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Problem : In the course of a merge sort on a 64 element list, how many times must the list be split?

6 times, or log2(64).

Problem : Consider the following pairs of lists:

  • A. (3, 5, 7, 9) and (2, 4, 6, 8)
  • B. (1, 2, 3, 4) and (5, 6, 7, 8)
Which pair is more efficiently merged?

Pair B can be merged more efficiently because after four comparisons the first list is empty. Since we know that the second list is already in order, we simply insert the elements one by one into the final list without making any more comparions.

Problem : Below is an 8 element list that has been broken down into 8 one element lists. Show the merging of the lists to form and ordered list. (6), (3), (8), (2), (9), (1), (5), (7)

(6) and (3) merge to (3, 6) (8) and (2) merge to (2, 8) (9) and (1) merge to (1, 9) (5) and (7) merge to (5, 7) (3, 6) and (2, 8) merge to (2, 3, 6, 8) (1, 9) and (5, 7) merge to (1, 5, 7, 9) (2, 3, 6, 8) and (1, 5, 7, 9) merge to (1, 2, 3, 5, 6, 7, 8, 9)

Problem : The list above required 7 merges to be sorted. In general, how many merges will be performed in an n element list (for the sake of simplicity, assume that n is a power of 2)?

n/2 + n/4 + n/8 + ... + 2 + 1 = n - 1
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