Chapter 13 — Worked Solutions

This chapter doesn't teach you algorithms. It teaches you how to think about problems — from the moment you read the statement to the moment you hit Submit. Each file is a full thinking transcript: wrong turns included, insights explained, implementation gotchas highlighted.

These aren't editorials. Editorials tell you the answer. These show you the process of finding it.

Navigation

Coming from: Chapter 12 — Practice Ladders — structured practice from CF 1100 to 2100
Going to: Chapter 14 — Problem Reduction — the meta-skill of transforming unfamiliar problems into familiar ones

Solutions by Technique

The "thinking pattern" column is the transferable move — the reframing or invariant that unlocks the problem. The technique column is the tool that follows once the reframing is in place.

#	Problem	Thinking pattern	Core technique	Rating	File
01	CF 1691D — Max GEQ Sum	fix the element controlling the max	monotonic stack + sparse table	1800	01-max-geq-sum.md
02	CF 1474C — Array Destruction	forced largest-element choice	greedy with multiset peel	1700	02-array-destruction.md
03	CF 1354D — Multiset	bounded values beat ordered sets	binary search on BIT	1900	03-multiset.md
04	CF 1175E — Minimal Segment Cover	jump structure on intervals	binary lifting	2000	04-minimal-segment-cover.md
05	CF 1559D2 — Mocha and Diana (Hard)	hub through node 1, then pair across forests	two DSUs	1900	05-mocha-and-diana.md
06	CF 1536D — Omkar and Medians	check feasibility, do not construct	invariant on a sorted set	1700	06-omkar-and-medians.md
07	CF 1385E — Directing Edges	orient along a topo order of the directed part	toposort certificate	1700	07-directing-edges.md
08	CF 1538F — Interesting Function	count each digit position independently	per-place arithmetic	1800	08-interesting-function.md
09	CF 1443D — Extreme Subtraction	switch to the difference array	monotone decomposition	1800	09-extreme-subtraction.md
10	CF 1498C — Planar Reflections	state = (mirror, remaining bounces, direction)	DP after collapsing symmetry	1600	10-planar-reflections.md

How to Use These

These files are deliberate practice, not passive reading. To extract the most:

1. Try the problem first. Spend at least 20 minutes on the original statement before opening the file.
2. Pause after the "First Read" section. Write down — out loud or on paper — what you would try first and why. Predict the wrong turn before the file shows it.
3. Read forward only after committing. Compare each step in the transcript against your written hypothesis. Where did your thinking diverge, and at what cost?
4. Extract the thinking pattern. Add the one-line reframing from the table to your mental pattern library. The technique is replaceable; the reframing is what transfers.

If you read the file like a normal editorial, you get the answer but not the training. The pause matters.