Exercise 1: Adding Talk G(13-14) After All Six Talks — Possible Solution ==================================================================== ROOM STATE AFTER ALL SIX ORIGINAL TALKS ------------------------------ Following this chapter's own Step 4 result, after processing A, B, F, C, D, E in sorted order, each room's most recent talk ends at: Room 0 (A, C, E): last talk E ends at 13 Room 1 (B, D): last talk D ends at 13 Room 2 (F): last talk F ends at 12 TRACING G(13-14) ------------------------------ The algorithm checks whether the room that frees up EARLIEST has already finished by G's start time (13). Room 2 frees up at 12, which is earlier than both Room 0 and Room 1 (both free at 13) - so Room 2 is the one the algorithm considers first. Is Room 2's free time (12) <= G's start time (13)? Yes (12 <= 13). So G reuses Room 2. FINAL ANSWER ------------------------------ G is assigned to Room 2. No new room is needed - the total room count stays at 3. WHY ROOM 2 SPECIFICALLY, NOT ROOM 0 OR ROOM 1 ------------------------------ Even though Room 0 and Room 1 would also technically be free by 13:00 (since G starts exactly at 13, when both D and E end), the algorithm's own rule is to reuse whichever room frees up EARLIEST among all available options, using a min-heap ordered by end time specifically so it always finds that room efficiently. Room 2, having been idle since 12:00, is the earliest-freeing option, so it's the one chosen - even though Room 0 or Room 1 would also have worked correctly. This doesn't change the correctness of the answer (any of the three would avoid a conflict), only which specific room ends up hosting G. WHY THIS WORKS AS AN ANSWER ------------------------------ The trace explicitly identifies each room's own current free time before checking G against them, correctly applies the chapter's own "reuse the earliest-freeing room" rule using the same touching- endpoints-allowed convention Step 1 established, and explains why Room 2 specifically was chosen over the other two technically-valid options.