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Turn the corner
Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2229 Accepted Submission(s): 856
Problem Description Mr. West bought a new car! So he is travelling around the city.
One day he comes to a vertical corner. The street he is currently in has a width x, the street he wants to turn to has a width y. The car has a length l and a width d.
Can Mr. West go across the corner?
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Input Every line has four real numbers, x, y, l and w.
Proceed to the end of file.
Output If he can go across the corner, print yes. Print no otherwise.
Sample Input
10 6 13.5 4
10 6 14.5 4
Sample Output
yes
no
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题意：
已知汽车的长和宽，l和w，以及俩条路的宽为x和y，汽车所处道路宽为x ，问汽车能否顺利转弯？
分析：汽车能否顺利转弯取决于在极限情况下，随着角度的变化，汽车离对面路的距离是否大于等于0
如图中
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在上图中需要计算转弯过程中h 的最大值是否小于等于y很明显，随着角度θ的增大，最大高度ｈ先增长后减小，即为凸性函数，可以用三分法来求解
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代码：
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#include
#include
#include
#include
using namespace std; #define pi 3.141592653 double x,y,l,w; double cal(double a) { double s=l*cos(a)+w*sin(a)-x; double 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,right=pi/2; double lm,rm; while(fabs(right-left)>1e-6) { lm=(left*2.0+right)/3.0; rm=(left+right*2.0)/3.0; if(cal(lm)>cal(rm)) right=rm; else left=lm; } if(cal(left)<=y) printf(yes ); else printf(no ); } return 0; }
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