Question: Your algorithm universe is the algorithms of Subject 1. Rad the problem very carefully and pick your problem size even more carefully. You are given

Your algorithm universe is the algorithms of Subject 1. Rad the problem very carefully and pick your problem size even more carefully.

You are given a sequence X of m comparable keys. You need to devise a DECISION algorithm that detects the presence of duplicate keys. Two keys X[ i ] and X[ j ] i not eq to j are duplicates if X[ i ]==X[ j ]. Your algorithm answers with a YES if there is a (one or more) pair of duplicate keys such as X[ i ],X[ j ] and NO otherwise. It is not an optimization algorithm that finds the i and j and the X[ i ]==X[ j ], i.e. locations and value of a pair of duplicates.

(a) What is the running time of a time efficient algorithm for detecting duplicates ?

(b) What is the running time of a time efficient algorithm for detecting duplicates that uses also constant extra space beyond the space for X ?

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