Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

class). Below, we show how to set up location-aware entries for several data
structures presented in this chapter.
• Unordered list : In an unordered list, L, implementing a dictionary, we can
maintain the location variable of each entry e to point to e's position in the
underlying linked list for L. This choice allows us to perform remove(e) as
L.remove(e.location()), which would run in O(1) time.
• Hash table with separate chaining : Consider a hash table,
with bucket array A and hash function h, that uses separate chaining for handling
collisions. We use the location variable of each entry e to point to e's position
in the list L implementing the mini-map A[h(k)]. This choice allows us to perform
the main work of a remove(e) as L.remove(e.location()), which would
run in constant expected time.
• Ordered search table : In an ordered table, T, implementing a dictionary,
we should maintain the location variable of each entry e to be e's index in T.
This choice would allow us to perform remove(e) as
T.remove(e.location()). (Recall that location() now returns an
integer.) This approach would run fast if entry e was stored near the end of T.
• Skip list : In a skip list, S, implementing a dictionary, we should maintain
the location variable of each entry e to point to e's position in the bottom level
of S. This choice would allow us to skip the search step in our algorithm for
performing remove(e) in a skip list.
We summarize the performance of entry removal in a dictionary with locationaware
entries in Table 9.5.
Table 9.5: Performance of the remove method in
dictionaries implemented with location-aware entries.
We use n to denote the number of entries in the
dictionary.
List
Hash Table
Search Table
Skip List
O(1)
O(1) (expected)
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