• [CodeForces]CodeForces


      题意:

        给出平面上n个点,问能在其中选出6个点,组成两个三角形,使得其互不相交

        问有多少种选法

      大致思路

         考虑枚举一条直线,将所有得点分为左右两部分,其中有两个点在直线上,

        以这两个点为顶点,分别统计左边有多少个三角形,右边有多少个三角形即可。

        枚举直线时,枚举一个点,然后对其他点极角排序,
        枚举另一个点,可快速算出该直线左右两边的点的数量(二分,叉积),组合一下即可。

        

      1 /*
      2 :    .                                                                                                                  
      3 :                                                                                                                       
      4 i                                                                                                                       
      5 i    .                                                                                                                  
      6 i                                                                                                                       
      7 :    .                                                                                                                  
      8 i    .                                                                                                                  
      9 i    .                                                                                                                  
     10 i                                                                                                                       
     11 :        .                                                                                                              
     12 i  .  i  i :     . .    .   .     .       . .           ..    .                                   .          .          
     13 .     .  . .       .                      .   .      .                                                          .       
     14 :   qQ  .   v2d   .  i: ..:ij.iBE .i            EBj        .irrivri.::iiiir7r.                       .    SPd.  :       
     15 i  UQB    .BBBBE     BBBQBBBBLiBB.1BBi    :X:   BBu    .   .KBBBBBBBBBBBBBBBQv                          :BBBBB          
     16 . iBY PD. BBY vBBv.  ..:gB1   rBM  7B1    RQP   MBgvPPQBB          uRq.        ..                 .    jBBQ.BBBr        
     17 :.BBrQBBBBBL   iQBB7:777gBSYvrKBBv:v71r..YPBBBBBBBBBBEBBB    7RBZQdBBBdEgBQE                         1QBB1   QBBB:      
     18 .:BBBBJ.qBBDBBBBBBBvrQBQBBBBBBBBBBBBBgg5UBBBBriiBQ1   rBB  .:.:i. :KQBi ..::    :.. . . .   .....  UBBB5  UJ: rBBBBXi   
     19 .  IQY     i:.:..       YBs   :BB   IE.   XBZ   QBs   7BB  rBBBBQBBBBBBBQBBBBq BQBBBBBBBBBBBBBBBBviBBE.  .BBZ   .BBgi.  
     20 . BBBQSJ.Kb5BQgRBPv :5gQBBBQBB:YBvrBBd    QBE   BBdiBBBB5      .BB     uBs     iririiiriir7iii77i. ii    .BBD  .        
     21 . uQ5Sv .BB::i::QBU  BBQMBK.   7BBBP.     DBq   QB1 DQ7.L. sBBdQBBMBBBQBBBBBQDi                           BB5           
     22 .    ...:BB     KBJ     uB1   UBBBL  QBL  RQb   i:.     BBPvi.UBBuY7v7iQBqrrur.                           BBE   .       
     23 :LBBBBBBJQBBBBQBBBJ  :rvBBu:BBB1jBBPbBB   SBBZIvSUguJXRBBB:  7QBB      BBu     ..                         BBQ           
     24 r.XX... .QBIYXDJBB1  qBBBBi ir   rMQBQ.   .sPBBBBBBBBRBBD7  XBBi       dB1. .  ..                        .BBg           
     25 i                .                   .                           . . .         ..                         ... .         
     26 :                                                                                                                       
     27 i    .                                                                   .                                              
     28 i                                                                                                                       
     29 i    .                                                                                                                  
