implementation of set operations

Wed, 13 Mar 2013 00:00:00 +0000

We got in a bit of a debate yesterday in the office over the implementation of associative containers, which I thought was pretty fun. We made up the big chart of complexity results you see below.

nomenclature:

$S$, $S_1$, and $S_2$ are subsets of $\Omega$.
Denote an element by $e\in\Omega$.
$n$,$n_1$,$n_2$,$N$ are the sizes of the set $S$, $S_1$, $S_2$, and $\Omega$, respectively, and $n_1 \geq n_2$.

Complexity

Operation\Approach	Hash Table	Hash Tree	Binary List	Entry List (sorted)	Entry List (unsorted)
$e \in S $	$O(1) $	$O(log(n)) $	$O(1) $	$O(log(n)) $	$O(n) $
$S_1 \cup S_2 $	$O(n_1+n_2) $	$O(n_1+n_2) $	$O(N) $	$O(n_1+n_2) $	$O(n_1n_2) $
$S_1 \cap S_2 $	$O(n_1) $	$O(log(n_1)n_2)$	$O(N) $	$O(n_2) $	$O(n_1n_2) $
space complexity	$O(n) $	$O(n) $	$O(N)$ bits.	$O(n) $	$O(n) $

As I said–this was just what came out of my memory of an informal discussion, so I make no guarantees that any of it is correct. Let me know if you spot something wrong! We used the examples $S_1 = {1,2,3,4,5}$ and $S_2 = {500000}$ to think through some things.

Cs-Theory on traviscj/blog

implementation of set operations

nomenclature:

Complexity