Data Structures and Algorithms

Learn to break problems into smaller parts, recognize patterns, and design step-by-step solutions before writing any code.

Understand how to measure and compare the time and space efficiency of algorithms using asymptotic notation (O, Ω, Θ).

Master the art of solving problems by having functions call themselves, and learn to analyze recursive algorithms using recurrence relations.

Understand contiguous memory storage, random access, resizing strategies, and the trade-offs between static and dynamic arrays.

Learn singly and doubly linked lists, pointer manipulation, and when linked structures outperform contiguous ones.

Understand the LIFO principle, implement stacks using arrays and linked lists, and apply them to parsing, undo systems, and expression evaluation.

Learn FIFO queues, double-ended queues, and circular buffers, and see how they model real-world waiting and scheduling problems.

Implement and analyze bubble sort, selection sort, and insertion sort to build intuition for sorting mechanics and best/worst-case behavior.

Master divide-and-conquer sorting algorithms, understand their O(n log n) performance, and learn how pivot selection affects quicksort.

Explore counting sort, radix sort, and bucket sort — algorithms that beat the O(n log n) lower bound by exploiting data properties.

Learn to halve your search space efficiently, and apply binary search to sorted arrays, answer spaces, and monotonic functions.

Understand how hash functions map keys to indices, and learn to build hash tables with O(1) average-case lookups.

Compare chaining vs. open addressing (linear probing, quadratic probing, double hashing) and understand load factors and rehashing.

Learn tree terminology (root, leaf, height, depth), implement binary trees, and master in-order, pre-order, post-order, and level-order traversals.

Understand how BSTs maintain sorted order, implement insertion, deletion, and search, and analyze their performance characteristics.

Learn why unbalanced BSTs degrade to O(n) and how self-balancing trees guarantee O(log n) operations through rotations.

Build min-heaps and max-heaps using arrays, implement heap sort, and use priority queues for scheduling and greedy algorithms.

Implement trie data structures for efficient string storage and retrieval, supporting autocomplete and dictionary lookups.

Understand adjacency matrices, adjacency lists, and edge lists, and learn when each representation is most appropriate.

Master breadth-first and depth-first search, understand their properties, and apply them to connectivity, cycle detection, and topological sorting.

Implement Dijkstra's, Bellman-Ford, and Floyd-Warshall algorithms and understand when to use each based on graph properties.

Learn Kruskal's and Prim's algorithms for finding minimum-cost spanning trees, and understand the role of the Union-Find data structure.

Implement the Union-Find structure with path compression and union by rank for near-constant-time connectivity queries.

Learn the greedy choice property and optimal substructure, and apply greedy strategies to interval scheduling, Huffman coding, and coin change.

Understand how to split problems into independent subproblems, solve them recursively, and combine results — beyond just sorting.

Master memoization and tabulation to solve overlapping-subproblem problems like knapsack, longest common subsequence, and edit distance.

Learn to systematically explore solution spaces by building candidates incrementally and abandoning paths that cannot lead to valid solutions.

Explore KMP, Rabin-Karp, and other pattern matching algorithms that find substrings faster than brute force.

Understand how to analyze the average cost of operations over a sequence, even when individual operations vary widely in cost.

Learn what makes problems computationally hard, understand P vs NP, and recognize NP-complete problems to avoid futile optimization attempts.