Question: We are given n points in the unit circle, p i = (x i , y i ), such that 0 < x 2 i

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.

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