Algorithms | Misc | Question 5

The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n integers is 

(A)

θ(n)

(B)

θ(logn)

(C)

θ(nlogn)

(D)

θ(1)

Answer: (B)

Explanation:

whenever there exists an element which is present in the array : more than n/2 times, then definitely it will be present at the middle index position; in addition to that it will also be present at anyone of the neighbourhood indices namely i−1 and i+1 
No matter how we push that stream of More than n/2 times of elements of same value around the Sorted Array, it is bound to be present at the middle index + atleast anyone of its neighbourhood once we got the element which should have occurred more that n/2 times we count its total occurences in O(log⁡n) time.

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