Data Structures & Algorithms

How to measure an algorithm by how its work grows with the input, not by seconds on your laptop. Big-O notation, the common growth classes (constant, logarithmic, linear, n log n, quadratic, exponential) and how to read them off a loop.

The two workhorse structures of everyday programming: contiguous arrays (and strings) and hash maps/sets for constant-time lookup. Learn the counting, two-pointer and prefix-sum patterns that turn many O(n²) brute-force ideas into O(n).

Linked lists and the two classic access disciplines: stack (last in, first out) and queue (first in, first out). They power undo history, expression parsing, bracket matching, call stacks and breadth-first search.

Why sorted data is powerful. Comparison sorts (insertion, merge, quick), what O(n log n) really means, when to use the built-in sort, and binary search, including searching for the first position where a condition becomes true and searching on the answer itself.

Trees (binary trees, binary search trees) and graphs as models of hierarchies, maps and networks. Representations (adjacency list vs matrix), depth-first and breadth-first traversal, grids as graphs, connected components and shortest paths in unweighted graphs.

Solve a big problem by solving smaller copies of itself. Base cases and the call stack, why naive recursion can explode exponentially, then memoization and bottom-up tables (Fibonacci, coin change, longest common subsequence, knapsack).

A priority queue always hands you the smallest (or largest) item next, and a binary heap does it in O(log n). Learn heap order, push/pop, heapify, top-k problems and merging sorted streams.

Weighted graphs: Dijkstra's algorithm with a heap, why negative edges break it, and when Bellman-Ford is needed. Plus the Union-Find (disjoint set) structure for connectivity and minimum spanning trees with Kruskal.