Q. The mode of a set of numbers is defined to be the number that occurs most

frequently in the set. The set {4, 6, 2, 4, 3, 1} has a mode of 4.

[1a] Suppose we know that there is an (unknown) element that occurs (n/2 + 1) times in the set.

Design an () time algorithm to find the mode. Justify the time complexity of your algorithm.

[1b]. Give an algorithm to compute the mode of a set of numbers. You should try to solve the problem in the smallest running time. Justify the time complexity of your algorithm.