Find the most common entry in an array

Question

You are given a 32-bit unsigned integer array with length up to 2³², with the property that more than half of the entries in the array are equal to N, for some 32

Answer 1

Notice that if the sequence a0, a1, . . . , an−1 contains a leader, then after removing a pair of elements of different values, the remaining sequence still has the same leader. Indeed, if we remove two different elements then only one of them could be the leader. The leader in the new sequence occurs more than n/2 − 1 = (n−2)/2 times. Consequently, it is still the leader of the new sequence of n − 2 elements.

Here is a Python implementation, with O(n) time complexity:

def goldenLeader(A):
    n = len(A)
    size = 0
    for k in xrange(n):
        if (size == 0):
            size += 1
            value = A[k]
        else:
            if (value != A[k]):
                size -= 1
            else:
                size += 1
    candidate = -1
    if (size > 0):
        candidate = value
    leader = -1
    count = 0
    for k in xrange(n):
        if (A[k] == candidate):
            count += 1
    if (count > n // 2):
        leader = candidate
    return leader