what are data structures and why do they matter? the relationship between data structures and algorithms, and how this course is structured.
DSA Fundamentals
32 lessons/ labs included
data structures and algorithms taught the right way - from first principles, with memory-first thinking. understand why things work, not just what to memorize. arrays, linked lists, trees, graphs, sorting, searching - all with real-world motivation and hands-on implementation.
what you'll learn
- Memory-first thinking — understand how data structures actually live in RAM
- Arrays, slices, and dynamic arrays — contiguous memory and cache performance
- Linked lists, stacks, and queues — when indirection makes sense
- Trees and binary search trees — traversals, balancing, and real-world use
- Graphs — representation, BFS, DFS, and shortest paths
- Sorting and searching — from bubble sort to quicksort, with complexity analysis
Foundations
memory as a giant array of bytes, addresses, cache hierarchy, and why understanding memory is the key to writing fast code.
Arrays
contiguous memory allocation, index-based access, and why O(1) access is possible. the foundation of all other data structures.
growing arrays on demand, amortized analysis, and why doubling beats incrementing. the implementation behind slices, vectors, and lists.
Linear Structures
LIFO principle, the call stack, and why recursion works. from function calls to expression parsing.
non-contiguous storage, pointer surgery, and the cache locality tradeoff. plus: what Rust teaches us about ownership in linked lists.
bidirectional traversal, LRU caches, and why doubly linked lists break Rust's ownership model.
FIFO principle, circular buffers, and the structure behind every job processing system.
Recursion
understanding recursion through the simplest example. base cases, recursive cases, and tracing the call stack.
when naive recursion explodes. branching recursion, memoization, and the gateway to dynamic programming.
Sorting
the card sorting algorithm. simple, in-place, and surprisingly useful for small or nearly-sorted data.
divide and conquer. guaranteed O(n log n), stable sorting, and the algorithm of choice when consistency matters.
partition around a pivot. cache-efficient, in-place, and why it's the default sort in most libraries despite O(n^2) worst case.
breaking the comparison lower bound. when you know your data's distribution, you can sort in linear time.
Binary Search
the power of sorted data. divide and conquer search, O(log n) explained, and common implementation pitfalls.
beyond exact matches. lower bound, upper bound, and the generalized binary search for finding boundaries.
Trees
hierarchical data structures. tree terminology, memory representation, and what Rust teaches us about tree ownership.
ordering in trees. the BST property, why it enables fast search, and how tree shape affects performance.
dynamic BST operations. inserting while maintaining order, and the three cases of deletion.
preorder, inorder, postorder. three ways to traverse a tree and when to use each.
level-order traversal. using a queue to explore trees layer by layer and find shortest paths.
from trees to collections. implementing ordered sets and maps with BSTs, plus range queries.
Heaps
complete binary trees with ordering. the heap property, array representation, and why heaps are perfect for priority queues.
heap operations. bubble up, bubble down, and maintaining the heap invariant in O(log n).
building heaps efficiently. why bottom-up heapify is O(n), not O(n log n), and its use in heap sort.
Hashing
the O(1) dream. hash tables and sets, when to use them, and solving problems with constant-time lookup.
under the hood. hash functions, collision handling with chaining and open addressing, and load factors.
Graphs
vertices and edges. directed vs undirected, representations, and what Rust's ownership model teaches about graph structure.
graphs in disguise. DFS on 2D grids for flood fill, island counting, and connected components.
shortest paths on grids. level-by-level exploration, multi-source BFS, and distance transforms.
the standard graph representation. building graphs efficiently, iterating neighbors, and DFS/BFS on general graphs.
Bit Manipulation
the lowest level. AND, OR, XOR, shifts, and the bit tricks that power permissions, sets, and low-level code.