1036: [ZJOI2008]树的统计Count 树链剖分+线段树

题目大意：给出一棵树，每个点有一个权值，要求三种操作：1.修改某个点的权值，2.询问x到y路径上各点的权值最大值，3.询问x到y路径上各点的权值之和。

算法讨论：树链剖分模板题。

题目地址：http://www.lydsy.com/JudgeOnline/problem.php?id=1036

#include<stdio.h>#include<string.h>#include<algorithm>#define N 30005#define inf 0x3fffffffusing namespace std;struct node{    int u,v,next;} bian[N*2];struct pp{    int x,y,max,sum;} a[N*3];int ma(int a,int b){    return a>b?a:b;}int e,dep[N],sz[N],father[N],son[N],top[N],head[N],ti[N],id;void add(int u,int v){    bian[e].u=u;    bian[e].v=v;    bian[e].next=head[u];    head[u]=e++;}void dfs1(int u,int fa){    int i,v;    dep[u]=dep[fa]+1;    sz[u]=1;    father[u]=fa;    son[u]=0;    for(i=head[u]; i!=-1; i=bian[i].next)    {        v=bian[i].v;        if(v==fa)  continue;        dfs1(v,u);        sz[u]+=sz[v];        if(sz[son[u]]<sz[v])            son[u]=v;    }}void dfs2(int u,int fa){    int i,v;    ti[u]=id++;    top[u]=fa;    if(son[u]!=0)        dfs2(son[u],fa);    for(i=head[u]; i!=-1; i=bian[i].next)    {        v=bian[i].v;        if(v==son[u]||v==father[u])            continue;        dfs2(v,v);    }}void build(int t,int x,int y){    a[t].x=x;    a[t].y=y;    a[t].max=a[t].sum=0;    if(x==y)  return;    int mid=(x+y)>>1,temp=t<<1;    build(temp,x,mid);    build(temp+1,mid+1,y);}void update(int t,int x,int w){    if(a[t].x==a[t].y)    {        a[t].max=a[t].sum=w;        return;    }    int mid=(a[t].x+a[t].y)>>1,temp=t<<1;    if(x<=mid)        update(temp,x,w);    else        update(temp+1,x,w);    a[t].sum=a[temp].sum+a[temp+1].sum;    a[t].max=ma(a[temp].max,a[temp+1].max);}int query(int x,int y,int t,int flag){    if(a[t].x==x&&a[t].y==y)    {        if(flag==0)            return a[t].max;        else            return a[t].sum;    }    int mid=(a[t].x+a[t].y)>>1,temp=t<<1;    if(y<=mid)        return query(x,y,temp,flag);    else if(x>mid)        return query(x,y,temp+1,flag);    else    {        if(flag==0)            return ma(query(x,mid,temp,flag),query(mid+1,y,temp+1,flag));        else            return query(x,mid,temp,flag)+query(mid+1,y,temp+1,flag);    }}int lca(int x,int y,int flag){    int ans=-inf, sum=0;    while(top[x]!=top[y])    {        if(dep[top[x]]<dep[top[y]])            swap(x,y);        if(flag==0)            ans=ma(ans,query(ti[top[x]],ti[x],1,flag));        else            sum+=query(ti[top[x]],ti[x],1,flag);        x=father[top[x]];    }    if(dep[x]>dep[y])        swap(x,y);    if(flag==0)        ans=ma(ans,query(ti[x],ti[y],1,flag));    else        sum+=query(ti[x],ti[y],1,flag);    if(flag==0)        return ans;    else        return sum;}int main(){    int n,i,u,v,w,q,x,y;    char str[100];    while(scanf("%d",&n)!=EOF)    {        e=0;        memset(head,-1,sizeof(head));        for(i=1; i<n; i++)        {            scanf("%d%d",&u,&v);            add(u,v);            add(v,u);        }        dep[1]=0;        sz[0]=0;        id=1;        dfs1(1,1);        dfs2(1,1);        build(1,1,n);        //for(i=1; i<=n; i++)           // printf("i=%d ti=%d dep=%d sz=%d son=%d top=%d father=%d\n",i,ti[i],dep[i],sz[i],son[i],top[i],father[i]);        for(i=1; i<=n; i++)        {            scanf("%d",&w);            update(1,ti[i],w);        }        scanf("%d",&q);        while(q--)        {            scanf("%s %d %d",str,&x,&y);            if(strcmp(str,"QMAX")==0)                printf("%d\n",lca(x,y,0));            else if(strcmp(str,"QSUM")==0)                printf("%d\n",lca(x,y,1));            else                update(1,ti[x],y);        }    }    return 0;}