Introduction to Data Structures and Algorithms

1. Importance of data structures and algorithms
2. Understanding Abstract Data Type (ADT)
3. Different data structures
0. Struct
1. Array
2. Linked list
3. Doubly linked list
4. Stack
5. Queue
6. Set
7. Map
8. Tree
9. Graph
10. Heap
4. Solving a problem - algorithmic approach
5. Writing pseudocode
0. Converting pseudocode to actual code
6. Algorithm analysis
0. Calculating the complexity
7. Understanding the big O (big oh) notation
8. Standard PHP Library (SPL) and data structures
9. Summary

Understanding PHP Arrays

1. Understanding PHP arrays in a better way
0. Numeric array
1. Associative array
2. Multidimensional array
2. Using an array as flexible storage
3. Use of multi-dimensional arrays to represent data structures
0. Creating fixed size arrays with the SplFixedArray method
4. Performance comparison between a regular PHP array and SplFixedArray
0. More examples using SplFixedArray
0. Changing from a PHP array to SplFixedArray
1. Converting a SplFixedArray to a PHP array
2. Changing the SplFixedArray size after declaration
3. Creating a multidimensional array using SplFixedArray
5. Understanding hash tables
6. Implementing struct using a PHP array
7. Implementing sets using a PHP array
8. Best usage of a PHP array
9. PHP array, is it a performance killer?
10. Summary

Using Linked Lists

1. What is a linked list?
2. Different types of linked list
0. Doubly linked lists
1. Circular linked lists
2. Multi-linked lists
3. Inserting, deleting, and searching for an item
0. Inserting at the first node
1. Searching for a node
2. Inserting before a specific node
3. Inserting after a specific node
4. Deleting the first node
5. Deleting the last node
6. Searching for and deleting a node
7. Reversing a list
8. Getting the Nth position element
4. Understanding complexity for linked lists
5. Making the linked list iterable
6. Building circular linked list
7. Implementing a doubly linked list in PHP
8. Doubly linked list operations
0. Inserting at first the node
1. Inserting at the last node
2. Inserting before a specific node
3. Inserting after a specific node
4. Deleting the first node
5. Deleting the last node
6. Searching for and deleting one node
7. Displaying the list forward
8. Displaying the list backward
9. Complexity for doubly linked lists
10. Using PHP SplDoublyLinkedList
11. Summary

Constructing Stacks and Queues

1. Understanding stack
2. Implementing a stack using PHP array
3. Understanding complexity of stack operations
4. Implementing stack using linked list
5. Using SplStack class from SPL
6. Real life usage of stack
0. Nested parentheses matching
7. Understanding queue
0. Implementing a queue using PHP array
1. Implementing a queue using linked list
8. Using SplQueue class from SPL
9. Understanding priority queue
0. Ordered sequence
1. Unordered sequence
10. Implementing priority queue using linked list
11. Implement a priority queue using SplPriorityQueue
12. Implementing a circular queue
13. Creating a double - ended queue (deque)
14. Summary

Applying Recursive Algorithms - Recursion

1. Understanding recursion
0. Properties of recursive algorithms
1. Recursion versus iterative algorithms
2. Implementing Fibonacci numbers using recursion
3. Implementing GCD calculation using recursion
2. Different types of recursions
0. Linear recursion
1. Binary recursion
2. Tail recursion
3. Mutual recursion
4. Nested recursion
3. Building an N-level category tree using recursion
0. Building a nested comment reply system
4. Finding files and directories using recursion
5. Analyzing recursive algorithms
6. Maximum recursion depth in PHP
7. Using SPL recursive iterators
8. Using the PHP built-in function array_walk_recursive
9. Summary

Understanding and Implementing Trees

1. Tree definition and properties
2. Implementing a tree using PHP
3. Different types of tree structures
0. Binary tree
1. Binary search tree
2. Self-balanced binary search tree
0. AVL tree
1. Red-black tree
3. B-tree
4. N-ary Tree
4. Understanding a binary tree
5. Implementing a binary tree
6. Creating a binary tree using a PHP array
7. Understanding the binary search tree
0. Inserting a new node
1. Searching a node
2. Finding the minimum value
3. Finding the maximum value
4. Deleting a node
8. Constructing a binary search tree
9. Tree traversal
0. In-order
1. Pre-order
2. Post-order
10. Complexity of different tree data structures
11. Summary

Using Sorting Algorithms

1. Understanding sorting and their types
2. Understanding bubble sort
0. Implementing bubble sort using PHP
1. Complexity of bubble sort
2. Improving bubble sort algorithm
3. Understanding selection sort
0. Implementing selection sort
1. Complexity of selection sort
4. Understanding insertion Sort
0. Implementing insertion sort
1. Complexity of insertion sort
5. Understanding divide-and-conquer technique for sorting
6. Understanding merge sort
0. Implementing merge sort
1. Complexity of merge sort
7. Understanding quick sort
0. Implementing quick sort
1. Complexity of quick sort
8. Understanding bucket sort
9. Using PHP's built-in sorting function
10. Summary

Exploring Search Options

1. Linear searching
2. Binary search
0. Analysis of binary search algorithm
1. Repetitive binary search tree algorithm
2. Searching an unsorted array - should we sort first?
3. Interpolation search
4. Exponential search
5. Search using hash table
6. Tree searching
0. Breadth first search
0. Implementing breadth first search
1. Depth first search
0. Implementing depth first search
7. Summary

Putting Graphs into Action

1. Understanding graph properties
0. Vertex
1. Edge
2. Adjacent
3. Incident
4. Indegree and outdegree
5. Path
2. Types of graphs
0. Directed graphs
1. Undirected graphs
2. Weighted graphs
3. Directed acyclic graphs (DAG)
4. Representing graphs in PHP
0. Adjacency lists
1. Adjacency matrix
3. Revisiting BFS and DFS for graphs
0. Breadth first search
1. Depth first search
4. Topological sorting using Kahn's algorithm
5. Shortest path using the Floyd-Warshall algorithm
6. Single source shortest path using Dijkstra's algorithm
7. Finding the shortest path using the Bellman-Ford algorithm
8. Understanding the minimum spanning tree (MST)
9. Implementing Prim's spanning tree algorithm
10. Kruskal's algorithm for spanning tree
11. Summary

Understanding and Using Heaps

1. What is a heap?
2. Heap operations
3. Implementing a binary heap in PHP
4. Analyzing the complexity of heap operations
5. Using heaps as a priority queue
6. Using heap sort
7. Using SplHeap, SplMaxHeap, and SplMinHeap
8. Summary

Solving Problems with Advanced Techniques

1. Memoization
2. Pattern matching algorithms
3. Implementing Knuth-Morris-Pratt algorithm
4. Greedy algorithms
5. Implementing Huffman coding algorithm
6. Understanding dynamic programming
7. 0 - 1 knapsack
8. Finding the longest common subsequence-LCS
9. DNA sequencing using dynamic programming
10. Backtracking to solve puzzle problem
11. Collaborative filtering recommendation system
12. Using bloom filters and sparse matrix
13. Summary

PHP Built-In Support for Data Structures and Algorithms

1. Built-in PHP features for data structure
0. Using PHP array
2. SPL classes
3. Built-in PHP algorithms
4. Hashing
5. Built-in support through PECL
0. Installation
0. Interfaces
6. Vector
7. Summary

Functional Data Structures with PHP

1. Understanding functional programming with PHP
0. First class functions
1. Higher order functions
2. Pure functions
3. Lambda functions
4. Closures
5. Currying
6. Partial applications