Data structures and algorithms

The standard interview canon, with the dynamic-programming section pointed straight at expected-value recursions.

1
Complexity
Big-O, amortised analysis, recurrences and the master theorem.
- 1.1Complexity: reading it off, and deriving itFree12 min
2
Linear structures
Arrays, hash maps, linked lists, stacks, queues and monotonic structures.
- 2.1Linear structures: arrays, hash maps and monotonic stacks12 min
3
Trees and heaps
BSTs, balanced trees, heaps, tries, segment and Fenwick trees.
- 3.1Trees and heaps: BSTs, priority queues and range queries12 min
4
Graphs
BFS, DFS, topological sort, shortest paths, MST and union–find.
- 4.1Graphs: traversal, shortest paths and union–find12 min
5
Core techniques
Sorting, binary search on the answer, two pointers and sliding windows.
- 5.1Core techniques: binary search on the answer, two pointers, sliding windows12 min
6
Dynamic programming
Knapsack, LIS, interval and bitmask DP — and its link to expected-value recursions.
- 6.1Dynamic programming, and why it is the same as an EV recursion14 min
7
Bit manipulation and number theory
Bitwise tricks, modular arithmetic, fast exponentiation and sieves.
- 7.1Bit manipulation and modular arithmetic11 min

Complexity