Data Structures & Algorithms Study Guide

Algorithm Analysis and Big-O Notation

Master time/space complexity analysis using Big-O, Big-Omega, Big-Theta to evaluate algorithm efficiency—foundational for all topics.

Arrays and Dynamic Arrays

Understand contiguous memory, indexing, resizing strategies, and amortized analysis—the building block for complex data structures.

Linked Lists

Implement singly, doubly, and circular linked lists; compare trade-offs with arrays for insertion, deletion, and traversal.

Stacks and Queues

Master LIFO/FIFO abstractions, implementations, and applications including expression evaluation, BFS, and scheduling problems.

Recursion and Backtracking

Develop recursive thinking, analyze call stacks, and solve constraint problems like N-queens and maze traversal.

Trees and Binary Search Trees

Navigate tree terminology, traversals, and BST operations; understand search, insertion, deletion, and successor algorithms.

Balanced Trees and Self-Balancing BSTs

Learn AVL rotations, balance factors, and Red-Black tree concepts to guarantee O(log n) operations.

Heaps and Priority Queues

Implement min/max heaps using arrays; master heapify, extract operations, and heap sort for priority-based problems.

Hash Tables and Hashing

Design hash functions, resolve collisions via chaining and open addressing, and analyze amortized O(1) operations.

Graphs: Representation and Traversal

Model problems using adjacency lists/matrices; implement BFS and DFS for connectivity, cycles, and topological sorting.

Graph Algorithms: Shortest Paths and MST

Apply Dijkstra's, Bellman-Ford, Prim's, and Kruskal's algorithms to solve weighted graph optimization problems.

Sorting Algorithms and Algorithm Design Strategies

Compare sorting algorithms' complexities; apply divide-and-conquer, greedy, and dynamic programming design paradigms systematically.