## 1036: [ZJOI2008] Statistics of trees Count

Time Limit: 10 Sec  Memory Limit: 162 MB
Submit: 10677  Solved: 4313
[Submit][Status][Discuss]

## Description

One
It's on a tree n Nodes , The numbers are 1 To n, Each node has a weight w. We're going to ask you to do something about this tree in the following form ： I. CHANGE u t :
Put the node u The weight of is changed to t II. QMAX u v: Ask from point u point-to-point v The maximum weight of the node on the path of III. QSUM u v:
Ask from point u point-to-point v The weight sum of nodes on the path of Be careful ： From the point of u point-to-point v The nodes on the path of include u and v In itself

## Input

transport
The first line in is an integer n, Represents the number of nodes . Next n –
1 That's ok , Each row 2 It's an integer a and b, Representation node a And nodes b There's an edge between them . Next n That's ok , One integer per row , The first i The whole number of lines wi Representation node i A weight . Next 1 That's ok , It's an integer
q, Represents the total number of operations . Next q That's ok , One operation per line , With “CHANGE u t” perhaps “QMAX u v” perhaps “QSUM u v” Given in the form of .
about 100％ The data of , Guarantee 1<=n<=30000,0<=q<=200000; The weight of each node is guaranteed in the midway operation w stay -30000 To
30000 Between .

## Output

For each “QMAX” perhaps “QSUM” The operation of , Each line outputs an integer to represent the result to be output .

4
1 2
2 3
4 1
4 2 1 3
12
QMAX 3 4
QMAX 3 3
QMAX 3 2
QMAX 2 3
QSUM 3 4
QSUM 2 1
CHANGE 1 5
QMAX 3 4
CHANGE 3 6
QMAX 3 4
QMAX 2 4
QSUM 3 4

## Sample Output

4
1
2
2
10
6
5
6
5
16

【 Ideas 】

The tree chain splits , Line segment tree

Line segment tree ： Interval query max sum , Single point operation set.

Just pay attention to negative numbers =-=.

【 Code 】

``` #include<cstdio>
#include<cstring>
#include<vector>
#include<iostream>
#include<algorithm>
#define FOR(a,b,c) for(int a=(b);a<=(c);a++)
using namespace std;

const int N = +;
const int INF = 1e9;

struct Node {
int mx,sum;
Node() {mx=-INF,sum=;}
}T[N<<];

int n,q,z;
char s[];
vector<int> g[N];
//INIT
int top[N],son[N],dep[N],fa[N],siz[N],w[N];
void dfs1(int u) {
son[u]=; siz[u]=;
for(int i=;i<g[u].size();i++) {
int v=g[u][i];
if(v!=fa[u]) {
fa[v]=u , dep[v]=dep[u]+;
dfs1(v);
siz[u]+=siz[v];
if(siz[v]>siz[son[u]]) son[u]=v;
}
}
}
void dfs2(int u,int tp) {
top[u]=tp; w[u]=++z;
if(son[u]) dfs2(son[u],tp);
for(int i=;i<g[u].size();i++) {
int v=g[u][i];
if(v!=fa[u] && v!=son[u]) dfs2(v,v);
}
}
//SEGMENT TREE
void update(int u,int L,int R,int r,int x) {
if(L==R) T[u].mx=T[u].sum=x;
else {
int M=(L+R)>>,lc=u<<,rc=lc|;
if(r<=M) update(lc,L,M,r,x);
else update(rc,M+,R,r,x);
T[u].mx=max(T[lc].mx,T[rc].mx);
T[u].sum=T[lc].sum+T[rc].sum;
}
}
int qsum,qmx;
void query(int u,int L,int R,int l,int r) {
if(l<=L && R<=r)
qsum+=T[u].sum , qmx=max(qmx,T[u].mx);
else {
int M=(L+R)>>;
if(l<=M) query(u<<,L,M,l,r);
if(M<r) query(u<<|,M+,R,l,r);
}
}
// The tree chain splits
int query(int u,int v,int flag) {
int sum=,mx=-INF;
while(top[u]!=top[v]) {
if(dep[top[u]]<dep[top[v]]) swap(u,v);
qsum= , qmx=-INF;
query(,,z,w[top[u]],w[u]);
sum+=qsum , mx=max(mx,qmx);
u=fa[top[u]];
}
if(dep[u]>dep[v]) swap(u,v);
qsum= , qmx=-INF;
query(,,z,w[u],w[v]);
sum+=qsum , mx=max(mx,qmx);
return flag? sum:mx;
}

char c=getchar(); int f=; x=;
while(!isdigit(c)) {if(c=='-')f=-;c=getchar();}
while(isdigit(c)) x=x*+c-'',c=getchar();
x*=f;
}
int main() {
int u,v,x;
FOR(i,,n-) {
g[u].push_back(v);
g[v].push_back(u);
}
dfs1(),dfs2(,);
FOR(i,,n)
while(q--) {
scanf("%s",s);
if(s[]=='C')  update(,,z,w[u],v);
else
if(s[]=='M') printf("%d\n",query(u,v,));
else printf("%d\n",query(u,v,));
}
return ;
}```

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