     30 i                                                                         :r:.                                          
     31 i    .                                                                .  vKKSj. .                                       
     32 r                                                                 ..    :B: js  .                                       
     33 i    .                                                             .    rK .S:                 :::                      
     34 r                                                                       :v LS             .  ibi7gv   .                 
     35 i                                                                       :Ligi               .QJ :g7  .                  
     36 .      ...5d:  .                                                        i2Sd               rb. vj:      .               
     37 .   .7:r27DBi                                                      .    .Bb:     .        7K..Ps                        
     38 uij1Pdr.  ri                                                       .     Sq              :Kj7Ii .  .     :v:            
     39 UvY:     7P. .                                                     .     .7             .vIqX. ..  .    .dBRS7.         
     40 .    .   qP     . .       .  ..                                       .     .  ..        :r.            .qi :2ZPi       
     41 .    .   gs     .    .:K2  .          .irvIs75K5XEKMKgZsD522YLri.              iBB1i                     Pr   .2r       
     42 i       iS:        .isjjQ.    .:rs5KPPMBBBZdBBgi:7Rd7XBBBRSMBBDZQZSr.        rDYiiYdQSr.                 dY             
     43 :       Ys      .iXbi.  7: 7v5gQZqPEKXUIjUIdbr   ur    jRQr1E:  .rJgBBDL:   iEv     .sdD5Yi.             MX  .   .      
     44 i       Si   .vU57i   .ibQBBgMPI175XUvsq5LBj   :Li.     jQLJ:  .    .rdBBQsYL           :r1ISv:         .gu    .        
     45 :   .. iU  r5Qu.   :sBBD7qDqbbijPj5ISXv22UK   .BY .     .gSP: .q:      rBBBBS    .   .      .7KEYi.      qv    .        
     46 .      qBsY1i   :IqBZqI2rUXLXQPrYjIuED2jZPv.  KI .  .    .BR. rd        .bBUBQu.          .    .isZK1:   5s             
     47 :      vPv.  .idDBEP1XYKXQR1r5d2SdPqEDv7IEY  Yv    .      KB.:U.  :Ui    .BJUBBB1        .         rXqIrrB2    .        
     48 v           rQDM1dj7SM1qIuPgXJKS2sKU5urLDMr :Bi   .  .dBMi7BPYJ 1PKL:     BjKIUPBB1       .       .   :irMX             
     49 i  .     .vKDDr1YREIPgv1qS1Qbju1IS2US5vUZBu sr .    :BBBBdXMDMgjv.   :    guJsP7rQgU:                    JdrsSv:        
     50 7       rQREJ5u2vuKv5dXKKPXqqXK1PSSqP2USqqBDj    .  7QBQRPQriQg:..v7i:.   MqEXBs72DQB:              .iYYr..iPRJ         
     51 7  .  .MRB221QqKrYSSXdXXuBZuSguL1sPMDQQDPPgBi    .  :RBBMB5  PELBBBj     vP.  irRBgRPEv           .Ju7ivv7vLi.   .      
     52 :    7DQUdSPqgIqUsKSYv5Si2PrruJSBZR5r::   :Z:        .irvX::qPPZMBBQgs  .Xs      LPuXBBi         :Dd2rLsr.      .       
     53 i   YBZ7Lg2bUPLb172Xr7PQvJuuuMBbX7.       .uRu.         :QEBQRRBZgggQBSrY.         :SQQX         :27:.       .          
     54 i .EP2PX1qJYIPuu5I2g2uB5YXbDZPJ   .rr.  .   7gZU7r7vYvvvJqBQRBMdgDMgBQQr            r5BBr                               
     55  .gB2LgEsPPuKE2IrM5Iu1U2JXgS.     :7vvvsYLL7. .rs77JJr.  JBQDBbdEZBRgBP      . .YIUvirvBQ:   .                          
     56 XQQSqgDJ7qg5bPXqLd1bQ2JQB2.              ..:7Lv7:        iBQSREEBQQRBP:     iSPL7.     rBu                              
     57 QgUjEE2qJbKsjX2duqYKr5BS.      ..             .rYr.       dBQBZBQBKgM. .  rZ2:          jEi                             
     58 vJdPIJI5UPSYKb5uLbLSDEu       .                            :BBgBPEBr  .  ....         . iBK.                            
     59 YvLb7K5L7ubsjgJuuSsPQ7  .....:iiirr77v7vrv1PXU77rr::.            :E.  .           .. ..  sgi                            
