Given the coordinates of two points A and B, there is a ray Representative AB.
To give a set point and a radius coordinate point O R, representative R is O as a center to a radius of the circle.
Ray asked whether there is a common point of the circle that exist and at some point both in the circle ray.
Total number of input 7, are non-negative integers not more than 100.
Output line, there is this point on output Y, otherwise N. output
Test Example:
Test Input: 232,100,211
Expected Output: N
Test Inputs: 101100211
expected output: Y
vector multiplication:
A * B = |a| |b| * * * B = cosxa | a | * | B | cosx *
a * B = coordinate |a| * |b| * cosx vector multiplication:
(X1, Y1) * (X2, Y2) = X1 * Y1 + X2 * Y2 (X1, y1) * (x2, y2) = x1 * x2 + y1 * y2 (x1, y1) * (x2, y2) = x1 * x2 + y1 * y2 Tip:
Comparative ∠OAB ∠OAP and size, if not ∠OAB greater than ∠OAP, the ray intersects the circle.
You can determine the size by comparing the value of sin.
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
int x1,y1,x2,y2,xo,yo;
double r,l,k=0;
cin>>x1>>y1>>x2>>y2>>xo>>yo>>r;
k=(y2-y1)/(x2-x1);
l=abs(k*xo-yo+y1-k*x1)/(sqrt(k*k+1));
if(l==r)
{
cout<<'Y';
}
else
{
cout<<'N';
}
}
or
#include <iostream>
#include <cmath>
using namespace std;
float len(int x1,int y1,int x2,int y2)
{
int t = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2);
return sqrt(t);
}
int main()
{
int xa,ya,xb,yb,xo,yo,R;
cin>>xa>>ya>>xb>>yb>>xo>>yo>>R;
if(xa==xb && ya==yb)
{
cout<<"N";return 0;
}
float OA = len(xa,ya,xo,yo);
float OB = len(xb,yb,xo,yo);
if(OA<=(float)R || OB<=(float)R)
{
cout<<"Y";return 0;
}
else
{
int son_cos = (xo-xa)*(xb-xa)+(yo-ya)*(yb-ya);
float mother_cos = len(xa,ya,xo,yo)*len(xa,ya,xb,yb);
float cos = (float)son_cos/mother_cos;
float my_sin = sqrt(1-cos*cos);
float sin = (float)R/len(xa,ya,xo,yo);
if(cos<=0)
{
cout<<"N";
return 0;
}
else if(my_sin<=sin)
{
cout<<"Y";
return 0;
}
else
{
cout<<"N";
return 0;
}
}
}