Linear time majority algorithm?

Question

Can anyone think of a linear time algorithm for determining a majority element in a list of elements? The algorithm should use O(1) space.

If n is the s

Answer 1

I think it is possible, using Boyer-Moore, though not directly.

As Matthew stated, Boyer-Moore only guarantees to find the majority element for a slightly different definition of majority, called strict majority. Your definition is slightly weaker, but not by much.

1. Execute Boyer-Moore: O(N) time, O(1) space
2. Check that the candidate fulfills the condition: O(N) time, O(1) space
3. If it doesn't, execute Boyer-Moore, but ignores the instances of the "failed" candidate: O(N) time, O(1) space
4. Check that the (new) candidate fulfills the condition: O(N) time, O(1) space

The 1. and 2. steps are straight-forward. The 3. works because by removing instances of the failed candidates, we are now looking for a strict majority element. The 4. is optional, and only to be used if there is a possibility that no majority element exists.