# L34 Pre-flight **Block 4: Aircraft Survivability and Mission Planning — Lesson 34: Optimal Path Planning** *Work this before L34. Pre-flights are never collected — in class, anyone may be cold-called to present any question at the board, and that recitation is the participation grade.* --- ## Assumed pre-class reading - L31's survival metric (independent encounters multiply; $-\ln P_S$ adds) and L32's detection contours and MEZ rings. - The Jupyter Book Reading page for L34 — routes as shortest paths on a graph, Dijkstra's algorithm (settle the cheapest frontier node, relax its edges), why exposure is written as $-\ln(1-p)$, the weight sweep and the fuel limit, and why aspect makes the route graph directed. --- ## Quiz questions (5 items, ~5 minutes) **Q1.** (Multiple choice) A planner's graph has five nodes, from the start S to the target T, and seven legs, each flyable in either direction, with these costs: S–A 4, S–B 2, A–B 1, A–C 5, B–C 8, B–T 11, C–T 3. Which route, at what total cost, does Dijkstra return? - [ ] (a) S–A–B–C–T, cost 16 - [ ] (b) S–A–C–T, cost 12 - [ ] (c) S–B–A–C–T, cost 11 - [ ] (d) S–B–T, cost 13 --- **Q2.** (Multiple choice) In Q1's graph a pop-up SAM raises the cost of leg A–B from 1 to 4; every other leg is unchanged. What does Dijkstra return now? - [ ] (a) S–B–A–C–T, cost 14 - [ ] (b) S–A–C–T, cost 12 - [ ] (c) S–B–C–T, cost 13 - [ ] (d) S–B–T, cost 13 --- **Q3.** (Multiple choice) A weight sweep on one threat map returns five routes: | w (km) | Route length (km) | $P_S$ | |---|---|---| | 0 | 412 | 0.38 | | 60 | 437 | 0.66 | | 150 | 468 | 0.84 | | 400 | 503 | 0.93 | | 1500 | 548 | 0.99 | The fuel limit allows at most 490 km of route. Which route do you fly? - [ ] (a) The w = 400 route: 503 km at $P_S$ 0.93 - [ ] (b) The w = 150 route: 468 km at $P_S$ 0.84 - [ ] (c) The w = 1500 route: 548 km at $P_S$ 0.99 - [ ] (d) The w = 0 route: 412 km at $P_S$ 0.38 --- **Q4.** (Multiple choice) Route X crosses one threat leg with kill probability 0.50. Route Y crosses three independent threat legs at 0.20 each. Which route survives better, and which one does a planner pick if its edge weights are the raw $p$'s? - [ ] (a) Y survives better (0.512 vs 0.500); the raw-$p$ planner picks X instead - [ ] (b) X survives better (0.500 vs 0.400); the raw-$p$ planner picks X too - [ ] (c) Y survives better (0.800 vs 0.500); the raw-$p$ planner picks X - [ ] (d) Y survives better (0.512 vs 0.500); the raw-$p$ planner picks Y too --- **Q5.** (Short answer) In one or two sentences, explain why an aspect-aware planner must use a directed graph (`digraph`): why can the leg from node a to node b cost something different from the same leg flown from b to a?