←back to thread

Google's “Director of Engineering” Hiring Test

(www.gwan.com)
1764 points fatihky | 4 comments | 13 Oct 16 15:15 UTC | HN request time: 0.638s | source
Show context
enjoylife ◴[13 Oct 16 15:48 UTC] No.12701550[source]▶
What the heck is a "Quicksort big-O score"? I've never heard anyone use the noun score when talking about complexity analysis.
replies(2): >>12701671 #>>12701675 #
protomyth ◴[13 Oct 16 16:04 UTC] No.12701675[source]▶
I assume they want the average O(n log n), but who the heck knows given the script from above.

I get the feeling this: http://bigocheatsheet.com would come in handy

replies(1): >>12701916 #
1. steven777400 ◴[13 Oct 16 16:28 UTC] No.12701916[source]▶
Big-O technically means "worst case", which for Quicksort is O(n^2), although usually (in normal cases) it runs better than that. Other sort algorithms can guarantee not worse than O(n log n).
replies(3): >>12702289 #>>12702370 #>>12703002 #
2. protomyth ◴[13 Oct 16 17:08 UTC] No.12702289[source]▶
Must have been a while, I thought you went with average, but I guess its been 20 years. I mostly lived in optimizing cache since college.
3. susi22 ◴[13 Oct 16 17:16 UTC] No.12702370[source]▶
That's incorrect. The /mathematical/ definition means that it's the upper bound. I.e. yes, the set of all functions of O(N) is a subset of the set of all functions O(N^2). So you could say Quicksort is O(N^100) and still be technically correct.

However, the big-O notation does NOT specify anything about worst/avg/best-case complexity of a given algorithm. That should still be defined in the analysis.

You mixed up those two slightly different concepts.

4. TimonKnigge ◴[13 Oct 16 18:39 UTC] No.12703002[source]▶
Depending on how the pivot is picked, Quicksort can actually be implemented in O(n lg n) worst-case time.

EDIT: I was going to link a proof for this but it's surprisingly hard to find. IIRC, the idea is to use the median of medians algorithm ([1]) to pick the median for the pivot, and deal with values equal to the pivot by alternatingly placing them in the left and right partition, or alternatively just keep them in a third partition in the middle.

[1] https://en.wikipedia.org/wiki/Median_of_medians