10 — Math & Random

Python's math module trades general-purpose float arithmetic for a handful of exact, integer-safe helpers, while random trades true unpredictability for a deterministic, seedable stream that only looks random. This chapter is what each module actually guarantees, where those guarantees quietly break, and the worked examples — a perfect-square check, reservoir sampling, Fisher–Yates — that lean on them.

Data Structures & Algorithms

A book-shaped table of contents for MAANG-interview DSA prep: Python language foundations, mathematical and algorithmic foundations, arrays/strings, linked structures, stacks/queues, trees, graphs, sorting/searching, dynamic programming, greedy algorithms, backtracking, bit manipulation, advanced data structures, advanced algorithms, interview problem patterns, and MAANG interview mastery — a book-length progression from fundamentals to Google/Meta/Amazon/Apple/Netflix/Microsoft (L4–L6) interview readiness.

7 — Matrix Exponentiation

Representing a linear recurrence as matrix multiplication to compute the n-th term in O(log n).

8 — Fast Exponentiation

Binary exponentiation for computing a^n (or a^n mod m) in O(log n) instead of O(n).

1 — Divide & Conquer Optimization

Speeding up a DP transition using divide-and-conquer or monotonic-decision-boundary tricks (e.g. the DC optimization, Knuth's optimization).

2 — Convex Hull

Finding the smallest convex polygon enclosing a set of points, via Graham scan or the gift-wrapping algorithm.