Lesson 4 · The Manhattan Algorithm — Knowledge ChecksAnswer key

Why can't the robot use a straight diagonal to shorten the trip?

1. A.Diagonals are slower than straight lines
2. B.The robot follows grid lines, so it can only move along rows and columns✓
3. C.The grid is too small
4. D.It can — the Manhattan algorithm just chooses not to

Like walking Manhattan's streets, the robot can't cut through the middle of a block — only along the lines. That's exactly why the distance is row steps + column steps.

Hand-tracing (2,0) → (2,3), what path do you get?

1. A.[(2,0), (2,1), (2,2), (2,3)]
2. B.[(2,1), (2,2), (2,3)]✓
3. C.[(2,3)]
4. D.[]

Same row, so no row moves — only three column moves. The start (2,0) is not included, so the path is [(2,1), (2,2), (2,3)]: three steps.

Why does the stage-1 function return [] for (3,3) → (1,0)?

1. A.append() is broken
2. B.Both while conditions are False from the start (3 is not < 1, 3 is not < 0), so neither loop runs✓
3. C.The start and end are the same
4. D.It runs forever

Stage 1 only handles increasing row/column. Moving up or left needs the two decreasing loops we add next.

For a trip that goes up and to the right, how many of the four while loops actually run?

1. A.All four
2. B.Two — the north loop and the east loop✓
3. C.Just one
4. D.None — it needs if/else

At most one row loop (north OR south) and one column loop (east OR west) run for any trip. Up-and-right means north + east; the other two are skipped.

What does compute_path((2, 2), (2, 2)) return, and why?

1. A.[(2, 2)] — the current position
2. B.[] — all four loop conditions are False, so nothing is appended✓
3. C.An error
4. D.0

Start equals destination, so every while condition is False from the start. No loop runs, the path stays empty, and len(path) is 0 — the robot is already there.