HDU-2438 Turn the corner

题意: 给定一个直角弯, 判断一辆矩形形状的车是否可以通过.
分析: 假设车辆是沿着右和下的边通过, 设车辆与x轴的夹角为a, 那么可以得到靠内侧的那条边的解析式 y = xtan(a) + lsin(a) + d/cos(a) 那么车辆要能通过这个转弯, 要求是内侧的角不能相撞, 那么另y = -X(注意是大写), 带入解得x(小写). x 若大于 Y(大写)则不能通过.

代码:

#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>

using namespace std;

const double eps = 1e-8;
const double pi = acos(-1);
double x, y, w, d;
double cal(double angle) {
  return (-x + w * sin(angle) + d / cos(angle)) / tan(angle);
}

int main() {

  while (cin >> x >> y >> w >> d) {

    if (d > y || d > x) {
      cout << "no" << endl;
      continue;
    }
    double l = 0, r = pi / 2, mid = 0, midmid = 0;
    while ((r - l) > eps) {
      mid = (l + r) / 2;
      midmid = (mid + r) / 2;
      double h1 = cal(mid);
      double h2 = cal(midmid);
      // cout << h1 << " " << h2 << endl;
      if (h1 < h2)
        l = mid;
      else
        r = midmid;
    }
    if (cal(l) > y) {
      cout << "no" << endl;
    } else {
      cout << "yes" << endl;
    }
  }
  return 0;
}