     60 LuKQrsSd5XQPqSij7bBu    :ivu5J7i::::::::::i::.::iri..            :Ei.     ..i715qLPdUqS. iBi     .                      
     61 7UPBv2IPqP1IdXLZZPr   .                                .         .sY       .ir:.     ..  .QE  ..                        
     62 UsJRubSv7ggUJr1Qg:                             ..                 r5                      vd.                           
     63 d5YPrSqX7QIvPRBX.  .  .            ..:i777r7vJvr:      .         .rZ  .                 .iE5rr                          
     64 2LKXj2E17DjSMSQi          ..ii7uqS522J7:.....              ..     7Z.    .  .75Y::.  7KdBZEXXBQ:                        
     65 r7PQqdEjJEPJuZJ       iIPK1j7:.:.         .:i:......              :P        .iLuvPSsXQbr     .JBP                       
     66 sLPP1uqs2XR7JQ:       .:i.        .:71ZBBBQEDDMbdMBBBdui:         rZ.               .          bB.                      
     67 UUqK7vSIv5PuDg                .YdQBBBBQBMESJ777s1bPdEgRQBBRUi.    .5       .                  .gq                       
     68 vLZPvvbKLdSIBv          .   1MBRQBBBMEbZPvgBRJrLY7Uj2J7rvPDQBBgUY722            ...       ..  iBJ                       
     69 irIKvUPI7M1SRi     .  .   7BB1JUvSd1Y512IYSBMKLPv1XirsivvUKgDgBBBBBBKr:.                  ..  uE.                       
     70 D2KIJ5D17EPdd.  .        qBJv.ivivYi7JvrLrLEgbbP1PE:71sS5sDq7vDQD2qbgBBBMJi                  rR7                        
     71 vJPbvJq2YgEQ2           .BP.L7ijIEuiivr7vii1PKgg5dRjXgUSujJ7JgJ7Piru1UKMBBQM2i             .2I:.                        
     72 vrXP1Xg2vJjbL    .  .   sBBuXI1gBgE2SI7vIrrsIiSISdBSEZ1bggQv7Es:U77YLirugggDBBBgKUJrri:.:7IEP.                          
     73 XU1UubPuLu7LY    .     :5RBgUBBPPdggBEUdqIKXviuJrYdPPq2PKKBqY1jrj75I1LL7UXZBBdPEQBP7jIIdKSBB.  .                        
     74 sIDbX5X5KRBSE         .ZXLXI7q57UJ5IRUUZP5KZguivSv1S55bS12BMBjJ7dXBgZIqr7dqMEPBEQQ:       KB7         ...       ..      
     75 PU7v5MPJ7KZPD         iBbU7v77:r7irYdIud5KqZPsrs2vYUsJuPP5SLKgQdEEgdPgMX7qvI5DXbMX       :BQ                            
     76 511sSdZXI51vg.     .  LgXgU77iir5dddBMMBBBP5dP52S2gBQ2vL22RdBQBPQP15SdMR1Jivrr:MBr       SBv   .jDBMbuv:      ..        
     77 vU52sujjUEq1E.   . .  2MrBDU5PQBZP7.:..irDQQPdBBRqi.      .:jXQMBPrIjXXBP1iuii.BE       .BX  rSQK:...i1dX7.             
     78 KJ1svuqsrEgPK      .  v1rDQDBj:.          .LQBS.              .JBE.r7555RbbK55PBr    .  Kg  7QM.        7BBv            
     79 PXdEu5PsLKv5di        7E1dKi                :J.                 :gg1iq1LsQRRYuBP   .r  KQi iBg           .2Q5.  .       
     80 IjPP1ID5UJYdBY        rBBS    .                 .                :BErj7YU5ZPdBZ       vBv :Rd              IBi          
     81 2UKK7JPXuIgQBb    .    bBi     .         .   .           .        EBPYv7srIKBB       vBr  sBi    .         .B1          
     82 vvbb15d5bSPLPB:   .    rB:    ..          .                       :qBKQvYLJRK       iQ2 :ZBBr   .           Rv .        
     83 SY57vDIKZLuuKBi        .BB.    .   .                             . bBXgudD5v      .2BBgqqbgBJ   .    ...   .E5          
     84 v75vYqPPq5KPjJE:  .     iBBr    .                                 .BMvBQEv:       BBq1EsSQS5Bi  .   .      :BL          
     85 vUUs7YuJrXJd7:BP     .   .PQqv:                          ..  .:77juBQJsi        rBQYiJU1JX5PRb:           vBL    .      
     86 dZsY55RS1qjdqrBBL          .JPMRP77.   .:.....:.:i7vjuSqEEbXqqquL7. .         .jBQJvdR5vuuuJ5BBq:       isBB  . .       
     87 BQ7v1KDu5qYSqsJgQ:             .r7IEPUs11uj25X21JJri::...                    7QB1rPQY2duIQKXZJ7BBdu7:isDZ5:    ..       
     88 LYRgsvSUPqX1UUI2Bd.                                                       ii2MEgI7dRSJ1sSBX7SPXsPZBBXr77.               
     89  vBB1PBZMQggZDZMXgBBDgMRbbEQQRZPZRPKSPbDRBDKujsuYv25Ys2qSEPDMMddZgZMQBBBgQBQEPsqXJSqsIP52M5UPPsvERZi                    
     90 s5QgPQBIDMMDgDgDgBBgEBBBBBBQQBBBBQBBBBBQQBBBBBBBBQBBBBBQBBBBBBBBBQBBBBBBBMBQgESDDSEKUPgU2qSqUrPBBv.   .                 
