Exercise 3: Why Brute Force, Not Greedy, Was the Honest Choice for the Override Question — Possible Solution ==================================================================== WHAT MAKES THE OVERRIDE QUESTION A DIFFERENT KIND OF QUESTION ------------------------------ Step 4's greedy algorithm answers "what is the minimum number of rooms needed, and how should talks be assigned to achieve it?" - an open-ended optimization question. The organizer's override question is a completely different shape: "is it possible to fit these four SPECIFIC talks into exactly 2 rooms?" - a yes/no feasibility question about a fixed, constrained scenario. Greedy room assignment, run normally on these four talks, would simply report the minimum number of rooms IT computes as optimal - it has no direct way to answer "can this be done with exactly this many rooms," especially if that number happens to differ from what greedy would naturally produce on its own. WHY BRUTE FORCE FITS CHAPTER 6'S OWN CRITERIA HERE ------------------------------ Chapter 6 established that brute force is the honest choice specifically when the number of candidates is small relative to how fast they can be checked. Checking every way to split 4 talks between 2 rooms means checking only 2^4 = 16 possible assignments - a search space small enough to check exhaustively in a trivial amount of time, exactly the kind of case Chapter 6 said doesn't need a cleverer strategy. Using brute force here isn't a compromise or a fallback; per Chapter 6's own standard, it's the simplest, most directly verifiable way to answer a small, specific feasibility question. WHY REUSING GREEDY WOULD HAVE BEEN THE WRONG TOOL, NOT JUST A WORSE ONE ------------------------------ Even setting efficiency aside, greedy's own algorithm doesn't naturally express the question "would exactly 2 rooms work" - it computes whatever number of rooms it determines is minimal on its own, given its own selection order. Answering the organizer's specific question by re-running greedy and checking whether the result happens to equal 2 would only work by coincidence (and does happen to work in this case, since Step 5 confirmed 2 is achievable and greedy would likely also find an assignment using 2 rooms for just these four talks) - but this chapter's own brute-force check is exhaustive and provides an unambiguous existence proof, independent of any particular assignment order, exactly the kind of small-scale verification Chapter 6's own criteria call for. WHY THIS WORKS AS AN ANSWER ------------------------------ The answer identifies the genuine difference in QUESTION SHAPE between Step 4's optimization task and Step 5's feasibility question, applies Chapter 6's own specific small-search-space criterion to justify brute force as the honest choice rather than a fallback, and explains why greedy - even though it might coincidentally produce a usable result - isn't actually built to answer the kind of yes/no question the organizer asked.