专题二 · 1005

代码及解释

#include <stdio.h>
#include <math.h>

// 拐弯的问题
// 高中数学做过一个很类似的
// 关键是在转向的时候，值不是单调的
// 所以不用二分

const double PI = acos(-1.0);

double x,y,l,w,s,h;

double ankle(double a) {
    s = l * cos(a) + w * sin(a) - x;
    h = s * tan(a) + w * cos(a);
    return h;
}

int main() {
    
    
    while(scanf("%lf%lf%lf%lf", &x, &y, &l, &w)!=EOF) {
        double left = 0.0;
        double right = PI/2;
        
        double mid1 = 0.0;
        
        while(fabs(right-left) > 1e-8) {
            mid1 = (left + right) / 2;
            double midmid2 = (mid1 + right) / 2;
            
            if(ankle(mid1) >= ankle(midmid2))
                right = midmid2;
            else
                left = mid1;
        }
        
        if(ankle(mid1)<=y)
            printf("yes\n");
        else
            printf("no\n");
    }
    return 0;
}