Chapter 0: Fundamentals

This is where everything begins. Before you can think about algorithms, you need fluency in C++, comfort with complexity analysis, and muscle memory for the STL. This chapter gives you the vocabulary and tools that show up in every single contest solution — from reading input fast enough to avoid TLE, to encoding subsets as bitmasks for brute-force searches. If you skip this chapter, you'll constantly trip over language mechanics instead of focusing on the actual problem.

Going to: Chapter 1 — Essential Techniques — core problem-solving techniques like binary search, greedy, and prefix sums
Bridge: BRIDGE-to-techniques.md — why fundamentals matter before learning techniques

Topics at a Glance

#	Topic	Difficulty	Key Trigger Phrase
01	C++ Language Essentials	Beginner	"How do I write idiomatic C++ for contests?"
02	Fast I/O and Pragmas	Beginner	TLE on correct solution → slow I/O
03	Complexity Analysis	Beginner	"Will O(n²) pass for n = 10⁵?"
04	Arrays and Strings	Beginner	Any problem with sequences or text
05	STL Containers	Beginner	"Which container gives me O(log n) lookups?"
06	STL Algorithms	Beginner	"Is there a built-in for this?"
07	Bit Manipulation	Intermediate	n ≤ 20 + "subsets" or "choose elements"
08	Bitset Optimization	Intermediate	"Need O(n/64) speedup on boolean vectors"
09	Math Toolkit	Beginner	GCD, power, factorials in contest code
10	Modular Arithmetic Basics	Beginner	"Print answer mod 10⁹+7"
11	Recursion and Backtracking	Beginner	"Generate all" + small n (≤ 20)
12	Graph and Tree Intro	Beginner	First encounter with nodes and edges
13	Debugging and Stress Testing	Beginner	WA on test 3 and you can't see why
14	Bitset Tricks	Intermediate	"O(n²) TLE, bitset gives 64x speedup"

If You Only Read 3 Files

1. Complexity Analysis — because reading constraints and knowing whether O(n²) will pass is the first thing you do on every problem. Get this wrong and nothing else matters.
2. STL Containers — because choosing between vector, map, set, and unordered_map is a decision you'll make dozens of times per contest. Know the tradeoffs cold.
3. Recursion and Backtracking — because recursive thinking is the foundation for DFS, DP, and divide-and-conquer. If you can't think recursively, Chapters 3 and 4 will be a wall.

Cross-Chapter Connections

• After Bit Manipulation here, you're ready for DP — Bitmask in Chapter 4
• After Recursion and Backtracking, continue to DP Thinking Framework — DP is recursion + memoization
• After Graph and Tree Intro, jump to Graph Representation in Chapter 3
• After Modular Arithmetic Basics, deepen your skills in Number Theory in Chapter 7
• Debugging and Stress Testing pairs well with Debugging Under Pressure in Chapter 11

File Listing

File	Topic	Level
cpp-language-essentials	C++ Language Essentials	⭐
complexity-analysis	Complexity Analysis	⭐
arrays-and-strings	Arrays and Strings	⭐
stl-containers	STL Containers	⭐
stl-algorithms	STL Algorithms	⭐
math-toolkit	Math Toolkit	⭐
modular-arithmetic-basics	Modular Arithmetic Basics	⭐
recursion-and-backtracking	Recursion and Backtracking	⭐
graph-and-tree-intro	Graph and Tree Intro	⭐
bit-manipulation	Bit Manipulation	⭐⭐
bitset-optimization	Bitset Optimization	⭐⭐
fast-io-and-pragmas	Fast I/O and Pragmas	⭐
debugging-and-stress-testing	Debugging and Stress Testing	⭐
bitset-tricks	Bitset Tricks for CP	⭐⭐

Suggested Reading Order

1. Complexity Analysis — learn to estimate what will pass within time limits
2. Arrays and Strings — the most common data types in every problem
3. STL Containers — when to use vector, map, set, queue
4. STL Algorithms — replace manual loops with standard library calls
5. Recursion and Backtracking — think recursively and prune branches
6. Bit Manipulation — encode sets as integers for subset enumeration
7. Bitset Optimization — squeeze O(n/64) speedups with std::bitset
8. Fast I/O and Pragmas — avoid TLE from slow I/O
9. Debugging and Stress Testing — systematic bug-finding techniques
10. C++ Language Essentials — C++ features every CP coder needs
11. Math Toolkit — essential math formulas for competitive programming
12. Modular Arithmetic Basics — handle "mod 10⁹+7" problems correctly
13. Graph and Tree Intro — visual dictionary of graph and tree vocabulary
14. Bitset Tricks — competitive programming bitset recipes for 64x speedups