Summary
Highlights
Explains Big O notation as a method to measure the efficiency and speed of data structures, comparing it to different modes of transportation with varying speeds. Covers O(1) constant time, O(n) linear time, O(n^2) quadratic time, and O(log n) logarithmic time with examples.
Arrays are described as a row of lockers with fixed positions, storing data contiguously. Accessing elements by index is O(1), but inserting beyond the array's size or deleting elements (requiring shifting) is O(n). Replacing an existing element is O(1), while deleting the last element is also O(1).
Linked lists are like a train, with each car (node) connected to the next via pointers. Accessing an element by index is O(n) because you need to traverse the list. Inserting or deleting an element is O(1) if you have the reference, but O(n) if you need to search for it. Linked lists don't require shifting elements like arrays.
Stacks follow a Last-In-First-Out (LIFO) principle, like a stack of chips. Insertion (pushing) and deletion (popping) occur only at the top, making them O(1) operations. Accessing or searching through a stack is O(n).
Queues follow a First-In-First-Out (FIFO) principle, like a line at a store. Elements are added to the back and removed from the front. Insertion and Deletion are O(1) operations. Accessing or searching through a queue is O(n).
Heaps are like a pyramid of boxes, with the smallest (Min Heap) or largest (Max Heap) element at the top. Insertion and deletion are O(log n) because of the need to maintain the heap property by 'bubbling' elements up or down after adjustments. Accessing root element is O(1) while any other element is O(n).
Hashmaps are like a mailroom, using key-value pairs and a hash function to determine storage location. Accessing, inserting, and deleting are typically O(1), but can degrade to O(n) in worst-case scenarios due to hash collisions which linked list chaining resolves.
Binary search trees have an ordering rule: the left child is smaller than the parent, and the right child is larger. Accessing, inserting, and deleting are O(log n) because the search space is halved at each step. However, if the tree is unbalanced (resembling a linked list), these operations become O(n).
Sets, described like Thanos's Infinity Gauntlet, store only unique, unordered elements. Implemented using a hash table, checking for the existence of an element is typically O(1), but can be O(n) with many hash collisions. Inserting and deleting are also usually O(1), with a possible O(n) worst-case scenario.