Data Structures And Algorithms In PHP

Explain what an algorithm is, show how to implement a step-by-step linear search in an array, detailing input, iteration, and index return, and that not found returns -1.

Identify a finite, non-ambiguous algorithm. Exits after a bounded number of steps; accepts zero or more inputs and yields at least one output; each step solves the problem.

Analyze why we analyze an algorithm by assessing time and space resources, compare solutions for optimality, and use big O and big Omega notations.

Explain O(1) constant time and how a single instruction or constant-time array access yields the best time complexity, with examples of indexing and simple variable operations.

Analyze how a for loop runs n times, yielding O(n) linear time as input size grows. See how linear search exemplifies this complexity in data structures and algorithms in PHP.

explain how O(log n) is logarithmic time and how for n = 1000 the iterations are about 10, noting base two is used for intuition but does not affect notation.

See how two loops produce O(n^2) quadratic time as input size grows, illustrated by counting iterations in a double-loop algorithm.

Examine cubic time complexity, showing how a triple-nested process yields O(n^3) operations, with examples of n=50 and references to interview expectations.

Analyze best case, worst case, and average case of algorithms, with the linear search example illustrating array access, complexity, and Big O notation in PHP.

Explore rate of growth in time complexity from constant to cubic, comparing constant, logarithmic, linear, quadratic, and cubic growth, and visualizing how run time scales with n.

Explore recursion in data structures and algorithms in PHP by showing how a function calls itself with smaller input, reaches a base case, and uses stack memory to manage calls.

Illustrate recursion with factorial: implement a recursive function factorial(n) with base case factorial(0)=1 and observe how nested calls stack and resolve to the final result.

PHP arrays are ordered maps, not standard arrays, storing key value pairs with numeric or string keys and dynamic, capable of simulating trees, graphs, and hash maps.

Explore SplFixedArray in PHP, a fixed-size array with numeric indices that uses less memory and enables faster operations than regular arrays, supports mixed values, and offers iteration with upfront size.

Explore the two-pointer approach to sum array elements by using i and j from the ends, accumulating values and breaking when they meet to reduce iterations.

Present the sum of maximum subarray problem, define contiguous subarrays, and compare a brute force O(n^2) solution with a more efficient approach called the contains algorithm.

Initialize with the first element and apply Kadane's algorithm to update the current max as you scan the array, promoting it to the total max when it grows.

This lecture introduces linked lists, showing how memory is allocated non-sequentially and how pointers link each node to the next, contrasting with fixed-size arrays that require copying.

Compare linked lists to arrays in PHP, showing how front or back insertions avoid shifting elements for constant-time updates, while noting drawbacks and middle-insertion advantages.

Implement a linked list in PHP by defining a node class with data and next, and a list class with head and count, initializing with null and providing insertion operation.

Insert a new node at the end of a linked list in php, creating the node, setting head if empty, or traversing to the last node to link it.

Learn how to insert a new node at the front of a linked list in PHP, handling empty and non-empty lists, updating the head, and achieving constant time insertion.

Insert a node at a given position in a list by updating next pointers, including inserting at the head and traversing to the target position, then display the list.

Learn how to delete the head node from a singly linked list in PHP, including updating the head pointer, handling single-node lists, and validating the deletion.

Delete the last node in a linked list by traversing to the end, updating the previous node's next pointer to null, calling display, handling single-node cases, and decrementing the account.

Traverse the linked list to locate the target node, then adjust the previous node's next pointer to the current node's next to remove it, including the head case.

explore how a doubly linked list uses nodes with data, a previous pointer, and a next pointer, with head and tail references and null termination.

Learn the base condition for inserting a node into a doubly linked list when the list is empty, setting the head and tail to the new node.

Demonstrates inserting a new node at the front of a doubly linked list in PHP, linking to the old head and updating the previous pointer, with empty-list handling.

Explore inserting a new node at a given position in a doubly linked list using next and previous pointers in PHP. See how to update head, tail, and surrounding nodes.

Learn to insert a node at the end of a list by creating the new node, linking it to the previous tail, and setting its pointers as the last element.

Learn to delete the head node of a linked list by setting the head to its next node, nulling the new head's previous pointer, and updating the count.

Delete the tail node in a linked list and update the tail pointer. Handle single-node and multi-node scenarios, maintain payload and previous references, and ensure constant time operations.

Delete a node in a linked list by traversing to the target, updating adjacent nodes' pointers, handling head deletion, and decrementing the list count.

Learn circular linked lists in PHP, where the last node points to the head to form a circle, avoid null pointers, and implement with node and circular list classes.

Insert at front of a circular linked list in PHP, handling empty and nonempty cases by updating next pointers so the new node becomes head and tail points to head.

Insert at last in a circular list by creating a node; set its next to head and update tail. If empty, point the node to itself; display starts at tail.next.

Learn how to insert an element at a specific position in a circular list by traversing to the target position, updating next pointers, and validating with tests.

Learn to delete the first node in a circular linked list by relinking tail.next to the head’s next, freeing the removed node, and updating the display after each deletion.

Delete the last node of a circular list in PHP by iterating from the tail, tracking the previous node, and updating the previous node’s next pointer to the head.

Display the linked list elements recursively by applying a base case, printing the current node's data, and recursing to the next node.

Learn to reverse a singly linked list iteratively in PHP by using current, previous, and next pointers, updating the head to the previous node to obtain a reversed list.

Learn to remove duplicates from an unsorted linked list using a two-loop approach, adjust node pointers, and understand why this takes N squared time.

Learn how to remove duplicates in a sorted linked list with a single scan by comparing each node's data to the next and bypassing duplicates.

Detect a cycle in a linked list by marking nodes as visited during traversal and checking for revisits; alternatively, apply a two-pointer approach to detect cycles.

explore detecting a cycle in a linked list using the two-pointer approach, where slow and fast pointers meet to confirm a cycle and handle edge cases.

Explore the stack data structure, its push and pop operations, and how last-in, first-out behavior governs insertion and removal at the top, with recursion and language runtimes as context.

Implement a stack using an array, with a constructor setting a 20-element limit, push adds to the end when room exists, otherwise throws an overflow, and pop removes last element.

Implement a stack using a linked list, push with insert last, delete last, and top with get last; check empty by count and throw a stack empty exception when needed.