[ryao]

Just to share since it is related, you can sort faster than a naive O(nlogn) algorithm whenever data is in the form of partitions where the partitions are sorted, but the contents of each partition are not. i.e. The largest element in each partition is smaller than the smallest in the next partition.

There the total number of elements are n and the average size of a partition is m. Then you need only apply any O(log(m)) algorithm to each partition to sort everything. That multiplies the time complexity by n/m. Then substitute n = m^c and the sort becomes O(n/c*log(n)) time. That gives you a factor of c speed up on what would otherwise be an O(nlogn) operation.

This trick is usable when you want to sort a B-Tree like structure where the data in each node is unsorted, but the nodes themselves are sorted. The file system hierarchy on a machine is like that. The default output of zfs list is also like that.