So far, we discussed different properties and practical usage of recursion. We have seen how to do the analysis of recursive algorithms. Computer programming and recursion are two inseparable parts. The usage of recursion is almost everywhere in the programming world. In the upcoming chapters, we will explore it more and apply wherever it's applicable. In the next chapter, we will discuss another special data structure called "tree".
- Preface
- Introduction to Data Structures and Algorithms
- Understanding PHP Arrays
- Understanding PHP arrays in a better way
- Using an array as flexible storage
- Use of multi-dimensional arrays to represent data structures
- Performance comparison between a regular PHP array and SplFixedArray
- Understanding hash tables
- Implementing struct using a PHP array
- Implementing sets using a PHP array
- Best usage of a PHP array
- PHP array, is it a performance killer?
- Summary
- Using Linked Lists
- What is a linked list?
- Different types of linked list
- Inserting, deleting, and searching for an item
- Understanding complexity for linked lists
- Making the linked list iterable
- Building circular linked list
- Implementing a doubly linked list in PHP
- Doubly linked list operations
- Complexity for doubly linked lists
- Using PHP SplDoublyLinkedList
- Summary
- Constructing Stacks and Queues
- Understanding stack
- Implementing a stack using PHP array
- Understanding complexity of stack operations
- Implementing stack using linked list
- Using SplStack class from SPL
- Real life usage of stack
- Understanding queue
- Using SplQueue class from SPL
- Understanding priority queue
- Implementing priority queue using linked list
- Implement a priority queue using SplPriorityQueue
- Implementing a circular queue
- Creating a double - ended queue (deque)
- Summary
- Applying Recursive Algorithms - Recursion
- Understanding recursion
- Different types of recursions
- Building an N-level category tree using recursion
- Finding files and directories using recursion
- Analyzing recursive algorithms
- Maximum recursion depth in PHP
- Using SPL recursive iterators
- Using the PHP built-in function array_walk_recursive
- Summary
- Understanding and Implementing Trees
- Tree definition and properties
- Implementing a tree using PHP
- Different types of tree structures
- Understanding a binary tree
- Implementing a binary tree
- Creating a binary tree using a PHP array
- Understanding the binary search tree
- Constructing a binary search tree
- Tree traversal
- Complexity of different tree data structures
- Summary
- Using Sorting Algorithms
- Exploring Search Options
- Putting Graphs into Action
- Understanding graph properties
- Types of graphs
- Revisiting BFS and DFS for graphs
- Topological sorting using Kahn's algorithm
- Shortest path using the Floyd-Warshall algorithm
- Single source shortest path using Dijkstra's algorithm
- Finding the shortest path using the Bellman-Ford algorithm
- Understanding the minimum spanning tree (MST)
- Implementing Prim's spanning tree algorithm
- Kruskal's algorithm for spanning tree
- Summary
- Understanding and Using Heaps
- Solving Problems with Advanced Techniques
- Memoization
- Pattern matching algorithms
- Implementing Knuth-Morris-Pratt algorithm
- Greedy algorithms
- Implementing Huffman coding algorithm
- Understanding dynamic programming
- 0 - 1 knapsack
- Finding the longest common subsequence-LCS
- DNA sequencing using dynamic programming
- Backtracking to solve puzzle problem
- Collaborative filtering recommendation system
- Using bloom filters and sparse matrix
- Summary
- PHP Built-In Support for Data Structures and Algorithms
- Functional Data Structures with PHP
Summary
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