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A whole class you haven't touched: flow networks. Learn Ford-Fulkerson and maximum flow.
(Why flow matters)
Directed graph with capacities
(How much flow on each edge)
(Simple network walkthrough)
(Find maximum throughput)
(Captures remaining capacity)
(Path that increases flow)
Knowledge check
Iterative augmentation fram...
(Correctness argument)
BFS for shortest augmenting...
(BFS-based max flow)
(Forward and backward edges)
Adjacency list with capacities
(Edmonds-Karp analysis)
Knowledge check
(CSES 1694)
(Direct translation to flow)
(Edmonds-Karp code)
(Example with 4 nodes)
(No path, single edge)
(Partitioning the graph)
(Cut with minimum capacity)
(Duality result)
Run BFS on final residual g...
Knowledge check
(CSES 1695)
Unit capacities mean edge-d...
(BFS on residual graph)
Edmonds-Karp + cut extraction
(Example with 4 cities)
(Classic flow application)
(CSES 1696)
(Source and sink setup)
(Check flow on middle edges)
(Bipartite matching via flow)
(Example with 3 boys, 2 girls)
(Unbalanced sides, no edges)
Knowledge check
Reduction to single source/...
(Split nodes into in/out)
Forcing minimum flow on edges
Integral capacities yield i...
(Counting independent routes)
(Recognizing flow problems)
(What to avoid)
Knowledge check
(Beyond Edmonds-Karp)
(Real-world applications)
(Path that increases flow)
Remaining capacities after ...
Partition separating source...
(How to get good at flow)
(What you learned)