Question: Input is a sorted array a[1 : n] of arbitrary real numbers. The array could only be of one of the following two types: 1)

Input is a sorted array a[1 : n] of arbitrary real numbers. The array could only be of one of the following two types: 1) Type I: All the elements in the array are distinct; or 2) Type II: The array has copies of one element, the other elements being distinct. Present a Monte Carlo algorithm that determines the type of the array in O(\\/1_Llog n) time. Show that the output of your algorithm will be correct with high probability. (Fact: (1 3:)1\" g 1/6 for any 1 > :1: > 0.)

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