Chapter 4: Orders of Growth and Tree Recursion

Analyzing Merge Sort 4

Since n cards are handled on each of log₂n + 1 passes, the total number of handlings H(n) is:

H(n) = n(log₂n + 1)
= nlog₂n + n

Since n ≤ nlog₂n, then

H(n) ≤ nlog₂n + nlog₂n
≤ 2nlog₂n

But H(n) ≥ nlog₂n, so

nlog₂n ≤ H(n) ≤ 2nlog₂n

Thus the time it takes to merge sort n cards is:

Θ(nlog₂n)

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