CS210- Lecture 15
July 7, 2005
Agenda
 Median Heaps
 Adaptable PQ
 Maps and Dictionaries
 Map ADT
 Linked list implementation of Maps
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Adaptable Priority Queues
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Suppose we have an online trading system where
orders to purchase and sell a given stock are stored
in two priority queues (one for sell orders and one for
buy orders) as (p,s) entries:
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The key, p, of an order is the price
The value, s, for an entry is the number of shares
A buy order (p,s) is executed when a sell order (p’,s’) with
price p’<p is added (the execution is complete if s’>s)
A sell order (p,s) is executed when a buy order (p’,s’) with
price p’>p is added
What if someone wishes to cancel their order before
it executes?
What if someone wishes to update the price or
number of shares for their order?
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Methods of the Adaptable PQ ADT
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remove(e): Remove and return entry e.
replaceKey(e,k): Replace with k and
return the key of entry e of P; an error
condition occurs if k is invalid (that is, k
cannot be compared with other keys).
replaceValue(e,x): Replace with x and
return the value of entry e of P.
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Example
Operation
insert(5,A)
insert(3,B)
insert(7,C)
min()
key(e2)
remove(e1)
replaceKey(e2,9)
replaceValue(e3,D)
remove(e2)
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Output
e1
e2
e3
e2
3
e1
3
C
e2
P
(5,A)
(3,B),(5,A)
(3,B),(5,A),(7,C)
(3,B),(5,A),(7,C)
(3,B),(5,A),(7,C)
(3,B),(7,C)
(7,C),(9,B)
(7,D),(9,B)
(7,D)
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Locating Entries
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In order to implement the operations
remove(k), replaceKey(e), and
replaceValue(k), we need fast ways of
locating an entry e in a priority queue.
We can always just search the entire
data structure to find an entry e, but
there are better ways for locating
entries.
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Location-Aware Entries
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A locator-aware entry identifies and
tracks the location of its (key, value)
object within a data structure
Main idea:
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Since entries are created and returned
from the data structure itself, it can return
location-aware entries, thereby making
future updates easier
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List Implementation
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A location-aware list entry is an object storing
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key
value
position (or rank) of the item in the list
In turn, the position (or array cell) stores the entry
nodes/positions
header
2 c
4 c
5 c
trailer
8 c
entries
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Heap Implementation
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A location-aware
heap entry is an
object storing
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2 d
key
value
position of the entry
in the underlying
heap
In turn, each heap
position stores an
entry
Back pointers are
updated during
entry swaps
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4 a
8 g
6 b
5 e
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9 c
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Performance
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Using location-aware entries we can achieve
the following running times:
Method
Unsorted List
size, isEmpty
O(1)
insert
O(1)
min
O(n)
removeMin
O(n)
remove
O(1)
replaceKey
O(1)
replaceValue
O(1)
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Sorted List
O(1)
O(n)
O(1)
O(1)
O(1)
O(n)
O(1)
CS210-Summer 2005, Lecture 15
Heap
O(1)
O(log n)
O(1)
O(log n)
O(log n)
O(log n)
O(1)
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Maps and Dictionaries
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The primary use of map or dictionary is
to store elements so that they can be
located quickly using keys.
The motivation for such searches is that
each element stores additional useful
information besides the search key, but
the only way to get at that information
is to use the search key.
Example: Bank account information.
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Maps and Dictionaries
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Like priority queues, maps and
dictionaries store key-value pairs, called
entries.
Maps require that each key be unique,
while dictionaries allow multiple entries
to have the same key, just like priority
queues.
Total order relation is always required
for keys in priority queues, it is optional
for dictionaries.
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The Map ADT
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A map stores key-value pairs (k, v),
which we call entries, where k is the
key and v is its corresponding value.
The map ADT requires each key be
unique.
We allow both the keys and the values
stored in a map to be of any Object
type.
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Map ADT
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size(): Return the number of entries in M.
isEmpty(): Test whether M is empty
get(k): if the map has an entry e with key k, then
returns the value of e, else returns null
put(k, v): if map does not have entry with key k,
then inserts the entry (k, v) to M and return null.
Otherwise replace with v the existing value of the
entry with key k and return the old value.
remove(k): remove from M the entry with key k and
returns its value. If M has no such entry then return
null.
keys(): returns an iterator of the keys stored in M.
values(): returns an iterator of the values associated
with keys stored in M.
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Map ADT
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When get(k), put(k, v) and remove(k)
are performed on a map that has no
entry with key equal to k, we use the
convention of returning null. What is
the disadvantage of doing this?
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Maps in the java.util.package
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java.util package includes an interface
for the Map ADT.
Interface java.util.Map does not have
any methods to directly return iterators
of a Maps keys or values, but it does
have methods to return a set of keys or
values, which can in turn provide an
iterator.
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A Simple List-Based Map implementation
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A simple way of implementing a map is
to store its n entries in a list S,
implemented as a doubly linked list.
get(k), put(k,v) and remove(k), involves
simple scan down S looking for an entry
with key k.
Each of the above methods take O(n)
time on a Map with n entries, because
each method involves searching
through the entire list in the worst case.
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