Since graphs are represented with vertices and edges, we have to consider both in representing the graph. There are several ways to represent a graph, but the most popular ones are as follows:
- Adjacency list
- Adjacency matrix
- 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
Representing graphs in PHP
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