III · Graph theory
Min-cut / Max-flow
What it is
The maximum flow from source to sink equals the minimum cut between them (Ford–Fulkerson).
Where it lives
Image segmentation, VLSI design, bipartite matching, network reliability.
The key insight
Max-flow algorithms range from O(V·E²) (Edmonds-Karp) to O(V²·√E) (Dinic) — pick by graph density.