1. Queue data structure
Roman R

2. # todo
- php impl of Queue as Linked List
- persistent queue (using 5 stacks)
- persistent queue (using 6 stacks)
- deque impl (double-end queue)
- change rair => tail, start => head, etc
- add gif-animation for algo
2

3. Queue: definition
data structure
set of items
earliest added item may be accessed (FIFO)
has two ends (head and rair/tail)
push (into tail) and pop (from head)
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4. Queue: examples IRL
- lines of people (line in a grocery store, buy a movie ticket)
- conveyor belt
- waiting lists
- access to shared resources (e.g. printer jobs)
- things that are in "time order"
- events in Windows
- keyboard strokes
- video frames
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5. Queue: types
- queue as array
- circular queue
- priority queue
- deque
- input restricted
- output restricted
- persistent queue
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6. Queue: interface
enqueue (put) - add to the tail
dequeue (get + delete) - get from the head
empty(Q):bool
count(Q):int
front(Q):item - peek (just get)
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7. Queue: axioms
new() returns a queue
add(v, new()).isEmpty() = false
front(add(v, new())) = v
remove(add(v, new())) = new()
front(add(v, add(w, Q))) = front(add(w, Q))
remove(add(v, add(w, Q))) = add(v, remove(add(w, Q)))
Q - queue; v and w - values;
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8. Queue: basic example
initial -> | | | | (assume 3 element capacity)
enqueue(a) -> |a| | |
enqueue(b) -> |a|b| |
enqueue(c) -> |a|b|c|
dequeue() -> | |b|c| (returns a)
dequeue() -> | | |c| (returns b)
dequeue() -> | | | | (returns c) (all gone!)
head |a|b|c| tail
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9. Queue: implementation
- as Array
- Cyclic Array
- as Linked List (doubly)
- as Stack (2 or 6)
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10. as array and two integer variables start and end
start = head of queue
end = element that will be filled when new el will come
@todo on images replace front->start, back->end
Queue: implementation using Array
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11. Queue: implementation using Array
enqueue(item): item => q[end], end++
dequeue(): item <= q[start], start++
if Queue not full
- put element at end Q[tail] <- elem
- increment tail tail <- tail + 1
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12. int A[10]
front = -1
tail = -1
function isEmpty() { front == -1 && tail == -1 }
function isFull() { tail == size(A)-1 }
function enqueue(v) {
if isFull() -> error Queue is full
if isEmpty() front <- tail <- 0 else tail+=1
A[tail] = v
}
Queue: implementation using Array
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13. Queue: implementation using Array
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14. Queue: implementation using Array
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15. Queue: implementation using Array
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16. Queue: implementation using Array
function dequeue() {
if isEmpty() -> error Queue is empty
elseif front == tail
front <- rear <- -1
else
front += 1
}
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17. Queue: implementation using Array
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18. Queue: implementation using Array
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19. no end on array
wrapping around
ring buffer / circular buffer
push/pop - O(1)
when item inserted to rair, tails’s pointer moves upwards
when item deleted, head’s pointer moves downwards
current_position = i
next_position = (i + 1) % N
prev_position = (N + i - 1) % N
Queue: implementation Cyclic Array
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20. function isFull() {
(tail + 1 ) % N == head
}
function enqueue(v) {
if isFull() -> error Queue is full
if isEmpty() front <- tail <- 0
else tail = (tail + 1) % N
A[tail] = v
}
function dequeue() {
if isEmpty() -> error Queue is empty
elseif front == tail front <- rear <- -1
else front = (front + 1) % N
}
Queue: implementation Cyclic Array
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21. Queue: implementation using Array: pros & cons
pros
- minor memory savings (compared with LinkedList impl)
- easier to develop
cons
- fixed size
- when is full, need create new arary, with reallocation
of memory and copy all els to the new array (costly
process, O(n))
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22. Queue: implementation using Linked List
one way Linked List (based on the work with dynamic memory)
insertion/removal: at head O(1), at tail O(n)
http://www.cosc.canterbury.ac.nz/mukundan/dsal/LinkQueueAppl.html
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23. Queue: implementation using Linked List
insert: create a node, update tail pointer
traversal is complex, O(n)
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24. Queue: implementation using Linked List
O(1)
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25. class Node {
Object data
Node next
}
class Queue {
Node front
Node rear
}
isEmpty() {
return rear == null
}
Queue: implementation using Linked List
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function enqueue(x) {
newNode = new Node
newNode->data = x
if isEmpty()
front = newNode
else
rear->next = newNode
rear = newNode
}
function dequeue(d) {
temp = front
if front = null { return }
if front == rear {
front = rear = null
}
else {
front = front->next
}
free(temp)
}

