NOI2014购票(树的cdq分治+凸壳)
BNUOJ 53081 线段树区间合并

hdu4918 (树分治的维护)

zjhl2 posted @ 2018年3月06日 21:34 in with tags 树状数组 树分治 , 818 阅读

题意:

一棵树,每个点有点权w,q次操作

1.将点x的点权修改为y 

2.问离x距离不超过d的点权和

 

思路:

将树分治中的计算部分需要的树状数组提出来,维护这个树状数组,每次查询修改均为O(log2n)

 

#include<bits/stdc++.h>
using namespace std;
const int N=100005;
vector<int>link[N];
struct MSG
{
    int id1,id2;
    int deep;
}msg[N][17];
int w[N];
int c[N*17];
int idn,L[N*2],R[N*2];
int maxfloor[N];
void add(int l,int r,int x,int y)
{
    for (int i=x;i<r-l;i+=(i&-i)) c[l+i]+=y;
}
int get(int l,int r,int x)
{
    if (x<1) return 0;
    if (x>=r-l) x=r-l-1;
    int ret=0;
    for (int i=x;i;i-=(i&-i)) ret+=c[l+i];
    return ret;
}
bool vis[N];
int cent,mxsz;
int size[N];
void findcent(int u,int fa,int n)
{
	size[u]=1;
	int mx=0;
	for (int v:link[u])
	{
		if (vis[v]||v==fa) continue;
		findcent(v,u,n);
		size[u]+=size[v];
		mx=max(mx,size[v]);
	}
	mx=max(mx,n-size[u]);
	if (mx<mxsz) cent=u,mxsz=mx;
}
int getmaxdeep(int u,int fa)
{
    int ret=1;
    for (int v:link[u])
        if (v!=fa&&!vis[v]) ret=max(ret,1+getmaxdeep(v,u));
    return ret;
}
void dfs(int u,int fa,int deep,int idn,int floor,int tp)
{
    if (tp==0) msg[u][floor].id1=idn;
    else msg[u][floor].id2=idn;
    msg[u][floor].deep=deep;
    add(L[idn],R[idn],deep,w[u]);
    for (int v:link[u])
        if (!vis[v]&&v!=fa) dfs(v,u,deep+1,idn,floor,tp);
}
void build(int u,int n,int floor)
{
    cent=u; mxsz=n;
    findcent(u,-1,n);
    u=cent; maxfloor[u]=floor;
    idn++; L[idn]=R[idn-1];
    R[idn]=L[idn]+getmaxdeep(u,-1)+1;

    dfs(u,-1,1,idn,floor,0);

    msg[u][floor].id2=-1;
    for (int v:link[u])
        if (!vis[v])
        {
            idn++; L[idn]=R[idn-1];
            R[idn]=L[idn]+getmaxdeep(v,u)+2;
            dfs(v,u,2,idn,floor,1);
        }

    vis[u]=1;
    for (int v:link[u])
        if (!vis[v])
            if (size[v]<size[u]) build(v,size[v],floor+1);
            else build(v,n-size[u],floor+1);

}
int main()
{
    int n,q;
    while(~scanf("%d%d",&n,&q))
    {
        for (int i=1;i<=n;i++) scanf("%d",&w[i]);
        for (int i=1;i<n;i++)
        {
            int x,y; scanf("%d%d",&x,&y);
            link[x].push_back(y);
            link[y].push_back(x);
        }
        build(1,n,0);
        while(q--)
        {
            char s[2]; int x,y;
            scanf("%s%d%d",s,&x,&y);
            if (s[0]=='?')
            {
                int ans=0;
                for (int floor=0;floor<=maxfloor[x];floor++)
                {
                    int id1=msg[x][floor].id1;
                    int id2=msg[x][floor].id2;
                    int deep=msg[x][floor].deep;
                    ans+=get(L[id1],R[id1],y+2-deep);
                    if (id2!=-1) ans-=get(L[id2],R[id2],y+2-deep);
                }
                printf("%d\n",ans);
            }
            else
            {
                for (int floor=0;floor<=maxfloor[x];floor++)
                {
                    int id1=msg[x][floor].id1;
                    int id2=msg[x][floor].id2;
                    int deep=msg[x][floor].deep;
                    add(L[id1],R[id1],deep,y-w[x]);
                    if (id2!=-1) add(L[id2],R[id2],deep,y-w[x]);
                }
                w[x]=y;
            }
        }
        memset(vis,0,sizeof(vis));
        memset(msg,0,sizeof(msg));
        memset(w,0,sizeof(w));
        memset(c,0,sizeof(c));
        idn=0;
        for (int i=1;i<=n;i++) link[i].clear();
    }
}

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