Given the radius and x-y positions of the center of a circle, write a function randPoint which generates a uniform random point in the circle.
Note:
- input and output values are in floating-point.
- radius and x-y position of the center of the circle is passed into the class constructor.
- a point on the circumference of the circle is considered to be in the circle.
- randPoint returns a size 2 array containing x-position and y-position of the random point, in that order.
Input:
["Solution","randPoint","randPoint","randPoint"]
[[1,0,0],[],[],[]]
Output: [null,[-0.72939,-0.65505],[-0.78502,-0.28626],[-0.83119,-0.19803]]
Input:
["Solution","randPoint","randPoint","randPoint"]
[[10,5,-7.5],[],[],[]]
Output: [null,[11.52438,-8.33273],[2.46992,-16.21705],[11.13430,-12.42337]]
Solutions (Click to expand)
To get a random point in the circle we'll need a random radian value out of 0 to 2 * PI and a random length from the center of the out of 0 to radius. We can then assume that our random point is at rand(radius) from the middle of the circle and at rand(2 * PI) radians. To find the coordinates we will use cosine to find x and sine to find y. If the point is len away from the middle and at deg degrees we can find x by x_center + len * cos(deg) and y by y_center + len * sin(deg)
Time: O(1)
Space: O(1)