26. <?php
@todo
Queue: php implementation using Linked List
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27. Queue: implementation using Linked List: pros & cons
pros
- size is limited by memory capacity
cons
- requires more memory
- more memory is fragmented
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28. Queue: implementation using 2 Stacks
- leftStack for push
- rightStack for pop
- push-/pop- -Left/-Right
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29. Queue: implementation using 2 Stacks: example
procedure enqueue(x):
S1.push(x)
function dequeue():
if S1 is empty and S2 is empty:
error: stack is empty
while S1 isn’t empty:
S2.push(S1.pop())
return S2.pop()
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30. Queue: implementation using 2 Stacks: pros & cons
Эту реализацию несложно модифицировать для получения минимума в
текущей очереди за O(1).
Если leftStack не пуст, то операция pop может выполняться O(n) времени,
в отличии от других реализаций, где pop всегда выполняется за O(1).
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31. Queue: implementation using 6 Stacks
- on 2 stack - worst case O(n) for operation
- persistent queue
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32. Queue: implementation using 6 Stacks: example
@ todo
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33. pros
- ??? O(1)
- can be improved to persistent queue, if use persistent stack
cons
- longer than the average operation is performed
- more memory consumption
- the greater complexity of implementation
Queue: implementation using 6 Stacks: pros & cons
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34. Queue: php (SPL)
SplQueue
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class SplQueue
extends SplDoublyLinkedList
implements Iterator, ArrayAccess, Countable {
mixed dequeue ()
void enqueue ($value)
void setIteratorMode ($mode) // IT_MODE_DELETE, IT_MODE_KEEP,
SplDoublyLinkedList::IT_MODE_FIFO,
+ inherited methods from SplDoublyLinkedList
}

35. Queue: php (SPL) IRL
@todo
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36. Queue: php (SPL)
$queue = new SplQueue();
$queue->setIteratorMode(SplDoublyLinkedList::IT_MODE_DELETE);
$queue->enqueue(1);
$queue->enqueue(2);
$queue->enqueue(3);
print_r($queue->dequeue());
print_r($queue->dequeue());
print_r($queue);
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Output:
1
2
SplQueue Object (
[flags:SplDoublyLinkedList:private] => 1
[dllist:SplDoublyLinkedList:private] => Array
(
[0] => 3
)
)

37. class Queue {
public function enqueue($item) { }
public function dequeue() { }
public function count() { }
}
Queue: implementation in php
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38. class Queue {
private $_queue = array();
public function enqueue($item) {
$this->_queue[] = $item;
}
public function dequeue() {
return array_shift($this->_queue);
}
public function count() {
return count($this->_queue);
}
}
Queue: implementation in php (using Array)
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39. class Queue {
private $_queue = array();
private $_headPosition = null,
$_tailPosition = null;
public function enqueue($item) {
$this->_queue[] = $item;
if ($this->count() == 1) {
$this->_headPosition
= 0;
$this->_tailPosition
= 0;
}
$this->rewind();
}
public function count() {
return count($this->_queue);
}
Queue: implementation in php (using Array)
39
public function dequeue() {
$item = $this->_queue[$this->_headPositio
$this->_headPosition++;
return $item;
}
public function hasNext() {
return isset($this->_queue[$this->_headPo
}
public function rewind() {
$this->_tailPosition = $this->_headPositi
}
}

