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LA3485 Bridge[(辛普森自适应)微积分]
做此题完全是为了练积分。
【普通求导版】
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#include<cstdio>#include<cmath>using namespace std;typedef double real;const real eps=1e-5;int cas,Cas,D,H,B,L;real F(real a,real x){ real a2=a*a; real x2=x*x; return (x*sqrt(a2+x2)+a2*log(fabs(x+sqrt(a2+x2))))/2.0;}real calc(real w,real h){ real a=4.0*h/(w*w); real A=1.0/(2.0*a); return (F(A,w/2.0)-F(A,0))*4.0*a;}int main(){ for(scanf("%d",&cas);cas--;){ scanf("%d%d%d%d",&D,&H,&B,&L); int n=(B+D-1)/D; real D1=(real)B/n; real L1=(real)L/n; real l=0.0,r=H,mid; while(l+eps<r){ mid=(l+r)/2.0; if(calc(D1,mid)<L1) l=mid;else r=mid; } printf("Case %d:\n%.2lf\n",++Cas,H-l); if(cas) putchar(‘\n‘); } return 0;}
【辛普森自适应版】
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#include<cstdio>#include<cmath>using namespace std;typedef double real;const real eps=1e-5;int cas,Cas,D,H,B,L;real a;real F(real x){ real a2=a*a; real x2=x*x; return sqrt(1.0+4.0*a2*x2);}real simpson(real a,real b){ real c=(a+b)/2.0; return (F(a)+4.0*F(c)+F(b))*(b-a)/6.0;}real asr(real a,real b,real eps,real A){ real c=(a+b)/2.0; real L=simpson(a,c),R=simpson(c,b); if(fabs(L+R-A)<=15*eps) return L+R+(L+R-A)/15; return asr(a,c,eps/2,L)+asr(c,b,eps/2,R);}real asr(real a,real b,real eps){ return asr(a,b,eps,simpson(a,b));}real calc(real w,real h){ a=4.0*h/(w*w); return asr(0,w/2.0,eps)*2.0;}int main(){ for(scanf("%d",&cas);cas--;){ scanf("%d%d%d%d",&D,&H,&B,&L); int n=(B+D-1)/D; real D1=(real)B/n; real L1=(real)L/n; real l=0.0,r=H,mid; while(l+eps<r){ mid=(l+r)/2.0; if(calc(D1,mid)<L1) l=mid;else r=mid; } printf("Case %d:\n%.2lf\n",++Cas,H-l); if(cas) putchar(‘\n‘); } return 0;}
LA3485 Bridge[(辛普森自适应)微积分]
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