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  • HDU 5738 Eureka 统计共线的子集个数

    Eureka

    题目连接:

    http://acm.hdu.edu.cn/showproblem.php?pid=5738

    Description

    Professor Zhang draws n points on the plane, which are conveniently labeled by 1,2,...,n. The i-th point is at (xi,yi). Professor Zhang wants to know the number of best sets. As the value could be very large, print it modulo 109+7.

    A set P (P contains the label of the points) is called best set if and only if there are at least one best pair in P. Two numbers u and v (u,v∈P,u≠v) are called best pair, if for every w∈P, f(u,v)≥g(u,v,w), where f(u,v)=(xu−xv)2+(yu−yv)2−−−−−−−−−−−−−−−−−−−√ and g(u,v,w)=f(u,v)+f(v,w)+f(w,u)2.

    Input

    There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

    The first line contains an integer n (1≤n≤1000) -- then number of points.

    Each of the following n lines contains two integers xi and yi (−109≤xi,yi≤109) -- coordinates of the i-th point.

    Output

    For each test case, output an integer denoting the answer.

    Sample Input

    3
    3
    1 1
    1 1
    1 1
    3
    0 0
    0 1
    1 0
    1
    0 0

    Sample Output

    4
    3
    0

    Hint

    题意

    问你有多少个子集是共线的。

    题解:

