bzoj 1604: [Usaco2008 Open]Cow Neighborhoods 奶牛的邻居 曼哈顿生成树

　　大致题意：统计平面上由曼哈顿距离小于等于c的点对组成联通块的个数。

　　曼哈顿生成树的模板题。有关讲解：http://blog.csdn.net/acm_cxlove/article/details/8890003

　　

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
#define MAXN 100100
#define MAXE MAXN*8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
typedef long long qword;
int n,m;
struct edge
{
        int x,y;
        qword d;
}e[MAXE];
int tope=-1;
bool cmp_d(edge e1,edge e2)
{
        return e1.d<e2.d;
}
int uf[MAXN];
int get_fa(int now)
{
        return uf[now]==now ? now : uf[now]=get_fa(uf[now]);
}
int comb(int x,int y)
{
        x=get_fa(x);
        y=get_fa(y);
        if (x==y)return false;
        uf[x]=y;
        return true;
}
struct point
{
        qword x,y;
        int id;
}pl[MAXN];
bool cmp_x(point p1,point p2)
{
        if (p1.x==p2.x)return p1.y>p2.y;
        return p1.x>p2.x;
}
void rotate1()
{
        for (int i=0;i<n;i++)
                pl[i].x=-pl[i].x;
}
void rotate2()
{
        for (int i=0;i<n;i++)
                pl[i].y=-pl[i].y;
}
void rotate3()
{
        for (int i=0;i<n;i++)
                swap(pl[i].x,pl[i].y);
}
qword h[MAXN],toph=-1;
qword tarr[MAXN];
int tarr_id[MAXN];
void Add_tarr(int pos,qword v,int id)
{
        while (pos<MAXN)
        {
                tarr[pos]=min(tarr[pos],v);
                if (v==tarr[pos])tarr_id[pos]=id;
                pos+=pos&(-pos);
        }
}
pair<qword,int> Qry_tarr(int pos)
{
        pair<qword,int> ret;
        ret.first=INFL;
        while (pos)
        {
                ret.first=min(ret.first,tarr[pos]);
                if (ret.first==tarr[pos])
                        ret.second=tarr_id[pos];
                pos-=pos&(-pos);
        }
        return ret;
}
void work()
{
        int i,j;
        toph=0;
        memset(tarr,0x3f,sizeof(tarr));
        for (i=0;i<n;i++)
                h[++toph]=pl[i].x-pl[i].y;
        sort(h+1,h+toph+1);
        toph=unique(h+1,h+toph+1)-h-1;
        sort(pl,pl+n,cmp_x);
        for (i=0;i<n;i++)
        {
                pair<qword,int> pr;
                qword t=pl[i].x-pl[i].y;
                t=lower_bound(h+1,h+toph+1,t)-h;
                pr=Qry_tarr(t);
                if (pr.first!=INFL)
                {
                        e[++tope].x=pl[i].id;
                        e[tope].y=pr.second;
                        e[tope].d=pr.first-pl[i].x-pl[i].y;
                }
                Add_tarr(t,pl[i].x+pl[i].y,pl[i].id);
        }
}
int is_root[MAXN],uf_size[MAXN];
int main()
{
        freopen("input.txt","r",stdin);
        //freopen("output.txt","w",stdout);
        int i,j,k,x,y,z;
        scanf("%d%d",&n,&m);
        for (i=0;i<n;i++)
        {
                scanf("%lld%lld",&pl[i].x,&pl[i].y);
                pl[i].id=i;
        }
        //1
        work();
        //2
        rotate3();
        work();
        rotate3();
        //3
        rotate2();
        rotate3();
        work();
        rotate3();
        rotate2();
        //4
        rotate2();
        work();
        rotate2();
        //5
        rotate2();
        rotate1();
        work();
        rotate1();
        rotate2();
        //6
        rotate1();
        rotate2();
        rotate3();
        work();
        rotate3();
        rotate2();
        rotate1();
        //7
        rotate1();
        rotate3();
        work();
        rotate3();
        rotate1();
        //8
        rotate1();
        work();
        rotate1();
        sort(e,e+tope+1,cmp_d);
        for (i=0;i<=n;i++)uf[i]=i;
        for (i=0;i<=tope && e[i].d<=m;i++)
        {
                comb(e[i].x,e[i].y);
        }
        int ans2=0;
        for (i=0;i<n;i++)
        {
                is_root[get_fa(i)]=1;
                uf_size[uf[i]]++;
        }
        for (i=1;i<n;i++)
                is_root[i]+=is_root[i-1];
        for (i=0;i<n;i++)
                ans2=max(ans2,uf_size[i]);
        printf("%d %d\n",is_root[n-1],ans2);
        return 0;
}