Suppose we want to partition N items into G equal-sized groups of size N/G, such that the smallest N/G items are in group 1, the next smallest N/G items are in group 2, and so on. The groups themselves do not have to be sorted. For simplicity, you may assume that N and G are powers of two.
a. Give an O(N log G) algorithm to solve this problem.
b. Prove an Ω(N log G) lower bound to solve this problem using comparison-based algorithms.
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