Suppose you are to perform a bucket sorting as follows: Assume the input is generated...

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Suppose you are to perform a bucket sorting as follows: • Assume the input is generated by a random process that distributes elements uniformly over [0, 1). Divide [0, 1) into n equal-sized buckets. • Distribute the n input values into the buckets. • Sort each bucket using the insertion sort. Then, go through buckets in order, listing elements in each one. The target bucket sort time is 7(n) 8(n) + Σ0(n)), where n? is a random variable to represent the number of elements placed in bucket i. Prove that the expected value of the bucket sort time, E[T(n)] = 0(n). I = Suppose you are to perform a bucket sorting as follows: • Assume the input is generated by a random process that distributes elements uniformly over [0, 1). Divide [0, 1) into n equal-sized buckets. • Distribute the n input values into the buckets. • Sort each bucket using the insertion sort. Then, go through buckets in order, listing elements in each one. The target bucket sort time is 7(n) 8(n) + Σ0(n)), where n? is a random variable to represent the number of elements placed in bucket i. Prove that the expected value of the bucket sort time, E[T(n)] = 0(n). I =

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To prove that the expected value of the bucket sort time ETn is n we need to show both an upper boun... View the full answer