HDU 1724 (simpson積分)

題目鏈接：點擊這裏

題意：給出一個橢圓和[l,r]，求橢圓橫座標在這個範圍內的面積。

根據橢圓公式可知y=b2−b2∗x2a2−−−−−−−−√ ，所以直接利用面積積分公式S=2∫rlydx ，套simpson積分即可。

#include <bits/stdc++.h>
using namespace std;
const double pi = 3.14159265;
const double eps = 1e-5;

double L, R, a, b;

double F (double x) {
    return sqrt (b*b-b*b/a/a*x*x);
}

double simpson (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 = simpson (a, c), R = simpson (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, simpson (a, b));
}

int main () {
    int t, kase = 0;
    cin >> t;
    while (t--) {
        cin >> a >> b >> L >> R;
        printf ("%.3f\n", 2*asr (L, R, eps));
    }
    return 0;
}