What is the worst case space complexity for this algorithm

A community of N pirates has recently conducted an election to choose their new leader. All pirates

vote, and any pirate may run as a candidate. There is no preferential system, each pirate simply

writes the number of their preered leader on the ballot paper. If a single pirate gets more than

50% of the votes, then that pirate is declared the new leader. If no pirate gets more than 50% of the

votes, then the old leader is retained.

N pirates have voted, and their choices have been collected in an array A. Your task is to determine

whether there will be a new leader and, if there will, who the new leader will be. For example, given

the array

4; 4; 7; 1; 7; 7; 2; 7; 7

pirate 7 has 5 votes out of 9, and becomes the new leader, whereas given the array

4; 4; 7; 1; 4; 7; 2; 4

pirate 4 has 4 votes out of 8 but doesn’t manage to get over 50% so the old leader is retained.

Your team has proposed the following algorithm to determine which, if any, candidate wins:

First, a possible winner must be found. This possible winner the only candidate that could pos-

sibly have more than 50% of the votes. To nd a possible winner in the array, A, create a second

array, B. Compare A[0] and A[1]. If they are equal, put one of them in B; otherwise do nothing.

Then compare A[2] and A[3]. Again if they are equal, add one of these to B; otherwise do nothing.

Continue like this until the entire array A has been used. Recursively nd a possible winner on the

array B, stopping when the array has less than 2 elements. If a possible winner has been found, scan

through the array and count the number of votes received by the possible winner. If the possible

winner has more than N/2 votes, print the possible winner out as the winner. If no possible winner

is found, or the possible winner does not have enough votes, print that the old leader is retained.

(a) What is the worst case space complexity for this algorithm (consider the array(s) B only)?

Explain your reasoning.

(b) Give the O,

and, if possible, time complexities for this algorithm. Explain your reasoning.

(c) Why does this algorithm work? You may assume the array size is even for all function calls.

(d) What problem occurs when the array size is odd? Propose a x for this problem, or describe

an alternative algorithm.

(e) What are the (Big-Oh) time and space1 complexities of your new algorithm? Compare this to

the previous algorithm and explain under what circumstances would you use one algorithm or

the other?

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