计数方法，博弈论（扫描线，树形SG）：HDU 5299 Circles Game

There are n circles on a infinitely large table.With every two circle, either one contains another or isolates from the other.They are never crossed nor tangent.
Alice and Bob are playing a game concerning these circles.They take turn to play,Alice goes first:
1、Pick out a certain circle A,then delete A and every circle that is inside of A.
2、Failling to find a deletable circle within one round will lost the game.
Now,Alice and Bob are both smart guys,who will win the game,output the winner's name.

Input

The first line include a positive integer T<=20,indicating the total group number of the statistic.
As for the following T groups of statistic,the first line of every group must include a positive integer n to define the number of the circles.
And the following lines,each line consists of 3 integers x,y and r,stating the coordinate of the circle center and radius of the circle respectively.
n≤20000，|x|≤20000，|y|≤20000，r≤20000。

Output

If Alice won,output “Alice”,else output “Bob”

Sample Input

2
1
0 0 1
6
-100 0 90
-50 0 1
-20 0 1
100 0 90
47 0 1
23 0 1

Sample Output

Alice
Bob
　　这道题目可以说是模板题……
　　就是那个SG函数的求法貌似是结论，我不会证明。

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 #include <cmath>
 #include <set>
 using namespace std;
 const int N=,M=;
 int cnt,fir[N],to[N],nxt[N];
 void addedge(int a,int b){
     nxt[++cnt]=fir[a];
     to[fir[a]=cnt]=b;
 }
 int sqr(int x){return x*x;}
 int tmp;
 struct Circle{
     int x,y,r;
     Circle(int _=,int __=,int ___=){x=_;y=__;r=___;}
 }c[N];

 struct Point{
     int x,id,tp;
     Point(int _=,int __=,int ___=){x=_;id=__;tp=___;}
     friend bool operator<(Point a,Point b){
         double x=c[a.id].y+a.tp*sqrt(sqr(c[a.id].r)-sqr(tmp-c[a.id].x));
         double y=c[b.id].y+b.tp*sqrt(sqr(c[b.id].r)-sqr(tmp-c[b.id].x));
         if(x!=y)return x<y;return a.tp<b.tp;
     }
 }st[M];

 bool cmp(Point a,Point b){return a.x<b.x;}
 set<Point>s;set<Point>::iterator it;

 int fa[N],sg[N];
 int DFS(int x){
     sg[x]=;
     for(int i=fir[x];i;i=nxt[i])
         sg[x]^=DFS(to[i])+;
     return sg[x];
 }

 void Init(){
     memset(fir,,sizeof(fir));
     cnt=;
 }
 int T,n;
 int main(){
     scanf("%d",&T);
     while(T--){
         Init();scanf("%d",&n);
         for(int i=;i<=n;i++){
             scanf("%d%d%d",&c[i].x,&c[i].y,&c[i].r);
             st[*i-]=Point(c[i].x-c[i].r,i,-);
             st[*i]=Point(c[i].x+c[i].r,i,);
         }
         sort(st+,st+*n+,cmp);
         for(int i=;i<=*n;i++){
             Point x=st[i];tmp=x.x;
             if(x.tp==-){
                 it=s.upper_bound(Point(,x.id,));
                 if(it==s.end())addedge(fa[x.id]=,x.id);
                 else{
                     Point y=*it;
                     if(y.tp==)
                         addedge(fa[x.id]=y.id,x.id);
                     else
                         addedge(fa[x.id]=fa[y.id],x.id);
                 }
                 s.insert(Point(,x.id,));
                 s.insert(Point(,x.id,-));
             }
             else{
                 s.erase(Point(,x.id,));
                 s.erase(Point(,x.id,-));
             }
         }
         printf(DFS()?"Alice\n":"Bob\n");
     }
     return ;
 }