4、博弈论例题

AcWing 891. Nim游戏

AcWing 892. 台阶-Nim游戏

AcWing 893. 集合-Nim游戏

AcWing 894. 拆分-Nim游戏

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 100010;


int main()
{
    int n;
    scanf("%d", &n);

    int res = 0;
    while (n -- )
    {
        int x;
        scanf("%d", &x);
        res ^= x;
    }

    if (res) puts("Yes");
    else puts("No");

    return 0;
}

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 100010;

int main()
{
    int n;
    scanf("%d", &n);

    int res = 0;
    for (int i = 1; i <= n; i ++ )
    {
        int x;
        scanf("%d", &x);
        if (i & 1) res ^= x;
    }

    if (res) puts("Yes");
    else puts("No");

    return 0;
}

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

using namespace std;

const int N = 110, M = 10010;

int n, m;
int s[N], f[M];


int sg(int x)
{
    if (f[x] != -1) return f[x];

    unordered_set<int> S;
    for (int i = 0; i < m; i ++ )
    {
        int sum = s[i];
        if (x >= sum) S.insert(sg(x - sum));
    }

    for (int i = 0; ; i ++ )
        if (!S.count(i))
            return f[x] = i;
}


int main()
{
    cin >> m;
    for (int i = 0; i < m; i ++ ) cin >> s[i];
    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;
}

#include <cstring>
#include <iostream>
#include <algorithm>
#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 ++ )
        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;
    while (n -- )
    {
        int x;
        cin >> x;
        res ^= sg(x);
    }

    if (res) puts("Yes");
    else puts("No");

    return 0;
}