    其实就是枚举直线,然后统计一下就好了。

    但是这道题会卡常数,所以得非常优越才行,我们队使用gcd去搞的,然后就搞过去了。。。。

    cmp的极角排序要么很慢,要么就被卡精度了,非常烦的一道题……

    代码

    #include<bits/stdc++.h>
    #define mp make_pair
    using namespace std;
    namespace fastIO{
        #define BUF_SIZE 100000
        #define OUT_SIZE 100000
        #define ll long long
        //fread->read
        bool IOerror=0;
        inline char nc(){
            static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
            if (p1==pend){
                p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin);
                if (pend==p1){IOerror=1;return -1;}
                //{printf("IO error!
    ");system("pause");for (;;);exit(0);}
            }
            return *p1++;
        }
        inline bool blank(char ch){return ch==' '||ch=='
    '||ch=='
    '||ch=='	';}
        inline void read(int &x){
            bool sign=0; char ch=nc(); x=0;
            for (;blank(ch);ch=nc());
            if (IOerror)return;
            if (ch=='-')sign=1,ch=nc();
            for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
            if (sign)x=-x;
        }
        inline void read(ll &x){
            bool sign=0; char ch=nc(); x=0;
            for (;blank(ch);ch=nc());
            if (IOerror)return;
            if (ch=='-')sign=1,ch=nc();
            for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
            if (sign)x=-x;
        }
        inline void read(double &x){
            bool sign=0; char ch=nc(); x=0;
            for (;blank(ch);ch=nc());
            if (IOerror)return;
            if (ch=='-')sign=1,ch=nc();
            for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
            if (ch=='.'){
                double tmp=1; ch=nc();
                for (;ch>='0'&&ch<='9';ch=nc())tmp/=10.0,x+=tmp*(ch-'0');
            }
            if (sign)x=-x;
        }
        inline void read(char *s){
            char ch=nc();
            for (;blank(ch);ch=nc());
            if (IOerror)return;
            for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch;
            *s=0;
        }
        inline void read(char &c){
            for (c=nc();blank(c);c=nc());
            if (IOerror){c=-1;return;}
        }
        //getchar->read
        inline void read1(int &x){
            char ch;int bo=0;x=0;
            for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
            for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
            if (bo)x=-x;
        }
        inline void read1(ll &x){
            char ch;int bo=0;x=0;
            for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
            for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
            if (bo)x=-x;
        }
        inline void read1(double &x){
            char ch;int bo=0;x=0;
            for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
            for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
            if (ch=='.'){
                double tmp=1;
                for (ch=getchar();ch>='0'&&ch<='9';tmp/=10.0,x+=tmp*(ch-'0'),ch=getchar());
            }
            if (bo)x=-x;
        }
        inline void read1(char *s){
            char ch=getchar();
            for (;blank(ch);ch=getchar());
            for (;!blank(ch);ch=getchar())*s++=ch;
            *s=0;
        }
        inline void read1(char &c){for (c=getchar();blank(c);c=getchar());}
        //scanf->read
        inline void read2(int &x){scanf("%d",&x);}
        inline void read2(ll &x){
            #ifdef _WIN32
                scanf("%I64d",&x);
            #else
            #ifdef __linux
                scanf("%lld",&x);
            #else
                puts("error:can't recognize the system!");
            #endif
            #endif
        }
        inline void read2(double &x){scanf("%lf",&x);}
        inline void read2(char *s){scanf("%s",s);}
        inline void read2(char &c){scanf(" %c",&c);}
        inline void readln2(char *s){gets(s);}
        //fwrite->write
        struct Ostream_fwrite{
            char *buf,*p1,*pend;
            Ostream_fwrite(){buf=new char[BUF_SIZE];p1=buf;pend=buf+BUF_SIZE;}
            void out(char ch){
                if (p1==pend){
                    fwrite(buf,1,BUF_SIZE,stdout);p1=buf;
                }
                *p1++=ch;
            }
            void print(int x){
                static char s[15],*s1;s1=s;
                if (!x)*s1++='0';if (x<0)out('-'),x=-x;
                while(x)*s1++=x%10+'0',x/=10;
                while(s1--!=s)out(*s1);
            }
            void println(int x){
                static char s[15],*s1;s1=s;
                if (!x)*s1++='0';if (x<0)out('-'),x=-x;
                while(x)*s1++=x%10+'0',x/=10;
                while(s1--!=s)out(*s1); out('
    ');
            }
            void print(ll x){
                static char s[25],*s1;s1=s;
                if (!x)*s1++='0';if (x<0)out('-'),x=-x;
                while(x)*s1++=x%10+'0',x/=10;
                while(s1--!=s)out(*s1);
            }
            void println(ll x){
                static char s[25],*s1;s1=s;
                if (!x)*s1++='0';if (x<0)out('-'),x=-x;
                while(x)*s1++=x%10+'0',x/=10;
                while(s1--!=s)out(*s1); out('
    ');
            }
            void print(double x,int y){
                static ll mul[]={1,10,100,1000,10000,100000,1000000,10000000,100000000,
                    1000000000,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL,
                    100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL};
                if (x<-1e-12)out('-'),x=-x;x*=mul[y];
                ll x1=(ll)floor(x); if (x-floor(x)>=0.5)++x1;
                ll x2=x1/mul[y],x3=x1-x2*mul[y]; print(x2);
                if (y>0){out('.'); for (size_t i=1;i<y&&x3*mul[i]<mul[y];out('0'),++i); print(x3);}
            }
            void println(double x,int y){print(x,y);out('
    ');}
            void print(char *s){while (*s)out(*s++);}
            void println(char *s){while (*s)out(*s++);out('
    ');}
            void flush(){if (p1!=buf){fwrite(buf,1,p1-buf,stdout);p1=buf;}}
            ~Ostream_fwrite(){flush();}
        }Ostream;
        inline void print(int x){Ostream.print(x);}
        inline void println(int x){Ostream.println(x);}
        inline void print(char x){Ostream.out(x);}
        inline void println(char x){Ostream.out(x);Ostream.out('
    ');}
        inline void print(ll x){Ostream.print(x);}
        inline void println(ll x){Ostream.println(x);}
        inline void print(double x,int y){Ostream.print(x,y);}
        inline void println(double x,int y){Ostream.println(x,y);}
        inline void print(char *s){Ostream.print(s);}
        inline void println(char *s){Ostream.println(s);}
        inline void println(){Ostream.out('
    ');}
        inline void flush(){Ostream.flush();}
        //puts->write
        char Out[OUT_SIZE],*o=Out;
        inline void print1(int x){
            static char buf[15];
            char *p1=buf;if (!x)*p1++='0';if (x<0)*o++='-',x=-x;
            while(x)*p1++=x%10+'0',x/=10;
            while(p1--!=buf)*o++=*p1;
        }
        inline void println1(int x){print1(x);*o++='
    ';}
        inline void print1(ll x){
            static char buf[25];
            char *p1=buf;if (!x)*p1++='0';if (x<0)*o++='-',x=-x;
            while(x)*p1++=x%10+'0',x/=10;
            while(p1--!=buf)*o++=*p1;
        }
        inline void println1(ll x){print1(x);*o++='
    ';}
        inline void print1(char c){*o++=c;}
        inline void println1(char c){*o++=c;*o++='
    ';}
        inline void print1(char *s){while (*s)*o++=*s++;}
        inline void println1(char *s){print1(s);*o++='
    ';}
        inline void println1(){*o++='
    ';}
        inline void flush1(){if (o!=Out){if (*(o-1)=='
    ')*--o=0;puts(Out);}}
        struct puts_write{
            ~puts_write(){flush1();}
        }_puts;
        inline void print2(int x){printf("%d",x);}
        inline void println2(int x){printf("%d
    ",x);}
        inline void print2(char x){printf("%c",x);}
        inline void println2(char x){printf("%c
    ",x);}
        inline void print2(ll x){
            #ifdef _WIN32
                printf("%I64d",x);
            #else
            #ifdef __linux
                printf("%lld",x);
            #else
                puts("error:can't recognize the system!");
            #endif
            #endif
        }
        inline void println2(ll x){print2(x);printf("
    ");}
        inline void println2(){printf("
    ");}
        #undef ll
        #undef OUT_SIZE
        #undef BUF_SIZE
    };
    using namespace fastIO;
    const int maxn = 1e3+15;
    const int mod = 1e9 + 7;
    const double PI = acos(-1.0);
    int vis[maxn];
    
