Derivation — Exchange-Argument Proofs for Greedy Correctness

Every greedy correctness proof in this unit — Dijkstra's, the MST cut property, interval scheduling — followed the identical logical shape: assume an optimal solution doesn't make the greedy choice, then show it can be modified (an "exchange") to include that choice without making it worse. This note names that shape explicitly as the exchange-argument template, then does something the previous, more optimistic lessons haven't: applies the same reasoning attempt to a problem where it fails — 0/1 knapsack — to build the instinct for recognising when greedy is unsafe, not just when it works.