40. Priority Queue: definition
abstract data type
each element has a "priority" attr
pop will find element with highest priority
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41. - bandwidth management
- discrete event simulation
- job scheduling
- Dijkstra's algorithm
- Huffman coding
- Best-first search algorithms
- ROAM triangulation algorithm
- Prim's algorithm for minimum spanning tree
Priority Queue: examples IRL
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42. Priority Queue: types
ascending (min) priority queue
descending (max) priority queue
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43. Priority Queue: interface
insert - insert with priority
find-minimum (or maximum)
delete-minimum (or maximum)
compare
meld - join two priority queues
delete an arbitrary item
decrease-key (increase) the priority of a item
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44. Priority Queue: basic example
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45. Priority Queue: implementation
array (unordered, ordered)
linked-list (unordered and reverse-ordered)
binary heap
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46. Priority Queue: implementation as Unordered Array
class QueueAsUnorderedArray {
...foreach..
}
http://algs4.cs.princeton.edu/24pq/UnorderedArrayMaxPQ.jav
a.html
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47. Priority Queue: implementation as Ordered Array
class QueueAsOrderedArray {
...foreach..
}
http://algs4.cs.princeton.edu/24pq/OrderedArrayMaxPQ.java.
html
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48. Priority Queue: implementation as Linked List
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49. Priority Queue: implementation as Heap
Heap-based priority queue
insert/deleteMin = O(log n)
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50. SplPriorityQueue impl using max-heap
Priority Queue: php (SPL)
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public bool isEmpty ()
public mixed key ()
public void next ()
public void recoverFromCorruption ()
public void rewind ()
public void setExtractFlags ($flags)
public mixed top ()
public bool valid ()
}
class SplPriorityQueue implements Iterator, Countable {
public __construct ()
public int compare ($priority1, $priority2)
public int count ()
public mixed current ()
public mixed extract ()
public void insert ($value, $priority)

51. count: 4
array { "data" => "D", "priority" => 9 }
array { "data" => "B", "priority" => 6 }
array { "data" => "A", "priority" => 3 }
array { "data" => "C", "priority" => 1 }
$queue = new SplPriorityQueue;
$queue->insert('A', 3); // A3
$queue->insert('B', 6); // B6, A3
$queue->insert('C', 1); // B6, A3, C1
$queue->insert('D', 9); // D9, B6, A3, C1
echo 'count: ' . $queue->count();
$queue->setExtractFlags(SplPriorityQueue::EXTR_BOTH);
while($queue->valid()){
var_dump($queue->current());
$queue->next();
}
Priority Queue: php (SPL)
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52. Priority Queue: php (SplMinHeap SPL)
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class SplMinHeap
extends SplHeap implements Iterator , Countable {
protected int compare ($value1, $value2)
+ inherited methods from SplHeap
}
SplMinHeap stores minimal el on head

53. Priority Queue: php (SplMinHeap SPL)
$pq = new SplMinHeap;
$pq->insert(array(3, 'Clear drains'));
$pq->insert(array(4, 'Feed cat'));
$pq->insert(array(5, 'Make tea'));
$pq->insert(array(1, 'Solve RC tasks'));
$pq->insert(array(2, 'Tax return'));
while (!$pq->isEmpty()) {
print_r($pq->extract());
}
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54. Priority Queue: php (unordered array)
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55. double-ended queue
els can be added to head or tail
is generalization of both stack and queue
DEQueue: definition
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56. input restricted deque
- restricts insertion of els at one end only
- allow deletion of both ends
output restricted deque
- restricts deletion of els at one end only
- allows insertion to both ends
Deque: types
56

57. double linked-list (with two additional reference
variables to refer the first and last items)
Deque: implementation
57

58. addLeft(item)
addRight(item)
isEmpty()
front()
back()
dequeueLeft()
dequeueRight()
Deque: interface
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59. # resources
- http://xlinux.nist.gov/dads//HTML/queue.html
- http://algs4.cs.princeton.edu/24pq/
- https://www.doc.ic.ac.uk/~ar3/lectures/ProgrammingII/LargePrintOut/Lecture5PrintOut.pdf
- http://neerc.ifmo.ru/wiki/index.php?title=Очередь
- http://neerc.ifmo.ru/wiki/index.php?title=Персистентная_очередь
- http://habrahabr.ru/post/241231/
- @ http://habrahabr.ru/post/240519/
- https://www.youtube.com/watch?v=okr-XE8yTO8 implementation Queue as Array
- https://www.youtube.com/watch?v=A5_XdiK4J8A implementation Queue as Linked `List
- https://www.cs.usfca.edu/~galles/visualization/QueueArray.html
- https://www.cs.usfca.edu/~galles/visualization/QueueLL.html
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