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Merge sort is adaptive because it can take advantage of "runs" that are already sorted. We call this algorithm the natural merge sort. Consider the traditional top-down merge sort:

Start : 3421758906

Divide: 34217|58906

Divide: 342|17|589|06

Divide: 34|2|1|7|58|9|0|6

Divide: 3|4|2|1|7|5|8|9|0|6

Merge: 34|12|57|89|06

Merge: 1234|5789|06

Merge 12345789|06

Merge: 0123456789

With natural merge sort, we get the following:

Start : 3421758906 Divide: 34217|58906

Divide: 342|17|589|06

Divide: 34|2|17|589|06

Merge: 234|15789|06

Merge: 12345789|06

Merge: 0123456789

As you can see, there is one less division and one less merge. However, note that the final division only divides one run (342), all the others are "already sorted" and don't need to be divided any further. With fewer (and longer) runs, there are fewer merges to perform.

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