Analyzing a Weighted Digital Sum Variant †
نویسندگان
چکیده
Consider the following weighted digital sum (WDS) variant: write integer n as n = 21 + 22 + · · · + 2k with i1 > i2 > · · · > ik ≥ 0 and set WM (n) := ∑k t=1 t 2t . This type of weighted digital sum arises (when M = 1) in the analysis of bottom-up mergesort but is not “smooth” enough to permit a clean analysis. We therefore analyze its average TWM (n) := 1 n ∑ j<n WM (j). We show that TWM (n) has a solution of the form
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