Preliminaries: Technically speaking, hash tables support order operations

01-prelim/prelim.tex

@@ -112,7 +112,8 @@ $\opdf{Succ}(x)$		& Return the successor of $x\in{\cal U}$ --- the smallest
 $\opdf{Pred}(x)$		& Similarly, the predecessor of~$x$ is the largest element
 				  smaller than~$x$. \cr
 }
-Except for hash tables, all our implementations of sets can support order operations:
+All our implementations of sets can support order operations,
+but their time complexity varies:
 $$\vbox{\halign{
 #\hfil\qquad&&$#$\hfil~~\cr
 			& \alg{Min}/\alg{Max}	& \alg{Pred}/\alg{Succ}	\cr
@@ -121,6 +122,7 @@ Linked list		& \O(n)			& \O(n)			\cr
 Array			& \O(n)			& \O(n)			\cr
 Sorted array		& \O(1)			& \O(\log n)		\cr
 Binary search tree	& \O(\log n)		& \O(\log n)		\cr
+Hash table		& \O(n)			& \O(n)			\cr
 }}$$
 A~sequence can be sorted by $n$~calls to \alg{Insert}, one \alg{Min}, and $n$~calls to \alg{Succ}.
 If the elements can be only compared, the standard lower bound for comparison-based sorting