学步园

uva 1356 Bridge ( 辛普森积分 )

不要问我辛普森怎么来的，其实我也不知道。。。

#include<stdio.h>
#include<math.h>
#include<string.h>
#include<algorithm>
using namespace std ;

double d , h , m , b , l , w ;

double f ( double x ) {
    double a = 4.0 * m / w / w ;
    return sqrt ( 1.0 + 4 * a * a * x * x ) ;
}

double simp ( double a , double b ) {
    double c = a + ( b - a ) / 2 ;
    return ( f( a ) + 4 * f ( c ) + f ( b ) ) * ( b - a ) / 6 ;
}

double asr ( double a , double b , double eps , double A ) {
    double c = ( a + ( b - a ) / 2 ) ;
    double L = simp ( a , c ) , R = simp ( c , b ) ;
    if ( fabs ( L + R - A ) <= 15 * eps )
        return L + R + ( L + R - A ) / 15.0 ;
    return asr ( a , c , eps / 2 , L ) + asr ( c , b , eps / 2 , R ) ;
}

double asr ( double a , double b , double eps ) {
    return asr ( a , b , eps , simp ( a , b ) ) ;
}

int main () {
    int T , ca = 0 ;
    scanf ( "%d" , &T ) ;
    while ( T -- ) {
        scanf ( "%lf%lf%lf%lf" , &d , &h , &b , &l ) ;
        double n = ceil ( b / d ) ;
        l = l / n , w = b / n ;
        double x = 0 , y = h ;
        while ( fabs ( y - x ) >= 1e-8 ) {
            m = ( x + y ) / 2 ;
            double k = 2 * asr ( 0 , w / 2 , 1e-8 , simp ( 0 , w / 2 ) ) ;
            if ( k < l ) x = m ;
            else y = m ;
        }
        printf ( "Case %d:\n" , ++ ca ) ;
        printf ( "%.2lf\n" , h - x ) ;
        if ( T ) puts ( "" ) ;
    }
    return 0 ;
}