POJ3237 Tree（树剖+线段树+lazy标记）

You are given a tree with N nodes. The tree’s nodes are numbered 1 through N and its edges are numbered 1 through N − 1. Each edge is associated with a weight. Then you are to execute a series of instructions on the tree. The instructions can be one of the following forms:

CHANGE i v	Change the weight of the ith edge to v
NEGATE a b	Negate the weight of every edge on the path from a to b
QUERY a b	Find the maximum weight of edges on the path from a to b

Input

The input contains multiple test cases. The first line of input contains an integer t (t ≤ 20), the number of test cases. Then follow the test cases.

Each test case is preceded by an empty line. The first nonempty line of its contains N (N ≤ 10,000). The next N − 1 lines each contains three integers a, b and c, describing an edge connecting nodes a and b with weight c. The edges are numbered in the order they appear in the input. Below them are the instructions, each sticking to the specification above. A lines with the word “DONE” ends the test case.

Output

For each “QUERY” instruction, output the result on a separate line.

Sample Input

1

3
1 2 1
2 3 2
QUERY 1 2
CHANGE 1 3
QUERY 1 2
DONE

Sample Output

1
3

题意：

对于一棵树，有几种操作：

  Q ：x y 。问x到y之间的路径的最大边权值为多少。

  C ：x y。把第x条边的权值改为y。

  N：x y。把x到y之间的边权值取反。

  D。结束。

思路：

 和前面一道树剖题的查询是一样的，所以同样需要树剖+线段树，对于C操作，同样是线段树单点更新即可。但是需要区间权值取反，得用lazy标记一下。记录最大和最小值，方便在取反后还能得到最大值。

