bzoj1604[Usaco2008 Open]Cow Neighborhoods 奶牛的邻居*

bzoj1604[Usaco2008 Open]Cow Neighborhoods 奶牛的邻居

题意:

n只牛,牛结成群当且仅当两只牛曼哈顿距离≤c或存在第三头牛使两头牛与它的曼哈顿距离都≤c,求最大的群和群数。n≤100000

题解:

好神啊。先把曼哈顿距离转成切比雪夫距离,(x,y)转为(x+y,x-y)。然后按x坐标排序,用两个指针维护使x坐标差值≤c,同时将新插入的y坐标放入set,每次在set里查找出与当前y差值不超过c的最大y,将这两个点合并成一个集合,用并查集维护。

代码:

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <algorithm>
 4 #include <set>
 5 #define inc(i,j,k) for(int i=j;i<=k;i++)
 6 #define maxn 100100
 7 #define INF 0x3fffffff
 8 using namespace std;
 9 
10 inline int read(){
11     char ch=getchar(); int f=1,x=0;
12     while(ch<'0'||ch>'9'){if(ch=='-')f=-1; ch=getchar();}
13     while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
14     return f*x;
15 }
16 struct p{int x,y;}; p ps[maxn];
17 bool cmp(p a,p b){return a.x==b.x?a.y<b.y:a.x<b.x;}
18 struct data{
19     int id,v;
20     bool operator < (const data &a)const{return v==a.v?id<a.id:v<a.v;}
21 };
22 set<data> s; int n,c,l,fa[maxn],cnt[maxn];
23 int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
24 void merge(int _x,int _y){int x=find(_x),y=find(_y); if(x!=y)fa[y]=x;}
25 int main(){
26     n=read(),c=read(); inc(i,1,n){int a=read(),b=read(); ps[i]=(p){a+b,a-b};} sort(ps+1,ps+1+n,cmp);
27     s.clear(); s.insert((data){0,INF}); s.insert((data){0,-INF});
28     l=1; s.insert((data){1,ps[1].y}); inc(i,1,n)fa[i]=i;
29     inc(i,2,n){
30         while(ps[i].x-ps[l].x>c)s.erase(s.find((data){l,ps[l].y})),l++;
31         set<data>::iterator x=s.lower_bound((data){0,ps[i].y}),y=x; y--;
32         if(x->v-ps[i].y<=c)merge(i,x->id); if(ps[i].y-y->v<=c)merge(i,y->id);
33         s.insert((data){i,ps[i].y});
34     }
35     inc(i,1,n)cnt[find(i)]++; int ans=0; inc(i,1,n)if(cnt[i])ans++; printf("%d ",ans);
36     ans=0; inc(i,1,n)ans=max(ans,cnt[i]); printf("%d",ans); return 0;
37 }

 

20160809

posted @ 2016-08-14 06:43  YuanZiming  阅读(245)  评论(0编辑  收藏  举报