     91 rrPBBgMDMQRRMQgQDMQBQBMgRQggDgRBBBgZgBBBQBBBBBBBBBBBBBS:     ..vbBBBQBQMbSQQMEYSuLI5uPKv1D77PBBXi      ...              
     92 i LdMdKKqqPgZSgd1PZPSLXPXSZZXPZIQZJ5EKdDgMMdqYr.::.:bB:          LBXIQBKPgBquP2PZuUuUSXj5ZqXBB7                         
     93 i:BP2j:vYs7q5sZI:2uvv7Ss7UYKs51r51rJLjDg7:          .BvPPgX1vrii:2Qi  vBbIMQuZrsDP55uu2XYdBQU:   .                      
     94 rPBLJ27PXu7SP2QIvSJsPKgYPPisXq1Lg51ZBdr             2Q: .. .qBU.:vbv.  :IQBqiSs2KYLudKv7QQb.                            
     95 BBXr7P1PXXsPSjD5757YPPE1JJiXPZj7sSQK:                1v     iBu   g7 .   iDBPQsIPuIP7vZB1.                       .      
     96 MuiK7uKKj11Pj:S1UbuJXv2JJSKKLU2rSgX  .....:::...::.: .Bd..i.:bj .SB7 .::  KBgMv1gu2KqDBZ:  .:ii:ri::iiirrrviii7i.        
     97 */
     98 
     99 
    100 
    101 #include<cstdio>
    102 #include<iostream>
    103 #include<cstring>
    104 #include<algorithm>
    105 #include<queue>
    106 #include<set>
    107 #include<map>
    108 #include<stack>
    109 #include<time.h>
    110 #include<cstdlib>
    111 #include<cmath>
    112 #include<list>
    113 using namespace std;
    114 #define MAXN 10000006
    115 #define eps 0
    116 #define For(i,a,b) for(int i=a;i<=b;i++)
    117 #define Fore(i,a,b) for(int i=a;i>=b;i--)
    118 #define lson l,mid,rt<<1
    119 #define rson mid+1,r,rt<<1|1
    120 #define mkp make_pair
    121 #define pb push_back
    122 #define cr clear()
    123 #define sz size()
    124 #define met(a,b) memset(a,b,sizeof(a))
    125 #define iossy ios::sync_with_stdio(false)
    126 #define fr freopen
    127 #define pi acos(-1.0)
    128 #define Vector Point
    129 #define fir first
    130 #define sec second
    131 #define it_s_too_hard main
    132 const long long inf=1LL<<62;
    133 const int iinf=1<<30;
    134 const double dinf=1e17;
    135 const int Mod=1e9+7;
    136 typedef long long ll;
    137 typedef long double ld;
    138 struct Point{
    139     ll x,y;
    140     double ang;
    141     Point(ll x=0,ll y=0):x(x),y(y) {}
    142     Point operator - (const Point &a)const { return Point(x-a.x,y-a.y);}
    143 };
    144 ll Cross(Vector a,Vector b){ return a.x*b.y-a.y*b.x;}
    145 int n; 
    146 Point o;
    147 Vector v1,v2;
    148 bool cmp(Point a,Point b){
    149     return a.ang<b.ang;
    150 }
    151 Point p[2050],tp[5050];
    152 void I_can_t_solve_it(){
    153     cin>>n;
    154     ll ans=0,cnt1,l,r,ct;
    155     For(i,1,n) cin>>p[i].x>>p[i].y;
    156     For(i,1,n){
    157         For(j,1,n) {
    158             if(j==i) continue;
    159             if(j>i) tp[j-1]=p[j]-p[i],tp[j-1].ang=atan2(tp[j-1].y,tp[j-1].x);
    160             else tp[j]=p[j]-p[i],tp[j].ang=atan2(tp[j].y,tp[j].x);
    161         }
    162         ct=n-1;cnt1=1;
    163         sort(tp+1,tp+ct+1,cmp);
    164         For(j,1,ct) tp[j+ct]=tp[j];
    165         For(j,1,ct){
    166             if(j>cnt1) cnt1=j;
    167             if(cnt1>ct*2) break;
    168             while(cnt1-j+2<=ct && cnt1<ct*2 && Cross(tp[j],tp[cnt1+1])>0) cnt1++;
    169             l=cnt1-j;r=n-1-l-1;
    170             ans+=l*(l-1)*r*(r-1)/4;
    171         }
    172     }
    173     cout<<ans/2<<endl;
    174     
    175 }
    176 int it_s_too_hard(){
    177     int t=1;
    178     iossy;
    179     For(i,1,t){
    180         I_can_t_solve_it();
    181     }
    182     return 0;
    183 }
    View Code
  • 相关阅读:
    Redission 中 RPermitExpirableSemaphore 用法
    Linux查询CPU核数
    Http超时时间之SocketTimeout
    In Theano, how to do Reverse-MaxPooling in the Convolutional MaxPooling Auto-Encoder
    如何让Ubuntu中virtualbox虚拟机用上USB设备
    Deep Learning Stuffs(持续更新中……)
    实例描述如何用python组件ctypes调用c的dll中的函数
    放弃MATLAB!简述winpython为什么比MATLAB更方便
    虚拟机Ubuntu10.04无法显示windows中文目录和文件
    W: GPG 错误
  • 原文地址:https://www.cnblogs.com/cjbiantai/p/9521392.html
Copyright © 2020-2023  润新知