Question

Suppose we are given an array A that contains n distinct integers. Our goal is to find a "nice" pivot A[m] that has the following property: A[m] lies between the (n/10)-th smallest and the (n/10)-th largest element of A. You have access to a quantum oracle Q that works as follows: Q(A0 ) returns the median of an array A0 in constant time whenever A0 has at most n 1/3 elements. Q does not work when the input array has more than n 1/3 elements. Design and describe an efficient algorithm that returns a nice pivot of A by using the quantum oracle Q. Analyze the running time and argue the correctness of your algorithm. You can assume that it only takes constant time to submit subarray A[i..j] of A to the quantum orcale Q. Creating an array of size k takes Θ(k) time.‘

Answer 1

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