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
#define swap(a,b) (a^=b,b^=a,a^=b)
using namespace std;
const int maxn=200010;
int Laxt[maxn],Next[maxn],To[maxn],e[maxn][3],cnt;
int n,q; char opt[10];
struct TreeCut
{
    int dpt[maxn],top[maxn],son[maxn],fa[maxn],sz[maxn],tot;
    int tid[maxn],Rank[maxn],tim;
    int Max[maxn<<2],Min[maxn<<2],Lazy[maxn<<2];
    void init()
    {
        cnt=1; tim=0;
        memset(Laxt,0,sizeof(Laxt));
        memset(Max,0,sizeof(Max));
        memset(Min,0,sizeof(Min));
        memset(Lazy,0,sizeof(Lazy));
    }
    void add_edge(int u,int v)
    {
        Next[++cnt]=Laxt[u];
        Laxt[u]=cnt; To[cnt]=v;
    }
    void dfs1(int u,int pre)
    {
        fa[u]=pre;dpt[u]=dpt[pre]+1;sz[u]=1;son[u]=0;
        for(int i=Laxt[u];i;i=Next[i]){
            int v=To[i]; if(v==pre) continue;
            dfs1(v,u);sz[u]+=sz[v];
            if(!son[u]||sz[v]>sz[son[u]]) son[u]=v;
        }
    }
    void pushdown(int Now)
    {
         swap(Max[Now<<1],Min[Now<<1]),Max[Now<<1]=-Max[Now<<1],Min[Now<<1]=-Min[Now<<1];
         swap(Max[Now<<1|1],Min[Now<<1|1]),Max[Now<<1|1]=-Max[Now<<1|1],Min[Now<<1|1]=-Min[Now<<1|1]; 
         Lazy[Now<<1]^=1;Lazy[Now<<1|1]^=1;Lazy[Now]=0; 
    }
    void pushup(int Now)
    {
        Max[Now]=max(Max[Now<<1],Max[Now<<1|1]);
        Min[Now]=min(Min[Now<<1],Min[Now<<1|1]); 
    }
    void dfs2(int u,int Top)
    {
        top[u]=Top; tid[u]=tim++;Rank[tid[u]]=u;
        if(!son[u]) return ;  dfs2(son[u],Top);
        for(int i=Laxt[u];i;i=Next[i])
           if(To[i]!=fa[u]&&To[i]!=son[u])  dfs2(To[i],To[i]);
    }
    void update(int Now,int L,int R,int pos,int val)
    {
        if(L==R){ Max[Now]=Min[Now]=val; return; }
        if(Lazy[Now]&1) pushdown(Now);
        int Mid=(L+R)>>1;
        if(Mid>=pos) update(Now<<1,L,Mid,pos,val);
        else update(Now<<1|1,Mid+1,R,pos,val);
        pushup(Now);
    }    
    int getmax(int Now,int L,int R,int l,int r)
    {
        if(L>=l&&R<=r) return Max[Now];
        if(Lazy[Now]&1) pushdown(Now);
        int Mid=(L+R)>>1,ans=-0x7fffffff;
        if(r<=Mid) ans=getmax(Now<<1,L,Mid,l,r);
        else if(l>Mid) ans=getmax(Now<<1|1,Mid+1,R,l,r);
        else ans=max(getmax(Now<<1,L,Mid,l,Mid),getmax(Now<<1|1,Mid+1,R,Mid+1,r));
        pushup(Now); return ans; 
    }
    void addsign(int Now,int L,int R,int l,int r)
    {
        if(L>=l&&R<=r) {
            Lazy[Now]^=1;swap(Max[Now],Min[Now]);
            Max[Now]=-Max[Now];Min[Now]=-Min[Now];
            return ;
        }
        if(Lazy[Now]&1) pushdown(Now);
        int Mid=(L+R)>>1;
        if(l<=Mid) addsign(Now<<1,L,Mid,l,r);
        if(r>Mid)  addsign(Now<<1|1,Mid+1,R,l,r);
        pushup(Now);
    }
    void Make_Tree()
    {
        scanf("%d",&n);
        for(int i=1;i<n;i++){
            scanf("%d%d%d",&e[i][0],&e[i][1],&e[i][2]);
            add_edge(e[i][0],e[i][1]);add_edge(e[i][1],e[i][0]);
        }  dfs1(1,0);  dfs2(1,1);
        for(int i=1;i<n;i++){
            if(dpt[e[i][1]]<dpt[e[i][0]])  swap(e[i][1],e[i][0]);
            update(1,1,n-1,tid[e[i][1]],e[i][2]);
        }
    }
    int query(int u,int v)
    {
        int f1=top[u],f2=top[v],ans=-0x7fffffff;
        while(f1!=f2){
           if(dpt[f1]<dpt[f2]) swap(f1,f2),swap(u,v);
           ans=max(ans,getmax(1,1,n-1,tid[f1],tid[u]));
           u=fa[f1]; f1=top[u];
        }
        if(u!=v){
            if(dpt[u]>dpt[v]) swap(u,v);
            ans=max(ans,getmax(1,1,n-1,tid[son[u]],tid[v]));
        } printf("%d
",ans);
    }
    int Add_lazy(int u,int v)
    {
        int f1=top[u],f2=top[v];
        while(f1!=f2){
           if(dpt[f1]<dpt[f2]) swap(f1,f2),swap(u,v);
           addsign(1,1,n-1,tid[f1],tid[u]);
           u=fa[f1]; f1=top[u];
        }
        if(u!=v){
            if(dpt[u]>dpt[v]) swap(u,v);
            addsign(1,1,n-1,tid[son[u]],tid[v]);
        }
    }
    void Query()
    {
        while(~scanf("%s",opt)) { 
            if(opt[0]=='D') return;
            int x,y; scanf("%d%d",&x,&y);
            if(opt[0]=='Q') query(x,y);
            else if(opt[0]=='N') Add_lazy(x,y);
            else update(1,1,n-1,tid[e[x][1]],y);
        }
    }
}Tc;
int main()
{
    int T; scanf("%d",&T);
    while(T--) {
         Tc.init();  
         Tc.Make_Tree();
         Tc.Query();
    }  return 0;
}