
#define  pii        pair<int, int>
#define  INOPEN     freopen("in.txt", "r", stdin)
#define  OUTOPEN    freopen("out.txt", "w", stdout)

typedef unsigned long long int ull;
typedef long long int ll;
const int    maxn = 1e3 + 10;
const int    maxm = 1e5 + 10;
const ll     mod  = 1e9 + 7;
const ll     INF  = 1e18 + 100;
const int    inf  = 0x3f3f3f3f;
const double pi   = acos(-1.0);
const double eps  = 1e-8;
using namespace std;

int n, m, k;
int cas, tol, T;

int a[maxn];
ll sg[maxn];

void dfs(int x) {
    if(sg[x] != -1) return ;
    vector<bool> vis(maxn, false);
    for(int i=0; i<=m; i++) {
        int up = x-i;
        if(up <= 0) break;
        int nxt = up - a[up];
        if(nxt < 0) continue;
        dfs(nxt);
        vis[sg[nxt]] = true;
    }
    for(int i=0; ; i++) {
        if(!vis[i]) {
            sg[x] = i;
            return ;
        }
    }
}

int main() {
    scanf("%d%d", &T, &m);
    ll ans = 0;
    while(T--) {
        scanf("%d", &n);
        mes(a, 0);
        mes(sg, -1);
        a[0] = sg[0] = 0;
        for(int i=1; i<=n; i++) {
            scanf("%d", &a[i]);
        }
        dfs(n);
        ans ^= sg[n];
    }
    if(ans) 
        printf("Alice can win.\n");
    else    
        printf("Bob will win.\n");
    return 0;
}