农场阳光 (simpson)

计算若干个圆与一个矩形的面积并

simpson公式 ans = ( f[l] + f[r] + 4 * f[mid] ) * (r-l) / 6

 uses math;
 type arr=record x,y:double; end;
 const eps=1e-8;
 var a,b,n,i:longint;
     sl,sr,sm:double;
     T:array[..] of record x,y,z,r:double; end;
     f:array[..] of arr;
     g:double;
 function sum(sl,sr,sm,l,r:double):double;
 begin
     exit((sl+sr+*sm)*(r-l)/);
 end;
 procedure sort(l,r:longint);
 var i,j:longint; x,y:double;
     temp:arr;
 begin
     i:=l;j:=r;x:=f[(i+j) div ].x; y:=f[(i+j) div ].y;
     while i<=j do
     begin
         while (f[i].x<x) or (f[i].x=x) and (f[i].y<y) do inc(i);
         while (x<f[j].x) or (x=f[j].x) and (y<f[j].y) do dec(j);
         if i<=j then
         begin
             temp:=f[i]; f[i]:=f[j]; f[j]:=temp;
             inc(i); dec(j);
         end;
     end;
     if l<j then sort(l,j);
     if i<r then sort(i,r);
 end;
 function calc(xx:double):double;
 var i,j,k:longint;
     cnt,yy:double;
 begin
     k:=;
     for i:= to n do
         if abs(T[i].x-xx)+eps<T[i].r then
         begin
             yy:=sqrt(sqr(T[i].r)-sqr(T[i].x-xx));
             inc(k);
             f[k].x:=T[i].y-yy;
             f[k].y:=T[i].y+yy;
         end;
     sort(,k);
     i:=; cnt:=;
     //if xx=a/ then writeln(f[].x::,f[].y::);
     while i<=k do
     begin
         j:=i;
         while (j<k) and (f[j+].x<=f[i].y) do
         begin
             inc(j);
             if f[j].y>f[i].y then f[i].y:=f[j].y;
         end;
         if not ((f[i].y<) or (f[i].x>b)) then
         begin
             if (f[i].y<=b) and (f[i].x>=) then cnt:=cnt+f[i].y-f[i].x else
             if (f[i].y>b)  and (f[i].x<)  then cnt:=cnt+b else
             if (f[i].y>b) then cnt:=cnt+b-f[i].x else
             if (f[i].x<) then cnt:=cnt+f[i].y;
         end;
         i:=j+;
     end;
     exit(cnt);
 end;
 function simpson(l,r,mid,sl,sr,sm,w:double):double;
 var sm1,sm2,m1,m2,w1,w2:double;
 begin
     m1:=(l+mid)/;
     m2:=(r+mid)/;
     sm1:=calc(m1);
     sm2:=calc(m2);
     w1:=sum(sl,sm,sm1,l,mid);
     w2:=sum(sm,sr,sm2,mid,r);
     if abs(w1+w2-w)<eps then exit(w);
     exit(simpson(l,mid,m1,sl,sm,sm1,w1)+simpson(mid,r,m2,sm,sr,sm2,w2));
 end;
 begin
     assign(input,'sun.in');reset(input);
     assign(output,'sun.out');rewrite(output);
     readln(a,b);
     readln(g);
     readln(n);
     for i:= to n do
     begin
         readln(T[i].x,T[i].y,T[i].z,T[i].r);
         T[i].x:=T[i].x+cos(g/*pi)/sin(g/*pi)*T[i].z;
     end;
     sl:=calc(); sr:=calc(a); sm:=calc(a/);
     //writeln(sl::,' ',sr::,' ',sm::);
     writeln(a*b-simpson(,a,a/,sl,sr,sm,sum(sl,sr,sm,,a))::);
     close(input);
     close(output);
 end.