Welcome to Algorithms 101, your gateway to understanding the fundamental concepts and techniques that form the backbone of computer science. This course is designed to introduce you to basic algorithms, data structures, and algorithmic complexity, equipping you with the essential tools to solve a wide range of computational problems.
Course Overview
Basic Algorithms
- Stack: Learn about this simple yet powerful data structure used for storing and retrieving data in a last-in, first-out (LIFO) manner.
- Queue: Understand how queues operate on a first-in, first-out (FIFO) basis and their applications in various scenarios.
- Recursion: Grasp the concept of functions calling themselves to solve problems by breaking them down into smaller sub-problems.
Types of Algorithms
- Sorting Algorithms
- Bubble Sort: A simple comparison-based sorting algorithm.
- Selection Sort: Learn how this algorithm selects the minimum element and moves it to the beginning.
- Insertion Sort: Understand how elements are inserted into their correct position in a sorted list.
- [Merge Sort](): A divide-and-conquer algorithm that splits the list into halves, sorts them, and merges them back together.
- [Quick Sort](): Explore this efficient sorting algorithm that uses partitioning to sort elements.
- Search Algorithms
- Linear Search: Learn the simplest method of searching for an element in a list.
- Binary Search: Understand this efficient algorithm that works on sorted lists by repeatedly dividing the search interval in half.
Algorithm Complexity
- Big O Notation: Master the standard notation for describing the performance of algorithms.
- Time Complexity: Learn to evaluate how the run time of an algorithm scales with the size of the input.
- Space Complexity: Understand how to measure the memory usage of an algorithm.
Data Structures
- Arrays: Discover the basic structure for storing elements in a contiguous block of memory.
- Linked Lists
- Singly Linked List: Learn about this dynamic data structure where each element points to the next.
- Doubly Linked List: Understand how each element can point to both the next and previous elements.
- Singly and Doubly Linked Lists and Their Reversal – Stack Interpretation
- Merge Two Sorted Linked Lists
- Adding Two Numbers Represented by Linked Lists
- Preserving Relative Position in Linked List
- Stacks: Dive deeper into this LIFO data structure and its various applications.
- Queues: Explore more about FIFO queues and their uses.
- Trees
- Binary Trees: Learn about tree structures where each node has at most two children.
- Binary Search Trees: Understand how these trees maintain sorted order among elements.
- AVL Trees: Discover self-balancing binary search trees that maintain logarithmic height.
- Red-Black Trees: Learn about another type of self-balancing binary search tree.
- Heaps: Understand heap structures that are used primarily for implementing priority queues.
- Max Heap
- Graphs: Discover how to represent and work with complex networks of nodes and edges.
- Hash Tables: Learn about this efficient data structure for key-value pair storage and retrieval.
Tree Algorithms
- Breadth-First Search (BFS): Explore this algorithm for traversing or searching tree or graph data structures level by level.
- Depth-First Search (DFS): Understand this algorithm for exploring as far down a branch as possible before backtracking.
- PreOrder: Learn the traversal method where the root node is visited before its children.
- InOrder: Understand the traversal method where the nodes are visited in ascending order.
- PostOrder: Discover the traversal method where the root node is visited after its children.
- Mastering Tree Algorithms
Graph Algorithms
- Breadth-First Search (BFS): Revisit this essential graph traversal technique.
- Depth-First Search (DFS): Revisit this depth-based exploration technique.
- Dijkstra’s Algorithm: Learn this algorithm for finding the shortest path between nodes in a graph.
- *A Search Algorithm**: Understand this popular algorithm used in pathfinding and graph traversal.
Dynamic Programming
- Introduction to Dynamic Programming: Discover how to solve complex problems by breaking them down into simpler subproblems and storing the results of subproblems to avoid redundant computations.
- Common Problems: Learn to solve classic dynamic programming problems such as the Knapsack problem and the Fibonacci sequence.
Greedy Algorithms
- Introduction to Greedy Algorithms: Understand this algorithmic paradigm that makes the locally optimal choice at each stage with the hope of finding a global optimum.
- Common Problems: Explore typical problems solved by greedy algorithms, such as the Coin Change problem and Huffman coding.
- Used for processing a series of data elements by examining a "window" of the data.
- Ideal for problems involving finding subsets of elements, like the longest substring with K unique characters.
Subset Pattern:
- Focuses on generating all possible combinations of elements from a set.
- Useful for problems requiring permutations or combinations, similar to breadth-first search (BFS).
Modified Binary Search:
- Adjusts the classic binary search algorithm for specific conditions, such as searching in a rotated sorted array.
- Understanding core binary search principles is essential for this pattern.
Top K Elements:
- Used to find the top K elements from a dataset.
- Employs a heap data structure to efficiently manage and retrieve the K largest elements.
Topological Sort:
- Arranges elements based on dependencies, especially in Directed Acyclic Graphs (DAGs).
- Useful for scheduling tasks or course prerequisites, ensuring all dependencies are resolved before processing.
- Utilizes two pointers to iterate through a sorted array to solve problems efficiently.
- Example problems include finding pairs or triplets that sum up to a specific target.
- Prefix: A prefix of a sequence is a subsequence that starts from the beginning of the sequence and includes any number of leading elements up to the entire sequence.
- Suffix: A suffix of a sequence is a subsequence that starts from any position in the sequence and continues to the end of the sequence.
This course will guide you step-by-step through each topic, providing detailed explanations, examples, and exercises to solidify your understanding. By the end of Algorithms 101, you will have a solid foundation in algorithms and data structures, empowering you to tackle more advanced topics and real-world computational problems.