[洛谷P3292][SCOI2016]幸运数字

题目大意：给一棵$n(nleqslant2 imes10^4)$个点的树，$m(mleqslant2 imes10^5)$个询问，每次问$x->y$路径上的树异或最大值

题解：可以点分治，线性基合并即可

卡点：一处查询的地方写成了$maxn$

C++ Code：

#include <algorithm>
#include <cstdio>
#include <cctype>
namespace __IO {
	namespace R {
		int x, ch;
		inline int read() {
			ch = getchar();
			while (isspace(ch)) ch = getchar();
			for (x = ch & 15, ch = getchar(); isdigit(ch); ch = getchar()) x = x * 10 + (ch & 15);
			return x;
		}
		long long X;
		inline long long readll() {
			ch = getchar();
			while (isspace(ch)) ch = getchar();
			for (X = ch & 15, ch = getchar(); isdigit(ch); ch = getchar()) X = X * 10 + (ch & 15);
			return X;
		}
	}
}
using __IO::R::read;
using __IO::R::readll;

#define maxn 20010
#define maxm 200010
const int inf = 0x3f3f3f3f;

int head[maxn], cnt = 1;
struct Edge {
	int to, nxt;
} e[maxn << 1];
inline void addedge(int a, int b) {
	e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;
	e[++cnt] = (Edge) {a, head[b]}; head[b] = cnt;
}

int headq[maxm], cntq = 1;
struct Query {
	int to, nxt;
	bool vis;
} qu[maxm << 1];
inline void addquery(int a, int b) {
	qu[++cntq] = (Query) {b, headq[a], false}; headq[a] = cntq;
	qu[++cntq] = (Query) {a, headq[b], false}; headq[b] = cntq;
}

struct Base {
#define M 60
	long long s[M + 1];

	inline Base& init() {
		for (int i = 0; i <= M; i++) s[i] = 0;
		return *this;
	}
	inline Base& insert(long long x) {
		for (int i = M; ~i; i--) if (x >> i & 1) {
			if (s[i]) x ^= s[i];
			else {s[i] = x; break;}
		}
		return *this;
	}
	inline friend Base operator + (Base a, const Base &b) {
		for (int i = M; ~i; i--) if (b.s[i]) a.insert(b.s[i]);
		return a;
	}
	long long query() {
		long long ans = 0;
		for (int i = M; ~i; i--) if (ans < (ans ^ s[i])) ans ^= s[i];
		return ans;
	}
#undef M
} f[maxn];

bool vis[maxn];
namespace Center_of_Gravity {
	int sz[maxn], __nodenum;
	int root, MIN;
#define n __nodenum
	void __getroot(int u, int fa = 0) {
		sz[u] = 1;
		int MAX = 0;
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (v != fa && !vis[v]) {
				__getroot(v, u);
				sz[u] += sz[v];
				MAX = std::max(MAX, sz[v]);
			}
		}
		MAX = std::max(MAX, n - sz[u]);
		if (MAX < MIN) MIN = MAX, root = u;
	}
	int getroot(int u, int nodenum = 0) {
		n = nodenum ? nodenum : sz[u];
		MIN = inf;
		__getroot(u);
		return root;
	}
#undef n
}
using Center_of_Gravity::getroot;

int n, Q;
long long w[maxn], ans[maxm];
int S[maxn], top, bel[maxn];

void getlist(int u, int fa, int tg) {
	bel[S[top++] = u] = tg;
	(f[u] = f[fa]).insert(w[u]);
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (v != fa && !vis[v]) getlist(v, u, tg);
	}
}
void solve(int u) {
	vis[u] = true, (f[u].init()).insert(w[u]), top = 0;
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (!vis[v]) getlist(v, u, v);
	}
	for (int i = headq[u]; i; i = qu[i].nxt) if (!qu[i].vis){
		ans[i >> 1] = f[qu[i].to].query();
		qu[i].vis = qu[i ^ 1].vis = true;
	}
	for (int j = 0; j < top; j++) {
		int u = S[j];
		for (int i = headq[u]; i; i = qu[i].nxt) if (!qu[i].vis) {
			int v = qu[i].to;
			if (bel[u] != bel[v]) {
				ans[i >> 1] = (f[u] + f[v]).query();
				qu[i].vis = qu[i ^ 1].vis = true;
			}
		}
	}
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (!vis[v]) solve(getroot(v));
	}
}

int main() {
	n = read(), Q = read();
	for (int i = 1; i <= n; i++) w[i] = readll();
	for (int i = 1, a, b; i < n; i++) {
		a = read(), b = read();
		addedge(a, b);
	}
	for (int i = 0, a, b; i < Q; i++) {
		a = read(), b = read();
		addquery(a, b);
	}

	solve(getroot(1, n));
	for (int i = 1; i <= Q; i++) printf("%lld
", ans[i]);
	return 0;
}