【POJ3237】Tree（树链剖分+线段树）

Description

You are given a tree with N nodes. The tree’s nodes are numbered 1 through N and its edges are numbered 1 throughN − 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:

CHANGEiv	Change the weight of the ith edge to v
NEGATEab	Negate the weight of every edge on the path from a to b
QUERYab	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】

指定一颗树上有3个操作：

　　询问操作,询问a点和b点之间的路径上最长的那条边的长度；

　　取反操作，将a点和b点之间的路径权值都取相反数；

　　变化操作，把某条边的权值x变成指定的值。

【分析】

　　人生第一道树剖题，调了好久啊，200+的代码还打了对拍= =

　　就是裸的树链剖分+线段树啦。

　　就是线段树打得不够熟练所以调了那么久，lazy标记不大会用~~

　　

　　树剖的主要过程就是两次的dfs，第一次求fa，第二次求top。询问过程就是一直跳，跳到两个东西在一条重链上去。

　　因为某种特殊性质，所以他很快。。

代码如下：

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define Maxn 10010
#define INF 100000000

int fa[Maxn],first[Maxn],size[Maxn],dep[Maxn],son[Maxn];
int w[Maxn],top[Maxn];int wl;
int b[Maxn][5];

struct node
{
    int x,y,c,next;
}t[2*Maxn];int len;

struct nnode
{
    int l,r,lc,rc,mx,mn;
    bool lazy;
}tr[2*Maxn];int tl;

int mymax(int x,int y) {return x>y?x:y;}
int mymin(int x,int y) {return x<y?x:y;}

void ins(int x,int y,int c)
{
    t[++len].x=x;t[len].y=y;t[len].c=c;
    t[len].next=first[x];first[x]=len;
}

void dfs1(int x,int f)
{
    fa[x]=f;dep[x]=dep[f]+1;size[x]=1;
    son[x]=0;
    for(int i=first[x];i;i=t[i].next) if(t[i].y!=f)
    {
        dfs1(t[i].y,x);
        size[x]+=size[t[i].y];
        if(size[t[i].y]>size[son[x]]) son[x]=t[i].y;
    }
}

void dfs2(int x,int tp)
{
    w[x]=++wl;
    top[x]=tp;
    if(size[x]!=1) dfs2(son[x],tp);
    for(int i=first[x];i;i=t[i].next) if(t[i].y!=fa[x]&&t[i].y!=son[x])
    {
        dfs2(t[i].y,t[i].y);
    }
}

int build(int l,int r)
{
    int x=++tl;
    tr[x].l=l;tr[x].r=r;tr[x].mx=-INF;tr[x].mn=INF;tr[x].lazy=0;
    if(l!=r)
    {
        int mid=(l+r)>>1;
        tr[x].lc=build(l,mid);
        tr[x].rc=build(mid+1,r);
    }
    return x;
}

void upd(int x)
{
    if(!tr[x].lazy) return;
    tr[x].lazy=0;
    int a=tr[x].mx;
    tr[x].mx=-tr[x].mn;tr[x].mn=-a;
    if(tr[x].l==tr[x].r) return;
    tr[tr[x].lc].lazy=!tr[tr[x].lc].lazy;
    tr[tr[x].rc].lazy=!tr[tr[x].rc].lazy;
}

void change(int x,int y,int c)
{
    upd(x);
    if(tr[x].l==tr[x].r)
    {
        tr[x].mx=c;
        tr[x].mn=c;
        return;
    }
    int mid=(tr[x].l+tr[x].r)>>1;
    if(y<=mid) change(tr[x].lc,y,c);
    else change(tr[x].rc,y,c);
    upd(tr[x].lc);upd(tr[x].rc);
    tr[x].mx=mymax(tr[tr[x].lc].mx,tr[tr[x].rc].mx);
    tr[x].mn=mymin(tr[tr[x].lc].mn,tr[tr[x].rc].mn);
}

int qtree(int x,int l,int r)
{
    upd(x);
    if(tr[x].l==l&&tr[x].r==r) return tr[x].mx;
    int mid=(tr[x].l+tr[x].r)>>1;
    if(r<=mid) return qtree(tr[x].lc,l,r);
    if(l>mid) return qtree(tr[x].rc,l,r);
    return mymax(qtree(tr[x].lc,l,mid),qtree(tr[x].rc,mid+1,r));
}

int query(int x,int y)
{
    int tmp=-INF;
    int f1=top[x],f2=top[y];
    while(f1!=f2)
    {
        if(dep[f1]<dep[f2]) 
        {
            swap(f1,f2);
            swap(x,y);
        }
        tmp=mymax(qtree(1,w[f1],w[x]),tmp);
        x=fa[f1];
        f1=top[x];
    }
    if(x==y) return tmp;
    if(dep[x]<dep[y]) swap(x,y);
    return mymax(tmp,qtree(1,w[son[y]],w[x]));
}

void change2(int x,int l,int r)
{
    upd(x);
    if(tr[x].l==l&&tr[x].r==r)
    {
        tr[x].lazy=!tr[x].lazy;
        upd(x);
        return;
    }
    int mid=(tr[x].l+tr[x].r)>>1;
    if(r<=mid) change2(tr[x].lc,l,r);
    else if(l>mid) change2(tr[x].rc,l,r);
    else
    {
        change2(tr[x].lc,l,mid);
        change2(tr[x].rc,mid+1,r);
    }
    upd(tr[x].lc);upd(tr[x].rc);
    tr[x].mx=mymax(tr[tr[x].lc].mx,tr[tr[x].rc].mx);
    tr[x].mn=mymin(tr[tr[x].lc].mn,tr[tr[x].rc].mn);
}

void negate1(int x,int y)
{
    int f1=top[x],f2=top[y];
    while(f1!=f2)
    {
        if(dep[f1]<dep[f2]) 
        {
            swap(f1,f2);
            swap(x,y);
        }
        change2(1,w[f1],w[x]);
        x=fa[f1];
        f1=top[x];
    }
    if(x==y) return;
    if(dep[x]<dep[y]) swap(x,y);
    change2(1,w[son[y]],w[x]);
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        int n;
        scanf("%d",&n);
        memset(first,0,sizeof(first));
        len=0;
        for(int i=1;i<n;i++)
        {
            int x,y,c;
            scanf("%d%d%d",&x,&y,&c);
            b[i][0]=x;b[i][1]=y;b[i][2]=c;
            ins(x,y,c);ins(y,x,c);
        }
        dep[0]=0;size[0]=0;
        dfs1(1,0);wl=0;
        dfs2(1,1);
        char s[10];
        tl=0;
        build(1,wl);
        for(int i=1;i<n;i++)
        {
            if(dep[b[i][0]]<dep[b[i][1]]) swap(b[i][0],b[i][1]);
            change(1,w[b[i][0]],b[i][2]);
        }
        while(1)
        {
            scanf("%s",s);
            if(s[0]=='D') break;
            if(s[0]=='Q')
            {
                int x,y;
                scanf("%d%d",&x,&y);
                printf("%d
",query(x,y));
            }
            else if(s[0]=='C')
            {
                int x,y;
                scanf("%d%d",&x,&y);
                change(1,w[b[x][0]],y);//单点修改
            }
            else
            {
                int x,y;
                scanf("%d%d",&x,&y);
                negate1(x,y);
            }
        }
    }
    return 0;
}

2016-05-08 14:50:31