Top-down Mergesort with a sorted check before each merge has merge cost M ≤ (H+3)n for any input, where H is the run-length entropy.
Adaptive Shivers Sort: An Alternative Sorting Algorithm , volume =
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Top-Down Mergesort with Sorted Check Has Mergecost $\le(\mathcal H+3)n$
Top-down Mergesort with a sorted check before each merge has merge cost M ≤ (H+3)n for any input, where H is the run-length entropy.