    struct point{
        int x,y;
    }now;
    
    int N , two[maxn];
    point p[maxn];
    vector<pair<int ,int> > v;
    
    int main(){
        two[0] = 1;
        for(int i = 1 ; i < maxn ; ++ i) two[i] = two[i - 1] * 2LL % mod;
        int T;
        read(T);
        while(T--){
            read(N);
            for(int i = 0 ; i < N ; ++ i){
                read(p[i].x),read(p[i].y);
            }
            int ans = 0;
            for(int i=0;i<N;i++) vis[i]=0;
            for(int i = 0 ; i < N ; ++ i)
            {
                if(vis[i]) continue;
                int tot=0;
                now=p[i];
                v.clear();
                for(int j=0;j<N;j++)
                {
                    if(now.x==p[j].x&&now.y==p[j].y)
                    {
                        tot++;
                        vis[j]=1;
                        continue;
                    }
                    int x=p[j].x-now.x,y=p[j].y-now.y;
                    int gc=__gcd(x,y);
                    if(gc<0) gc=-gc;
                    x/=gc,y/=gc;
                    v.push_back(make_pair(x,y));
                }
                int t1=two[tot]-tot-1,t2;
                if(t1<0) t1+=mod;
                ans+=t1;
                if(ans>=mod) ans-=mod;
                sort(v.begin(),v.end());
         //       cout<<v.size()<<endl;
         //       for(int i=0;i<v.size();i++) cout<<v[i].first<<" "<<v[i].second<<endl;
                int start=0,ed=1;
                t1+=tot;
                if(t1>=mod) t1-=mod;
                while(start<v.size())
                {
                    if(v[start].first>0||(v[start].first==0&&v[start].second>0)) break;
                    for(ed=start+1;ed<v.size();ed++)
                        if(v[start]!=v[ed]) break;
                    t2=two[ed-start]-1;
                    if(t2<0) t2+=mod;
                    ans+=(1LL*t1*t2%mod);
                    if(ans>=mod) ans%=mod;
                    start=ed;
                }
            }
    
            println1(ans);
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/qscqesze/p/5692893.html
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