Merge Sort, continued

Let T(n) be number of "steps" needed to sort n items using Merge Sort.

Then:

T(1) = 1

T(n) = 2 * T(n / 2) + n, for even n.

n T(n) n*[(log2 n + 1] n2

1 1 1 * [0 + 1] = 1 1

2 2 * 1 + 2 = 4 2 * [1 + 1] = 4 4

4 2 * 4 + 4 = 12 4 * [2 + 1] = 12 16

8 2 * 12 + 8 = 32 8 * [3 + 1] = 32 64

16 2 * 32 + 16 = 80 16 * [4 + 1] = 80 256

32 2 * 80 + 32 = 192 32 * [5 + 1] = 192 1024

�

1024 2 * 5120 + 1024 1024 * [10+1] 1,048,576

= 11,264 = 11,264

All cases: O(n log n)

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