UVALive - 3662 曼哈顿最小生成树

题意：平面上有n个点，求这些点的曼哈顿最小距离生成树。

裸的模板题。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>

using namespace std;
typedef long long ll;
const int maxn=100050;
const int INF=0x3f3f3f3f;
struct point{
    int x,y,id;
}p[maxn];
bool cmp(point a,point b)
{
    if(a.x!=b.x) return a.x<b.x;
    else return a.y<b.y;
}
struct BIT
{
    int min_val,pos;
    void init()
    {
        min_val=INF;
        pos=-1;
    }
}bit[maxn];
struct Edge{
    int u,v,d;
}edge[maxn<<2];
bool cmpedge(Edge a,Edge b)
{
    return a.d<b.d;
}
int tot;
int n;
int F[maxn];
int find(int x)
{
    if(F[x]==-1) return x;
    else return F[x]=find(F[x]);
}
void addedge(int u,int v,int d)
{
    edge[tot].u=u;
    edge[tot].v=v;
    edge[tot++].d=d;
}
int lowbit(int x){return x&-x;}
void update(int i,int val,int pos)
{
    while(i>0)
    {
        if(val<bit[i].min_val)
        {
            bit[i].min_val=val;
            bit[i].pos=pos;
        }
        i-=lowbit(i);
    }
}
int ask(int i,int m)
{
    int min_val=INF,pos=-1;
    while(i<=m)
    {
        if(bit[i].min_val<min_val)
        {
            min_val=bit[i].min_val;
            pos=bit[i].pos;
        }
        i+=lowbit(i);
    }
    return pos;
}
int dist(point a,point b)
{
    return abs(a.x-b.x)+abs(a.y-b.y);
}
void Manhattan_minimum_spanning_tree(int n,point p[])
{
    int a[maxn],b[maxn];
    tot=0;
    for(int dir=0;dir<4;dir++)
    {
        if(dir==1||dir==3)
        {
            for(int i=0;i<n;i++)
                swap(p[i].x,p[i].y);
        }
        else if(dir==2)
        {
            for(int i=0;i<n;i++)
                p[i].x=-p[i].x;
        }
        sort(p,p+n,cmp);
        for(int i=0;i<n;i++)
            a[i]=b[i]=p[i].y-p[i].x;
        sort(b,b+n);
        int m=unique(b,b+n)-b;
        for(int i=1;i<=m;i++)
            bit[i].init();
        for(int i=n-1;i>=0;i--)
        {
            int pos=lower_bound(b,b+m,a[i])-b+1;
            int ans=ask(pos,m);
            if(ans!=-1)
                addedge(p[i].id,p[ans].id,dist(p[i],p[ans]));
            update(pos,p[i].x+p[i].y,i);
        }
    }
}
ll solve()
{
    Manhattan_minimum_spanning_tree(n,p);
    memset(F,-1,sizeof F);
    sort(edge,edge+tot,cmpedge);
    ll ans=0;
    for(int i=0;i<tot;i++)
    {
        int u=edge[i].u;
        int v=edge[i].v;
        int t1=find(u),t2=find(v);
        if(t1!=t2)
        {
            F[t1]=t2;
            ans+=1ll*edge[i].d;
        }
    }
    return ans;
}

int main()
{
    //freopen("in.txt","r",stdin);
    int cas=0;
    while(scanf("%d",&n),n)
    {
        for(int i=0;i<n;i++)
        {
            scanf("%d%d",&p[i].x,&p[i].y);
            p[i].id=i;
        }
        ll ans=solve();
        printf("Case %d: Total Weight = %lld\n",++cas,ans);
    }

    return 0;
}