[HNOI2012]archery

题意:略

思路:略

实践证明:单纯形法比裸半平面交(nlog^2n)略快!!!!!!

半平面交(nlogn)的code:

program std;uses math;type        int=longint;        real=extended;        point=record                x,y:real;        end;//(x,y)        line=record                a,b,c:real;        end;//ax+by>cconst e=1e-16;maxn=400000;operator **(a,b:point)c:real;begin c:=a.x*b.x+a.y*b.y;end;{dian ji}operator *(a,b:point)c:real;begin c:=a.x*b.y-a.y*b.x;end;{cha ji}operator *(a,b:line)c:point;var s,x,y:real;begin        s:=a.b*b.a-a.a*b.b;        x:=a.b*b.c-a.c*b.b;        y:=a.a*b.c-a.c*b.a;        c.x:=x/s;c.y:=-y/s;end;procedure get(var x:real;y:real);begin        x:=y+(random(1000)/1000000)*e;end;var        l,r,mid,i,j,k,m,n:int;        t,d:real;        a:array[1..2*maxn]of line;        x,y,z,s:array[1..maxn]of real;        p,q:array[1..2*maxn]of int;        c:array[1..2*maxn]of point;procedure sort(l,r:int);var i,j:int;begin        i:=l;j:=r;        d:=s[p[(l+r)>>1]];        repeat                while s[p[i]]<d do inc(i);                while s[p[j]]>d do dec(j);                if i<=j then begin                        k:=p[i];p[i]:=p[j];p[j]:=k;                        inc(i);dec(j);                end;        until i>j;        if i<r then sort(i,r);        if j>l then sort(l,j);end;procedure ins(x,y,z:real);begin        inc(m);p[m]:=m;        get(a[m].a,x);get(a[m].b,y);get(a[m].c,z);        s[m]:=arctan2(x,y);end;function ok(n:int):boolean;var h,r:int;l:line;begin        n:=n*2+4;        h:=2;r:=2;q[1]:=p[1];q[2]:=p[2];        c[2]:=a[p[1]]*a[p[2]];        for i:=3 to m do if p[i]<=n then begin                l:=a[p[i]];                while(r>=h)and(c[r].x*l.a+c[r].y*l.b<l.c)do dec(r);                while(h<=r)and(c[h].x*l.a+c[h].y*l.b<l.c)do inc(h);                inc(r);q[r]:=p[i];                c[r]:=a[q[r-1]]*l;        end;        l:=a[q[r]];        while(h<=r)and(c[h].x*l.a+c[h].y*l.b<l.c)do inc(h);        l:=a[q[h-1]];        while(r>=h)and(c[r].x*l.a+c[r].y*l.b<l.c)do dec(r);        ok:=h<>r;end;begin        assign(input,'archery.in');reset(input);        assign(output,'archery.out');rewrite(output);        read(n);        for i:=1 to n do read(x[i],y[i],z[i]);        m:=0;        ins(1,0,-1e+20);ins(0,-1,-1e+20);        ins(-1,0,0);ins(0,1,0);        for i:=1 to n do begin                ins(x[i]*x[i],x[i],y[i]);                ins(-x[i]*x[i],-x[i],-z[i]);        end;        sort(1,m);        l:=0;r:=n+1;        while l<>r-1 do begin                mid:=(l+r)>>1;                if ok(mid)then l:=mid                        else r:=mid;        end;        write(l);        close(input);close(output);end.

其实半平面交也不长.

单纯形的程序以后再搞上来.

无数事实表明,虽然单纯形法的复杂度几乎无法估计,但实际的效果还是很好的.

另外,这个程序没有判平行的情况,所以精度很成问题.但是因为hnoi的数据过水,所以就懒得改了....