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[0..100] of record x,y,z,r:double; end;
    f:array[0..100] of arr;
    g:double;
function sum(sl,sr,sm,l,r:double):double;
begin
    exit((sl+sr+4*sm)*(r-l)/6);
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 2].x; y:=f[(i+j) div 2].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:=0;
    for i:=1 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(1,k);
    i:=1; cnt:=0;
    //if xx=a/2 then writeln(f[1].x:4:2,f[1].y:4:2);
    while i<=k do
    begin
        j:=i;
        while (j<k) and (f[j+1].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<0) or (f[i].x>b)) then
        begin
            if (f[i].y<=b) and (f[i].x>=0) then cnt:=cnt+f[i].y-f[i].x else
            if (f[i].y>b)  and (f[i].x<0)  then cnt:=cnt+b else
            if (f[i].y>b) then cnt:=cnt+b-f[i].x else
            if (f[i].x<0) then cnt:=cnt+f[i].y;
        end;        
        i:=j+1;
    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)/2;
    m2:=(r+mid)/2;
    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:=1 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/180*pi)/sin(g/180*pi)*T[i].z;
    end;
    sl:=calc(0); sr:=calc(a); sm:=calc(a/2);
    //writeln(sl:4:2,' ',sr:4:2,' ',sm:4:2);
    writeln(a*b-simpson(0,a,a/2,sl,sr,sm,sum(sl,sr,sm,0,a)):0:2);
    close(input);
    close(output);
end.