AcWing 894. 拆分-Nim游戏 (博弈论)

题目
数论章节中的最后一题，也是博弈论的最后一节。
堆ai拆分成b1,b2后，一个重要的性质就是sg（b1,b2） = sg(b1) ^ sg(b2)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

class Main {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter pw = new PrintWriter(System.out);
    static int N = 110;
    static int f[] = new int[N];

    public static void main(String[] args) throws IOException {
        String[] s = br.readLine().split(" ");
        int n = Integer.parseInt(s[0]);
        Arrays.fill(f, -1);
        int res = 0;
        s = br.readLine().split(" ");
        for (int i = 0; i < n; i++) {
            int x = Integer.parseInt(s[i]);
            res ^= sg(x);
        }

        if (res == 0) pw.println("No");
        else pw.println("Yes");
        pw.flush();
        pw.close();
        br.close();
    }

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

        Set<Integer> set = new HashSet<>();

        for (int i = 0; i < x; i++)
            for (int j = 0; j < i; j++)
                set.add(sg(i) ^ sg(j));

        //mex
        for (int i = 0; ; i++)
            if (!set.contains(i))
                return f[x] = i;
    }
}