可爱小萌新刚学 博弈论 ,求助 10 分
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可爱小萌新刚学 博弈论 ,求助 10 分
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Loser_Syx楼主2024/8/4 14:36
#include <iostream>
#include <cassert>
#include <queue>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <random>
#include <ctime>
#include <map>
#include <set>
using namespace std;
// #define int long long
#define pii pair<int, int>
#define eb emplace_back
#define F first
#define S second
#define test(x) cout << "Test: " << (x) << '\n'
#define lowbit(x) (x & -x)
#define debug puts("qwq");
#define open(x) freopen(#x".in", "r", stdin);freopen(#x".out", "w", stdout);
#define close fclose(stdin);fclose(stdout);
namespace FastIO {
	template <typename T = int>
	inline T read() {
		T s = 0, w = 1;
		char c = getchar();
		while (!isdigit(c)) {
			if (c == '-') w = -1;
			c = getchar();
		}
		while (isdigit(c)) s = (s << 1) + (s << 3) + (c ^ 48), c = getchar();
		return s * w;
	}
	template <typename T>
	inline void read(T &s) {
		s = 0;
		int w = 1;
		char c = getchar();
		while (!isdigit(c)) {
			if (c == '-') w = -1;
			c = getchar();
		}
		while (isdigit(c)) s = (s << 1) + (s << 3) + (c ^ 48), c = getchar();
		s = s * w;
	}
	template <typename T, typename... Arp> inline void read(T &x, Arp &...arp) {
		read(x), read(arp...);
	}
	template <typename T>
	inline void write(T x, char ch = '\n') {
		if (x < 0) x = -x, putchar('-');
		static char stk[25];
		int top = 0;
		do {
			stk[top++] = x % 10 + '0', x /= 10;
		} while (x);
		while (top) putchar(stk[--top]);
		putchar(ch);
		return;
	}
	template <typename T>
	inline void smax(T &x, T y) {
		if (x < y) x = y;
	}
	template <typename T>
	inline void smin(T &x, T y) {
		if (x > y) x = y;
	}
	void quit() {
		exit(0);
	}
} using namespace FastIO;
const int N = 1e5 + 19;
int t[N * 20][2], tot = 1, vis[N], tag[N * 20], siz[N * 20], f[N], g[N], rt[N];
vector<int> e[N];
void pushup(int k) {
	siz[k] = siz[t[k][0]] + siz[t[k][1]];
}
void pushdown(int k, int dep) {
	if (tag[k]) {
		if ((tag[k] >> dep) & 1) swap(t[k][0], t[k][1]);
		tag[t[k][0]] ^= tag[k];
		tag[t[k][1]] ^= tag[k];
		tag[k] = 0;
	}
}
void insert(int &k, int w, int dep = 18) {
	if (!k) k = ++tot;
	if (!~dep) return siz[k] = 1, void();
	pushdown(k, w);
	insert(t[k][(w >> dep) & 1], w, dep - 1);
	pushup(k);
}
void merge(int &x, int y, int dep = 18) {
	if (!x || !y) return x |= y, void();
	if (dep == -1) return ;
	pushdown(x, dep); pushdown(y, dep);
	merge(t[x][0], t[y][0], dep - 1);
	merge(t[x][1], t[y][1], dep - 1);
	pushup(x);
}
int mex(int k, int x = 0) {
	for (int i = 18; ~i; --i) {
		if (siz[t[k][0]] != (1 << i)) k = t[k][0];
		else k = t[k][1], x |= (1 << i);
	}
	return x;
}
void dfs(int u, int fa) {
	vis[u] = 1;
	insert(rt[u], 0);
	for (int i : e[u]) {
		if (i == fa) continue;
		dfs(i, u);
		merge(rt[u], rt[i]);
		g[u] ^= f[i];
	}
	tag[rt[u]] ^= g[u];
	tag[rt[u]] ^= (f[u] = mex(rt[u]));
}
signed main() {
	int T = read();
	while (T--) {
		int n, m, ans = 0; read(n, m);
		for (int i = 1, u, v; i <= m; ++i) {
			read(u, v);
			e[u].eb(v), e[v].eb(u);
		}
		for (int i = 1; i <= n; ++i) {
			if (vis[i]) continue;
			dfs(i, i);
			ans ^= f[i];
		}
		puts(ans ? "Alice" : "Bob");
		for (int i = 0; i <= tot; ++i) t[i][0] = t[i][1] = tag[i] = siz[i] = 0;
		for (int i = 1; i <= n; ++i) vis[i] = f[i] = g[i] = rt[i] = 0;
		for (int i = 1; i <= n; ++i) e[i].clear();
		tot = 1;
	}
	return 0;
}
2024/8/4 14:36
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