Version 5.0 The LEDA User Manual

Iteration
forall items(it, S) { “the items of S are successively assigned to it” }
forall rev items(it, S) { “the items of S are successively assigned to it in reverse order”
}
forall(i, S) { “the informations of all items of S are successively assigned to i” }
forall defined(k, S) { “the keys of all items of S are successively assigned to k” }
5. Implementation
Sorted sequences are implemented by skiplists [77]. Let n denote the current size of
the sequence. Operations insert, locate, lookup and del take time O(log n), operations
succ, pred, max, min item, key, inf , insert at and del item take time O(1). clear takes
time O(n) and reverse items O(l), where l is the length of the reversed subsequence.
Finger lookup(x) and finger locate(x) take time O(log min(d, n − d)) if x is the d-th item
in S. Finger lookup from front(x) and finger locate from front(x) take time O(log d) if x
is the d-th item in S. Finger lookup from rear(x) and finger locate from rear(x) take time
O(log d) if x is the n−d-th item in S. Finger lookup(it, x) and finger locate(it, x) take time
O(log min(d, n−d)) where d is the number of items between it and the item containing x.
Note that min(d, n−d) is the smaller of the distances from it to x if sequences are viewed
as circularly closed. Split, delete subsequence and conc take time O(log min(n 1 , n 2 )) where
n 1 and n 2 are the sizes of the results of split and delete subsequence and the arguments of
conc respectively. Merge takes time O(log((n 1 + n 2 )/n 1 )) where n 1 and n 2 are the sizes
of the two arguments. The space requirement of sorted sequences is linear in the length
of the sequence (about 25.5n Bytes for a sequence of size n plus the space for the keys
and the informations.).
6. Example
We use a sorted sequence to list all elements in a sequence of strings lying lexicographically
between two given search strings.
#include
#include
using leda::sortseq;
using leda::string;
using leda::seq_item;
using std::cin;
using std::cout;