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Give an algorithm to find a majority element if one exists

Question: A majority element in an array A of size N is an element that appears more than times (thus there is at most one such element).

For example, the array

3, 3, 4, 2, 4, 4, 2, 4, 4

has a majority element (4), whereas the array

3, 3, 4, 2, 4, 4, 2, 4

does not. Give an algorithm to find a majority element if one exists, or reports that one does not. What is the running time of your algorithm?

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