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Slide da cadeira de Estrutura de Dados, ministrado pelo Prof. Dr. Christian Pagot, na Universidade Federal da Paraíba.
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Universidade Federal da ParaíbaCentro de Informática
Queues, Deques and DictionariesLecture 9
1107186 – Estruturas de Dados
Prof. Christian Azambuja PagotCI / UFPB
2Universidade Federal da ParaíbaCentro de Informática
What is a Queue?
● A queue is an abstract data type where elements can be inserted (pushed) and removed (popped) according to the following policies:– Push inserts a new item in the back of the queue.
– Pop removes the item at the front of the queue.
– The above insert/remove policy is also called FIFO (First In-First Out).
3Universidade Federal da ParaíbaCentro de Informática
What is a Queue?
● Example:
A
front back
A B
front back
A B C
front back
B C
front back
1) push('A')
2) push('B')
3) push('C')
4) pop()
4Universidade Federal da ParaíbaCentro de Informática
What is a Deque?
● Deque: Double Ended Queue.● A deque is an abstract data type where
elements can be inserted (pushed) and removed (popped) according to the following policies:– Push inserts a new item in the back or in the
front of the deque.
– Pop removes the item at the front or at the back of the deque.
5Universidade Federal da ParaíbaCentro de Informática
What is a Deque?
● Example:
A
front back
A B
front back
C A B
front back
C A
front back
1) push_front('A')
2) push_back('B')
3) push_front('C')
4) pop_back()
6Universidade Federal da ParaíbaCentro de Informática
What is a Dictionary?
● Associative array, map, symbol table or dictionary.
● A dictionary is an abstract data type composed by a collection of (key, value) pairs, where key is unique.
7Universidade Federal da ParaíbaCentro de Informática
What is a Dictionary?
● Example:– The set of loans in a library:
“Computer Networks” Christian
“Ordinary Differential Equations” Paulo
“Dicionário Gremista” Christian
Key
Data item
8Universidade Federal da ParaíbaCentro de Informática
What is a Dictionary?
● Common operations:– Search(D, k).
– Insert(D, x).
– Delete(D, x).
– Max(D), Min(D).
– Predecessor(D, k), Successor(D, k).
D: dictionary.k: key.x: data item.
Searches for key k in D, and returns a pointer to the corresponding x data item.
Add the x data item to D.
Given a pointer to the x data item in D, removes it from D.
Returns a pointer to the data itemwith largest (or smallest) key.
Returns a pointer to the data itemwhose key is immediately before
(after) k in sorted order.
9Universidade Federal da ParaíbaCentro de Informática
Analysis of Some Possible Dictionary Implementations (by Steven S. Skiena)
● Array:
Operation Unsorted Array
Sorted Array
Search(D, k)
Insert(D, x)
Delete(D, x)
Successor(D, k)
Predecessor(D, k)
Minimum(D)
Maximum(D)
O(n)
O(1)
O(1)*
O(n)
O(n)
O(n)
O(n)
O( log n)O(n)
O(n)
O(1)
O(1)
O(1)
O(1)
10Universidade Federal da ParaíbaCentro de Informática
Analysis of Some Possible Dictionary Implementations (by Steven S. Skiena)
● Single Linked List:
Operation Unsorted List
Sorted List
Search(D, k)
Insert(D, x)
Delete(D, x)
Successor(D, k)
Predecessor(D, k)
Minimum(D)
Maximum(D)
O(n)
O(1)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(1)
O(n)
O(1)
O(1)
11Universidade Federal da ParaíbaCentro de Informática
Analysis of Some Possible Dictionary Implementations (by Steven S. Skiena)
● Doubly Linked List:
Operation Unsorted List
Sorted List
Search(D, k)
Insert(D, x)
Delete(D, x)
Successor(D, k)
Predecessor(D, k)
Minimum(D)
Maximum(D)
O(n)
O(1)
O(1)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(1)
O(1)
O(1)
O(1)
O(1)
12Universidade Federal da ParaíbaCentro de Informática
Analysis of Some Possible Dictionary Implementations (by Steven S. Skiena)
● Comparing all possibilities:
Operation UA SA USLL SSLL UDLL SDLLSearch(D, k)
Insert(D, x)
Delete(D, x)
Successor(D, k)
Predecessor(D, k)
Minimum(D)
Maximum(D)
O(n)
O(1)
O(1)
O(n)
O(n)
O(n)
O(n)
O( log n)O(n)
O(n)
O(1)
O(1)
O(1)
O(1)
O(n)
O(1)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(1)
O(n)
O(1)
O(1)
O(n)
O(1)
O(1)
O(n)
O(n)
O(n)
O(n)
O(n)
O(n)
O(1)
O(1)
O(1)
O(1)
O(1)
UA: Unsorted array SA: sorted array.USSL: Unsorted Single Linked List SSSL: Sorted Single Linked ListUDSL: Unsorted Doubly Linked List SDSL: Sorted Doubly Linked List
