Data Structures & Algorithms

Flows and Matching

This branch collects problems where the cleanest solution is to phrase the whole task as conserved flow or structural matching.

4 published notes
2 planned topics
3 advanced or expert notes
advanced starting level

Flows and Matching

Network formulations for path packing, assignment, and constrained transfer.

Overview

Some problems only look combinatorial until the constraints line up and the clean model is flow. This category is for those reductions: send units through a network, enforce conservation, and let the residual structure do the work.

Current Focus

The current baseline covers the three core tools I expect to reuse most often: Dinic for max flow, bipartite matching when the graph structure is already clean, and min-cost max-flow when the model needs an optimization layer on top of feasibility. The next additions here should be more specialized routines such as Hungarian or general matching.

How this branch is distributed

The labels are not cosmetic. They are there to signal the amount of prerequisite structure and implementation fragility you should expect before opening the note.

basic: 0 intermediate: 1 advanced: 3 expert: 0
1 intermediate
intermediate

These notes assume the base routine is already familiar and focus on the first real structural upgrades.

Bipartite Matching

3 advanced
advanced

These are the notes where proofs, reductions, or implementation details become the main bottleneck.

Dinic, Hopcroft-Karp, Min-Cost Max-Flow

What is already written

These are the finished note pages in this category, each with rendered TeX, C++ code, references, and practice suggestions.

Recommended order to read this branch

The default order follows each note's dependency weight: early notes establish primitives, later notes reuse them or assume the same invariants without re-explaining them.

Next topics in this branch

These are still intentionally shown as planned or outline topics rather than shallow filler. The branch should feel incomplete in honest places instead of fake-complete everywhere.

Hungarian algorithm outline General matching outline

Source Files and Assets

Raw files are still available here when you want the original TeX, C++, or statement assets.

Show raw files