HDU1432+几何

题意：给N个点，求最多有多少个点在同一直线上

方法一：求出所有能形成的直线，两两比较，统计最多有多少条重合。

 #include<stdio.h>
 #include<stdlib.h>
 #include<string.h>
 #include<algorithm>
 #include<set>
 #include<iostream>
 using namespace std;
 typedef long long int64;
 const int64 maxn = ;
 const int64 maxm = ;
 const int64 inf = -;
 struct Point64{
     int x,y;
 }pnt[ maxn ];
 struct Node{
     int64 a,b,c;
     int x,y;
 }tp[ maxm ];

 bool s[ maxn ];
 //set<int>s;

 void init( int n ){
     for( int i=;i<n;i++ )
         s[ i ] = false;
 }

 int64 cmp( Node p1,Node p2 ){
     if( p1.a!=p2.a ) return p1.a<p2.a;
     else if( p1.b!=p2.b ) return p1.b<p2.b;
     else return p1.c<p2.c;
 }

 int64 gcd( int64 a,int64 b ){
     int64 r;
     while( b ){
         r = a%b;
         a = b;
         b = r;
     }
     return a;
 }

 void solve_gcd( int id ){
     int64 Gcd = gcd( tp[ id ].a,tp[ id ].b );
     Gcd = gcd( tp[ id ].c,Gcd );
     tp[ id ].a /= Gcd;
     tp[ id ].b /= Gcd;
     tp[ id ].c /= Gcd;
 }    

 int main(){
     int n;
     while( scanf("%d",&n)!=EOF ){
         for( int64 i=;i<n;i++ ){
             cin>>pnt[i].x>>pnt[i].y;
             //scanf("%lld%lld",&pnt[i].x,&pnt[i].y);
             s[ i ] = false;
         }
     if( n==||n== ){
         printf("%d\n",n);
         continue;
     }
         int cnt = ;
         for( int i=;i<n;i++ ){
             for( int j=i+;j<n;j++ ){
                 tp[ cnt ].a = pnt[ i ].y - pnt[ j ].y;
                 tp[ cnt ].b = pnt[ j ].x - pnt[ i ].x;
                 tp[ cnt ].c = pnt[ i ].x*pnt[ j ].y - pnt[ j ].x*pnt[ i ].y;
                 tp[ cnt ].x = i;
                 tp[ cnt ].y = j;
                 solve_gcd( cnt );
                 cnt ++;
             }
         }
         sort( tp,tp+cnt,cmp );
         int64 ans = ;
         int64 ans_tp = ;
         int64 prea = inf;
         int64 preb = inf;
         int64 prec = inf;
         for( int i=;i<cnt;i++ ){
             if(( prea!=tp[ i ].a || preb!=tp[ i ].b || prec!=tp[ i ].c )){
                 ans_tp = ;
                 prea = tp[ i ].a;
                 preb = tp[ i ].b;
                 prec = tp[ i ].c;
                 memset( s,false,sizeof( s ) );
                 s[ tp[i].x ] = true;
                 s[ tp[i].y ] = true;
             }
             else {
                 if( s[ tp[i].x ]==false ) {
                     ans_tp ++;
                     s[ tp[i].x ] = true;
                 }
                 if( s[ tp[i].y ]==false ) {
                     ans_tp ++;
                     s[ tp[i].y ] = true;
                 }
                 ans = max( ans,ans_tp );
             }
         }
         cout<<ans<<endl;
         //printf("%lld\n",ans);
     }
     return ;
 }

方法二：利用极角来排序 判断

 /*
 几何
 极角排序
 */
 #include<algorithm>
 #include<iostream>
 #include<string.h>
 #include<stdlib.h>
 #include<stdio.h>
 #include<math.h>
 #include<queue>
 #include<stack>
 #include<map>
 #include<set>
 using namespace std;
 typedef long long int64;
 //typedef __int64 int64;
 typedef pair<int64,int64> PII;
 #define MP(a,b) make_pair((a),(b))
 const int inf = 0x3f3f3f3f;
 const double inf2 = 987654321.0;
 const double pi=acos(-1.0);
 const int dx[]={,-,,};
 const int dy[]={,,,-};
 const double eps = 1e-;
 const int maxm = ;
 const int maxn = ;  

 struct Point{
     double x,y;
 }pnt[ maxn ],pnt2[ maxn ];
 Point C;

 double td[ maxn ];

 void initC( double x,double y ){
     C.x = x;
     C.y = y;
 }

 void initP( int n ){
     for( int i=;i<n;i++ ){
         pnt2[ i ].x = pnt[ i ].x - C.x;
         pnt2[ i ].y = pnt[ i ].y - C.y;
     }
     return ;
 } 

 void initTD( int n ){
     for( int i=;i<n;i++ ){
         td[ i ] = atan2( pnt2[ i ].y,pnt2[ i ].x );
         if( td[i]< ) td[ i ] += pi;
         //printf("%.2lf ",td[i]);
     }
     //printf("\n");
     sort( td,td+n );
     return ;
 }

 double dis( Point A,Point B ){
     A.x -= C.x,A.y -= C.y;
     B.x -= C.x,B.y -= B.y;
     return sqrt( (A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y) );
 }

 double cmp( Point A,Point B ){
     double t1 = atan2( A.y-C.y,A.x-C.x );
     double t2 = atan2( B.y-C.y,B.x-C.x );
     if( t1< ){
         t1 = t1 + pi*2.0;
     }
     if( t2< ){
         t2 = t2 + pi*2.0;
     }
     if( t1==t2 ){
         return fabs( A.x )< fabs( B.x );
     }
     else{
         return t1<t2;
     }
 }
 /*******************************************
 绕原点 以x正半轴开始逆时针旋转
 角度相同 按距离原点距离比较
 *******************************************/

 int main(){
     //freopen("in.txt","r",stdin);
     int n ;
     while( scanf("%d",&n)!=EOF ){
         for( int i=;i<n;i++ ){
             scanf("%lf%lf",&pnt[i].x,&pnt[i].y);
         }
         int ans = ;
         double f = inf2;
         for( int i=;i<n;i++ ){
             initC( pnt[ i ].x,pnt[ i ].y );
             initP( n );
             initTD( n );
             int cnt ;
             double pre = inf2;
             for( int j=;j<n;j++ ){
                 if( pre!=td[ j ] ){
                     pre = td[ j ];
                     cnt = ;
                 }
                 else {
                     cnt ++;
                     if( cnt>ans ){
                         ans = cnt;
                         f = pre;
                     }
                     //ans = max( ans,cnt+1 );
                 }
             }
         }
         if( f!= ) ans ++;
         printf("%d\n",max(,ans));
     }
     return ;
 }