[AcWing 894] 拆分-Nim游戏

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点击查看代码

#include<iostream>
#include<cstring>
#include<unordered_set>

using namespace std;
const int N = 110;
int n;
int f[N];

int sg(int x)
{
    if (f[x] != -1)     return f[x];
    unordered_set<int> S;
    for (int i = 0; i < x; i ++)
        // 避免重复
        for (int j = 0; j <= i; j ++)
            S.insert(sg(i) ^ sg(j));
    for (int i = 0; ; i ++)
        if (!S.count(i))
            return f[x] = i;
}
int main()
{
    cin >> n;
    memset(f, -1, sizeof f);
    int res = 0;
    for (int i = 0; i < n; i ++) {
        int x;
        cin >> x;
        res ^= sg(x);
    }
    if (res)    puts("Yes");
    else    puts("No");
    return 0;
}

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1. $SG$ 定理
   $SG(b_1, b_2) = SG(b_1) \oplus SG(b_2)$