# Exercise 11.2.3

Professor Marley hypothesizes that he can obtain substantial performance gains by modifying the chaining scheme to keep each list in sorted order. How does the professor's modification affect the running time for successful searches, unsuccessful searches, insertions, and deletions?

I'm not sure the professor is right.

If we assume with delete with a key (instead of a pointer to an element), we have the following times (with regards to the number of collisions) without sorting:

operation complexity
SEARCH linear (both)
INSERT constant
DELETE linear

The only thing that changes when we sort the list, is that instead of prepending the item to the list, we have to find its right place, making INSERT linear:

operation complexity
SEARCH linear (both)
INSERT linear
DELETE linear

I'm not sure what the professor had in mind, but I believe he was mistaken.