We are given n points in the unit circle, p i = (x i , y i

Question:

We are given n points in the unit circle, p_i = (x_i, y_i), such that 0 < x²_i + y²_i ≤ 1 for i = 1, 2, . . . ,n. Suppose that the points are uniformly distributed; that is, the probability of finding a point in any region of the circle is proportional to the area of that region. Design an algorithm with an average-case running time of Θ(n) to sort the n points by their distances d_i = √x²_i + y²_i from the origin. Design the bucket sizes in BUCKET-SORT to reflect the uniform distribution of the points in the unit circle.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...