Big O notation O( )

• Describe the complexity of an algorithm
• Time and space
• Relative to the input size

• For O(1), size does not effect the algorithm
   
• For O(log n), size effects the algorithm logarithmically
   
• For O(n), size effects the algorithm proportionally
   
• For, O(n^2), size effects the algorithm exponentionally

Examples

PHP Arrays!!!

An array in PHP is actually an ordered map. A map is a type that associates values to keys. This type is optimized for several different uses; it can be treated as an array, list (vector), hash table (an implementation of a map), dictionary, collection, stack, queue, and probably more. As array values can be other arrays, trees and multidimensional arrays are also possible.

http://php.net/manual/en/language.types.array.php

Trying to be a lot of things in the same time can be UGLY

Or COOL

PHP Arrays

• Large waste of memory

• 14,649,072 bytes
  = 13.97 MBs

SplFixedArray

• Better for real arrays

• 5,600,648 bytes
  = 5.34 MBs

http://nikic.github.io/2011/12/12/How-big-are-PHP-arrays-really-Hint-BIG.html

• Memory: 81.87 MBs
• Time: 0.093 ms

• Memory: 49.37 MBs
• Time: 0.238 ms

Creating 100,000 Users

What are true arrays?

• Fixed-size integer-indexed collections

When to use arrays?

• Fixed size collection
• Maintain order
• Not linked
• Memory efficient

SplFixedArray

class SplFixedArray implements Iterator , ArrayAccess , Countable {
	public __construct ([ int $size = 0 ] )
	public count() : int
	public current() : mixed
	public fromArray(array $array [, bool $save_indexes = true ] ) : static
	public getSize() : int
	public key() : int
	public next() : void
	public rewind() : void
	public setSize(int $size ) : int
	public toArray() : array
	public valid() : bool

}

Lists

Types of Lists

• Singly-linked lists

• Doubly-linked lists

SplDoublyLinkedList

class SplDoublyLinkedList implements Iterator , ArrayAccess , Countable {
    public __construct()
    public add(mixed $index , mixed $newval) : void
    public top() : mixed
    public bottom() : mixed
    public count() : int
    public current() : mixed
    public isEmpty() : bool
    public key() : mixed
    public next() : void
    public pop() : mixed
    public prev() : void
    public push(mixed $value) : void
    public rewind() : void
    public shift() : mixed
    public unshift(mixed $value) : void
    public valid() : bool
    public serialize() : string
    public unserialize(string $serialized) : void
}

Queues

Queue Representation

HEAD

TAIL

When to use a Queue?

• FIFO
• Sequential Processing
• Size doesn't matter
• Messaging
• Priority Queues?

<?php

interface Queue
{
    // Enqueue an item
    public enqueue($item);

    // Dequeue the first item
    public dequeue();















}

SplQueue

http://php.net/manual/en/class.splqueue.php

SplQueue extends SplDoublyLinkedList implements Iterator , ArrayAccess , Countable {
    public __construct()
    public dequeue() : mixed
    public enqueue(mixed $value) : void
    public SplDoublyLinkedList::isEmpty() : bool
    public SplDoublyLinkedList::count() : int
    public SplDoublyLinkedList::add(mixed $index , mixed $newval) : void
    public SplDoublyLinkedList::push(mixed $value) : void
    public SplDoublyLinkedList::pop() : mixed
    public SplDoublyLinkedList::shift() : mixed
    public SplDoublyLinkedList::unshift(mixed $value) : void
    public SplDoublyLinkedList::top() : mixed
    public SplDoublyLinkedList::bottom() : mixed
    public SplDoublyLinkedList::current() : mixed
    public SplDoublyLinkedList::key() : mixed
    public SplDoublyLinkedList::next() : void
    public SplDoublyLinkedList::prev() : void
    public SplDoublyLinkedList::rewind() : void
    public SplDoublyLinkedList::valid() : bool
}

Stack

Stack Representation

TOP

Stack Overflow ?

When to use a Stack?

• LIFO
• Keeping record of progress
• Syntax parsing (parenthesis)

<?php

interface Stack
{
    // Pop an item
    public pop();

    // Push an item to the stack
    public push($item);















}

SplStack

http://php.net/manual/en/class.splstack.php

SplQueue extends SplDoublyLinkedList implements Iterator , ArrayAccess , Countable {
    public __construct()
    public SplDoublyLinkedList::isEmpty() : bool
    public SplDoublyLinkedList::count() : int
    public SplDoublyLinkedList::add(mixed $index , mixed $newval) : void
    public SplDoublyLinkedList::push(mixed $value) : void
    public SplDoublyLinkedList::pop() : mixed
    public SplDoublyLinkedList::shift() : mixed
    public SplDoublyLinkedList::unshift(mixed $value) : void
    public SplDoublyLinkedList::top() : mixed
    public SplDoublyLinkedList::bottom() : mixed
    public SplDoublyLinkedList::current() : mixed
    public SplDoublyLinkedList::key() : mixed
    public SplDoublyLinkedList::next() : void
    public SplDoublyLinkedList::prev() : void
    public SplDoublyLinkedList::rewind() : void
    public SplDoublyLinkedList::valid() : bool
}

Trees

Larry D. Moore CC BY-SA 3.0 http://en.wikipedia.org/wiki/The_Big_Tree,_Rockport#mediaviewer/File:Big_tree.jpg

Tree Representation

Types of trees

• Binary trees
• Heaps
• AVL Trees
• ...
• http://en.wikipedia.org/wiki/List_of_data_structures#Trees

SplHeap

http://php.net/manual/en/class.splheap.php

http://php.net/manual/en/class.splmaxheap.php

http://php.net/manual/en/class.splminheap.php

abstract class SplHeap implements Iterator , Countable {
	public __construct()
	abstract protected int compare(mixed $value1 , mixed $value2)
	public count() :  int
	public current() :  mixed
	public extract() :  mixed
	public insert(mixed $value) :  void
	public isEmpty() :  bool
	public key() :  mixed
	public next() :  void
	public recoverFromCorruption() :  void
	public rewind() :  void
	public top() :  mixed
	public valid() :  bool
}

Traversal strategies

• Pre-order
• In-order
• Post-order
• Level-order