# RE8 | deepseek/deepseek-v4-pro | run 2

## Prompt

Minimize total time to finish these tasks, one at a time, respecting dependencies: A (2h, no deps); B (3h, needs A); C (1h, no deps); D (2h, needs B and C). Give a valid order and the total time.

## Response

A valid order that respects all dependencies while processing tasks one at a time is **C → A → B → D**. The total completion time is **8 hours**.

## Why this is minimal

Since tasks are executed sequentially (no parallel processing), the total time is the sum of all durations as long as no idle time is forced by dependencies. The precedence constraints are:

- A must finish before B starts.
- Both B and C must finish before D starts.

This forms a directed acyclic graph with A and C as independent starting points. Any topological ordering that satisfies these rules avoids gaps. Three equally optimal sequences:

| Order | Duration breakdown | Total |
|-------|-------------------|-------|
| C → A → B → D | 1 + 2 + 3 + 2 | 8 h |
| A → C → B → D | 2 + 1 + 3 + 2 | 8 h |
| A → B → C → D | 2 + 3 + 1 + 2 | 8 h |

All complete in **8 hours** — the sum of the four task durations — because no slack is required. No shorter schedule is possible under sequential single-task execution.

What changes if you could work on up to two tasks in parallel?
