1502: [NOI2005]月下柠檬树 - BZOJ
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
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 uses math; 2 const 3 maxn=510; 4 eps=1e-7; 5 var 6 x,rr,fx1,fy1,fx2,fy2,k:array[0..maxn]of double; 7 n:longint; 8 a,l,r,m,fl,fr,fm:double; 9 10 function simpson(l,r,fl,fr,fm:double):double; 11 begin 12 exit((r-l)/6*(fl+fr+4*fm)); 13 end; 14 15 function f(a:double):double; 16 var 17 i:longint; 18 begin 19 f:=0; 20 for i:=1 to n do 21 begin 22 if abs(a-x[i])<rr[i] then f:=max(f,sqrt(sqr(rr[i])-sqr(a-x[i]))); 23 if (a>fx1[i]) and (a<fx2[i]) then f:=max(f,fy1[i]+(a-fx1[i])*k[i]); 24 end; 25 end; 26 27 function area(l,m,r,fl,fm,fr,pre:double):double; 28 var 29 ll,rr,fll,frr,ls,rs:double; 30 begin 31 ll:=(l+m)/2;rr:=(m+r)/2;fll:=f(ll);frr:=f(rr); 32 ls:=simpson(l,m,fl,fm,fll);rs:=simpson(m,r,fm,fr,frr); 33 if abs(ls+rs-pre)<eps then exit(pre); 34 exit(area(l,ll,m,fl,fll,fm,ls)+area(m,rr,r,fm,frr,fr,rs)); 35 end; 36 37 procedure main; 38 var 39 i:longint; 40 begin 41 read(n,a);a:=1/tan(a); 42 for i:=1 to n+1 do read(x[i]); 43 for i:=2 to n+1 do x[i]:=x[i]+x[i-1]; 44 for i:=1 to n+1 do x[i]:=x[i]*a; 45 for i:=1 to n do read(rr[i]); 46 r:=x[n+1];l:=x[n+1]; 47 for i:=1 to n do 48 begin 49 if x[i]-rr[i]<l then l:=x[i]-rr[i]; 50 if x[i]+rr[i]>r then r:=x[i]+rr[i]; 51 end; 52 for i:=1 to n do 53 if (x[i]-rr[i]<x[i+1]-rr[i+1]) and (x[i]+rr[i]<x[i+1]+rr[i+1]) then 54 begin 55 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])); 56 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])); 57 if abs(fx2[i]-fx1[i])>eps then k[i]:=(fy2[i]-fy1[i])/(fx2[i]-fx1[i]); 58 end; 59 m:=(l+r)/2;fl:=f(l);fr:=f(r);fm:=f(m); 60 writeln(2*area(l,m,r,fl,fm,fr,simpson(l,r,fl,fr,fm)):0:2); 61 end; 62 63 begin 64 main; 65 end.