Equivalence testing of n objects

Question

Assume that we are given \'n\' objects and a subroutine that takes two inputs and says if they are equivalent or not (e.g. it can give output as 1 if they are equal).

<

Answer 1

You can use the Boyer-Moore majority voting algorithm, which does at most n-1 comparisons.

function find_majority(A)
    majority = None
    count = 0
    for a in A:
        if count == 0
            majority = a
        else if a == majority
            count += 1
        else
            count -= 1
    return majority

It returns the most common element if appears more than n/2 times in the array.

If you need to know if there is a majority item, then you can make a second pass through the array counting how many times the value returned from the find_majority function appears. This adds another n comparisons.