We can categorize data structures in to two different groups:

• Linear data structures
• Nonlinear data structures

In linear data structures, items are structured in a linear or sequential manner. Array, list, stack, and queue are examples of linear structures. In nonlinear structures, data are not structured in a sequential way. Graph and tree are the most common examples of nonlinear data structures.

Let us now explore the world of data structures, with different types of data structures and their purposes in a summarized way. Later on, we will explore each of the data structures in details.

There are many different types of data structures that exist in the programming world. Out of them, following are the most used ones:

• Struct
• Array
• Linked list
• Doubly linked list
• Stack
• Queue
• Priority queue
• Set
• Map
• Tree
• Graph
• Heap

Usually, a variable can store a single data type and a single scalar data type can only store a single value. There are many situations where we might need to group some data types together as a single complex data type. For example, we want to store some student information together in a student data type. We need the student name, address, phone number, email, date of birth, current class, and so on. In order to store each student record to a unique student data type, we will need a special structure which will allow us to do that. This can be easily achieved by struct. In other words, a struct is a container of values which is typically accessed using names. Though structs are very popular in C programming language, we can use a similar concept in PHP as well. We are going to explore that in coming chapters.

Though an array is considered to be a data type in PHP, an array is actually a data structure which is mostly used in all programming platforms. In PHP, the array is actually an ordered map (we are going to know about maps after a few more sections). We can store multiple values in a single array as a single variable. Matrix type data are easy to store in an array and hence it is used widely in all programming platforms. Usually arrays are a fixed size collection which is accessed by sequential numeric indexes. In PHP, arrays are implemented differently and you can define dynamic arrays without defining any fixed size of the array. We will explore more about PHP arrays in the next chapter. Arrays can have different dimensions. If an array has only one index to access an element, we call it a single dimension array. But if it requires two or more indexes to access an element, we call it two dimensional or multidimensional arrays respectively. Here are two diagrams of array data structures:

A linked list is a linear data structure which is a collection of data elements also known as nodes and can have varying sizes. Usually, listed items are connected through a pointer which is known as a link and hence it is known as a linked list. In a linked list, one list element links to the next element through a pointer. From the following diagram, we can see that the linked list actually maintains an ordered collection. Linked lists are the most common and simplest form of data structures used by programming languages. In a single linked list, we can only go forward. In Chapter 3, Using Linked Lists we are going to dive deep inside the linked list concepts and implementations:

A doubly linked list is a special type of linked list where we not only store what is the next node, but we also store the previous node inside the node structure. As a result, it can move forward and backward within the list. It gives more flexibility than a single linked list or linked list by having both the previous and next pointers. We are going to explore more about these in Chapter 3, Using Linked Lists. The following diagram depicts a doubly linked list:

As we talked about the stack in previous pages, we already know that stack is a linear data structure with the LIFO principle. As a result, stacks have only one end to add a new item or remove an item. It is one of the oldest and most used data structures in computer technology. We always add or remove an item from a stack using the single point named top. The term push is used to indicate an item to be added on top of the stack and pop to remove an item from the top; this is shown in the following diagram. We will discuss more about stacks in Chapter 4, Constructing Stacks and Queues.

A queue is another linear data structure which follows the FIFO principle. A queue allows two basic operations on the collection. The first one is enqueue which allows us to add an item to the back of the queue. The second one is dequeue which allows us to remove an item from the front of the queue. A queue is another of the most used data structures in computer technology. We will learn details about queues in Chapter 4, Consrtucting Stacks and Queues.

A set is an abstract data type which is used to store certain values. These values are not stored in any particular order but there should not be any repeated values in the set. Set is not used like a collection where we retrieve a specific value from it; a set is used to check the existence of a value inside it. Sometimes a set data structure can be sorted and we call it an ordered set.

A map is a collection of key and value pairs where all the keys are unique. We can consider a map as an associative array where all keys are unique. We can add and remove using key and value pairs along with update and look up from a map using a key. In fact, PHP arrays are ordered map implementations. We are going to explore that in the next chapter.

A tree is the most widely used nonlinear data structure in the computing world. It is highly used for hierarchical data structures. A tree consists of nodes and there is a special node which is known as the root of the tree which starts the tree structure. Other nodes descend from the root node. Tree data structure is recursive which means a tree can contain many subtrees. Nodes are connected with each other through edges. We are going to discuss different types of trees, their operations, and purposes in Chapter 6, Understanding and Implementing Trees.

A graph data structure is a special type of nonlinear data structure which consists of a finite number of vertices or nodes, and edges or arcs. A graph can be both directed and undirected. A directed graph clearly indicates the direction of the edges, while an undirected graph mentions the edges, not the direction. As a result, in an undirected graph, both directions of edge are considered as a single edge. In other words, we can say a graph is a pair of sets (V, E), where V is the set of vertices and E is the set of edges:

V = {A, B, C, D, E, F}

E = {AB, BC, CE, ED, EF, DB}

In a directed graph, an edge AB is different from an edge BA while in an undirected graph, both AB and BA are the same. Graphs are handy to solve lots of complex problems in the programming world. We are going to continue our discussion of graph data structures in Chapter 9, Putting Graphs into Action. In the following diagram, we have:

A heap is a special tree-based data structure which satisfies the heap properties. The largest key is the root and smaller keys are leaves, which is known as max heap. Or, the smallest key is the root and larger keys are leaves, which is known as min heap. Though the root of a heap structure is either the largest or smallest key of the tree, it is not necessarily a sorted structure. A heap is used for solving graph algorithms with efficiency and also in sorting. We are going to explore heap data structures in Chapter 10, Understanding and Using Heaps.