CF766 E. Mahmoud and a xor trip

题目传送门：https://codeforces.com/problemset/problem/766/E

题目大意：
给定一棵节点数为\(n\)的树，求树上任意两点之间异或路径值之和，记 \(x,y\) 之间的最短路经过点\(p_1,p_2,...,p_k\)，其中\(p_1=x,p_k=y\)，则异或路径值\(V=p_1\otimes p_2\otimes...\otimes p_k\)

---

经典的Tree DP吧

记\(F[x][K][0/1]\)表示所有从\(x\)出发的路径中，第\(K\)位为\(0/1\)的情况总数

之后我们再进行二次换根，对所有节点做根的情况都进行统计即可

/*program from Wolfycz*/
#include<map>
#include<cmath>
#include<cstdio>
#include<vector>
#include<cstring>
#include<iostream>
#include<algorithm>
#define Fi first
#define Se second
#define ll_inf 1e18
#define MK make_pair
#define sqr(x) ((x)*(x))
#define pii pair<int,int>
#define int_inf 0x7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
	static char buf[1000000],*p1=buf,*p2=buf;
	return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
template<typename T>inline T frd(T x){
	int f=1; char ch=gc();
	for (;ch<'0'||ch>'9';ch=gc())	if (ch=='-')    f=-1;
	for (;ch>='0'&&ch<='9';ch=gc())	x=(x<<1)+(x<<3)+ch-'0';
	return x*f;
}
template<typename T>inline T read(T x){
	int f=1; char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar())	if (ch=='-')	f=-1;
	for (;ch>='0'&&ch<='9';ch=getchar())	x=(x<<1)+(x<<3)+ch-'0';
	return x*f;
}
inline void print(int x){
	if (x<0)	putchar('-'),x=-x;
	if (x>9)	print(x/10);
	putchar(x%10+'0');
}
const int N=1e5,M=20;
int pre[(N<<1)+10],now[N+10],child[(N<<1)+10],tot;
ll V[N+10],F[N+10][M+10][2];
void join(int x,int y){pre[++tot]=now[x],now[x]=tot,child[tot]=y;}
void insert(int x,int y){join(x,y),join(y,x);}
#define T(x) ((V[x]>>K)&1)
void Dfs(int x,int fa){
	for (int K=0;K<=M;K++)	F[x][K][T(x)]++;
	for (int p=now[x];p;p=pre[p]){
		int son=child[p];
		if (son==fa)	continue;
		Dfs(son,x);
		for (int K=0;K<=M;K++){
			F[x][K][0]+=F[son][K][T(x)^0];
			F[x][K][1]+=F[son][K][T(x)^1];
		}
	}
}
void Rorate(int x,int fa){
	if (fa){
		for (int K=0;K<=M;K++){
			ll delta[2];
			delta[0]=F[fa][K][T(x)^0]-F[x][K][T(fa)^T(x)^0];
			delta[1]=F[fa][K][T(x)^1]-F[x][K][T(fa)^T(x)^1];
			F[x][K][0]+=delta[0];
			F[x][K][1]+=delta[1];
		}
	}
	for (int p=now[x];p;p=pre[p]){
		int son=child[p];
		if (son==fa)	continue;
		Rorate(son,x);
	}
}
#undef T
int main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	int n=read(0);
	for (int i=1;i<=n;i++)	V[i]=read(0ll);
	for (int i=1;i<n;i++){
		int x=read(0),y=read(0);
		insert(x,y);
	}
	Dfs(1,0); Rorate(1,0);
	ll Ans=0;
	for (int K=0;K<=M;K++){
		ll res=0;
		for (int i=1;i<=n;i++)	res+=F[i][K][1];
		Ans+=(1ll<<K)*res;
	}
	for (int i=1;i<=n;i++)	Ans+=V[i];
	Ans>>=1;
	printf("%lld\n",Ans);
	return 0;
}