1502: [NOI2005]月下柠檬树

Description

Input

文件的第1行包含一个整数n和一个实数alpha，表示柠檬树的层数和月亮的光线与地面夹角(单位为弧度)。第2行包含n+1个实数h0,h1,h2,…,hn，表示树离地的高度和每层的高度。第3行包含n个实数r1,r2,…,rn，表示柠檬树每层下底面的圆的半径。上述输入文件中的数据，同一行相邻的两个数之间用一个空格分隔。输入的所有实数的小数点后可能包含1至10位有效数字。
Output

输出1个实数，表示树影的面积。四舍五入保留两位小数。
Sample Input
2 0.7853981633
10.0 10.00 10.00
4.00 5.00
Sample Output
171.97
HINT

1≤n≤500，0.3

存个simpson模板

uses math;
const
    maxn=510;
    eps=1e-7;
var
    x,rr,fx1,fy1,fx2,fy2,k:array[0..maxn]of double;
    n:longint;
    a,l,r,m,fl,fr,fm:double;
 
function simpson(l,r,fl,fr,fm:double):double;
begin
    exit((r-l)/6*(fl+fr+4*fm));
end;
 
function f(a:double):double;
var
    i:longint;
begin
    f:=0;
    for i:=1 to n do
        begin
            if abs(a-x[i])<rr[i] then f:=max(f,sqrt(sqr(rr[i])-sqr(a-x[i])));
            if (a>fx1[i]) and (a<fx2[i]) then f:=max(f,fy1[i]+(a-fx1[i])*k[i]);
        end;
end;
 
function area(l,m,r,fl,fm,fr,pre:double):double;
var
    ll,rr,fll,frr,ls,rs:double;
begin
    ll:=(l+m)/2;rr:=(m+r)/2;fll:=f(ll);frr:=f(rr);
    ls:=simpson(l,m,fl,fm,fll);rs:=simpson(m,r,fm,fr,frr);
    if abs(ls+rs-pre)<eps then exit(pre);
    exit(area(l,ll,m,fl,fll,fm,ls)+area(m,rr,r,fm,frr,fr,rs));
end;
 
procedure main;
var
    i:longint;
begin
    read(n,a);a:=1/tan(a);
    for i:=1 to n+1 do read(x[i]);
    for i:=2 to n+1 do x[i]:=x[i]+x[i-1];
    for i:=1 to n+1 do x[i]:=x[i]*a;
    for i:=1 to n do read(rr[i]);
    r:=x[n+1];l:=x[n+1];
    for i:=1 to n do
        begin
            if x[i]-rr[i]<l then l:=x[i]-rr[i];
            if x[i]+rr[i]>r then r:=x[i]+rr[i];
        end;
    for i:=1 to n do
        if (x[i]-rr[i]<x[i+1]-rr[i+1]) and (x[i]+rr[i]<x[i+1]+rr[i+1]) then
        begin
            fx1[i]:=x[i]+rr[i]*(rr[i]-rr[i+1])/(x[i+1]-x[i]);fy1[i]:=sqrt(sqr(rr[i])-sqr(fx1[i]-x[i]));
            fx2[i]:=x[i+1]+rr[i+1]*(rr[i]-rr[i+1])/(x[i+1]-x[i]);fy2[i]:=sqrt(sqr(rr[i+1])-sqr(fx2[i]-x[i+1]));
            if abs(fx2[i]-fx1[i])>eps then k[i]:=(fy2[i]-fy1[i])/(fx2[i]-fx1[i]);
        end;
    m:=(l+r)/2;fl:=f(l);fr:=f(r);fm:=f(m);
    writeln(2*area(l,m,r,fl,fm,fr,simpson(l,r,fl,fr,fm)):0:2);
end;
 
begin
    main;
end.