#线性基，点分治#洛谷 3292 [SCOI2016]幸运数字

题目

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分析

题目就是将\(x\)到\(y\)路径上的线性基合并求解，

这里用的是点分治，每次换根到重心的时候维护前缀线性基，

查询的时候如果属于不同的子树就能询问答案，记得\(x=y\)要特判

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代码

#include <cstdio>
#include <cctype>
#include <cstring>
#define rr register
using namespace std;
typedef long long lll; const int N=20011,M=200011;
struct node{int y,next;}e[N<<1],E[M<<1];
int n,siz[N],big[N],as[N],SIZ,et=1,Et=1,tot,Q;
int v[N],root,b[N],is_ed[M],hs[N],st[N]; long long a[N],ans[M];
inline lll iut(){
	rr lll ans=0; rr char c=getchar();
	while (!isdigit(c)) c=getchar();
	while (isdigit(c)) ans=(ans<<3)+(ans<<1)+(c^48),c=getchar();
	return ans;
}
inline void print(lll ans){
	if (ans>9) print(ans/10);
	putchar(ans%10+48);
}
struct Vector_Space{
	lll re[61];
	inline void BUILD(){
		memset(re,0,sizeof(re));
	}
	inline void Insert(lll x){
		for (rr int i=60;~i;--i)
		if ((x>>i)&1){
			if (!re[i]) {re[i]=x; return;}
			x^=re[i];
		}
	}
	inline lll query(lll x){
		for (rr int i=60;~i;--i)
		    if ((x^re[i])>x) x^=re[i];
		return x;
	}
}H[N];
inline Vector_Space comb(Vector_Space A,Vector_Space B){
	rr Vector_Space C; C=A;
	for (rr int i=60;~i;--i) C.Insert(B.re[i]);
	return C;
}
inline signed max(int a,int b){return a>b?a:b;}
inline void dfs(int x,int fa){
	siz[x]=1,big[x]=0;
	for (rr int i=as[x];i;i=e[i].next)
	if (e[i].y!=fa&&!v[e[i].y]){
		dfs(e[i].y,x);
		siz[x]+=siz[e[i].y];
		big[x]=max(big[x],siz[e[i].y]);
	}
	big[x]=max(big[x],SIZ-siz[x]);
	if (big[x]<big[root]) root=x;
}
inline void Get(int x,int fa,int bel){
	st[++tot]=x,b[x]=bel,H[x]=H[fa],H[x].Insert(a[x]);
	for (rr int i=as[x];i;i=e[i].next)
	    if (!v[e[i].y]&&e[i].y!=fa) Get(e[i].y,x,bel);
}
inline void calc(int x){
	st[tot=1]=b[x]=x,H[x].BUILD(),H[x].Insert(a[x]);
	for (rr int i=as[x];i;i=e[i].next)
	    if (!v[e[i].y]) Get(e[i].y,x,e[i].y);
	for (rr int i=1;i<=tot;++i)
	for (rr int j=hs[st[i]];j;j=E[j].next)
	if (!is_ed[j>>1]&&(b[st[i]]^b[E[j].y]))
		is_ed[j>>1]=1,ans[j>>1]=comb(H[st[i]],H[E[j].y]).query(0);
}
inline void dp(int x){
	v[x]=1,calc(x);
	for (rr int i=as[x];i;i=e[i].next)
	if (!v[e[i].y]){
		big[0]=SIZ=siz[e[i].y];
		dfs(e[i].y,root=0),dp(root);
	}
}
signed main(){
	n=iut(),Q=iut();
	for (rr int i=1;i<=n;++i) a[i]=iut();
	for (rr int i=1;i<n;++i){
		rr int x=iut(),y=iut();
		e[++et]=(node){y,as[x]},as[x]=et;
		e[++et]=(node){x,as[y]},as[y]=et;
	}
	for (rr int i=1;i<=Q;++i){
		rr int x=iut(),y=iut();
		if (x==y) ans[i]=a[x],is_ed[i]=1;
		E[++Et]=(node){y,hs[x]},hs[x]=Et;
		E[++Et]=(node){x,hs[y]},hs[y]=Et;
	}
	big[0]=SIZ=n,dfs(1,root=0),dp(root);
	for (rr int i=1;i<=Q;++i)
	    print(ans[i]),putchar(10);
	return 0;
}