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| 1 | +## Group B - Exercise 3 |
| 2 | + |
| 3 | +### Context |
| 4 | +An Airline has to schedule $N$ flights during a predefined time period.\ |
| 5 | +Each flight can be referenced using an id $(1, 2, 3 ... N)$. |
| 6 | + |
| 7 | +The airline has pre-generated $M$ flight combinations (pairings).\ |
| 8 | +Each pairing $P_i$ (where $ 1 \le i \le M$), may include a subset of the flights $1, 2, 3 ... N$. It is **feasible**, and is assigned to a **specific captain**. |
| 9 | + |
| 10 | +The task is to select a subset of the available pairings, so that |
| 11 | +each flight is assigned to **exactly 1 captain**. |
| 12 | + |
| 13 | +A $P_i$ pairing has a cost of $C_i$. The **sum of costs** of the selected pairings, is the **total cost** for the selection. |
| 14 | + |
| 15 | +### Task |
| 16 | +You will use [get_flight_data(I, N, P, C)](./flight_data.pl) to get pre-generated pairings. |
| 17 | +- `I` is an index number, from **1 to 16**. |
| 18 | +- `N` returns the number of flights. |
| 19 | +- `P` returns the pairings (list of lists). |
| 20 | +- `C` returns a list with the pairing costs. |
| 21 | + |
| 22 | +Implement a `flights(I, Pairings, Cost)` predicate: |
| 23 | +- `I` is the index number to be provided to `get_flight_data`. |
| 24 | +- `Pairings` returns the optimal pairings selection. |
| 25 | +- `Cost` returns the total cost of the selection. |
| 26 | + |
| 27 | +### Execution Example |
| 28 | +Input: |
| 29 | + |
| 30 | + ?- member(I, [1, 2, 3, 4]), |
| 31 | + write('I = '), writeln(I), |
| 32 | + flights(I, Pairings,Cost), |
| 33 | + write('Pairings = '), writeln(Pairings), |
| 34 | + write('Cost = '), writeln(Cost), nl, fail. |
| 35 | + |
| 36 | + |
| 37 | +Output: |
| 38 | + |
| 39 | + I = 1 |
| 40 | + Pairings = [[1, 2, 3, 7] / 10, |
| 41 | + [5, 8] / 12, |
| 42 | + [4, 9, 10] / 34, |
| 43 | + [6] / 34] |
| 44 | + Cost = 90 |
| 45 | + |
| 46 | + I = 2 |
| 47 | + Pairings = [[1, 2, 5, 8] / 10, |
| 48 | + [3, 6, 9] / 25, |
| 49 | + [4, 7, 10] / 20] |
| 50 | + Cost = 55 |
| 51 | + |
| 52 | + I = 3 |
| 53 | + Pairings = [[6, 9] / 32, |
| 54 | + [2, 5, 8] / 10, |
| 55 | + [1, 3, 4, 7, 10] / 28] |
| 56 | + Cost = 70 |
| 57 | + |
| 58 | + I = 4 |
| 59 | + Pairings = [[1, 5, 11] / 2, |
| 60 | + [7, 10, 12] / 3, |
| 61 | + [2, 9, 15, 16] / 1, |
| 62 | + [4, 8, 14] / 2, |
| 63 | + [3, 6, 13] / 1] |
| 64 | + Cost = 9 |
| 65 | + |
| 66 | +### Implementation |
| 67 | +- The `flights` predicate is implemented in `flights.pl`, along with several helper predicates. |
| 68 | +- The `get_flight_data` predicate was pre-implemented in `flight_data.pl`. |
| 69 | +- The `acsdata` directory contains data used by `get_flight_data`, for indexes from 7 up to 16. |
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