| 1 | 1 | def can_chain(dominoes: list[tuple[int, int]]) -> list[tuple[int, int]] | None: |
| 2 | | pass |
| 2 | # Edge Case: Empty set of dominoes |
| 3 | if not dominoes: |
| 4 | return [] |
| 5 | |
| 6 | # Edge Case: Single domino - must be able to form a loop with itself |
| 7 | if len(dominoes) == 1: |
| 8 | a, b = dominoes[0] |
| 9 | if a == b: |
| 10 | return dominoes |
| 11 | else: |
| 12 | return None |
| 13 | |
| 14 | # Try all possible starting dominoes and orientations |
| 15 | for i in range(len(dominoes)): |
| 16 | # Try the domino in original orientation |
| 17 | chain = [dominoes[i]] |
| 18 | remaining = dominoes[:i] + dominoes[i+1:] |
| 19 | result = _build_chain(chain, remaining) |
| 20 | if result is not None: |
| 21 | return result |
| 22 | |
| 23 | # Try the domino flipped |
| 24 | flipped_domino = (dominoes[i][1], dominoes[i][0]) |
| 25 | chain = [flipped_domino] |
| 26 | remaining = dominoes[:i] + dominoes[i+1:] |
| 27 | result = _build_chain(chain, remaining) |
| 28 | if result is not None: |
| 29 | return result |
| 30 | |
| 31 | return None |
| 32 | |
| 33 | def _build_chain(chain: list[tuple[int, int]], remaining: list[tuple[int, int]]) -> list[tuple[int, int]] | None: |
| 34 | # If no dominoes left, check if chain is valid (first matches last) |
| 35 | if not remaining: |
| 36 | if chain[0][0] == chain[-1][1]: |
| 37 | return chain |
| 38 | else: |
| 39 | return None |
| 40 | |
| 41 | # Get the value we need to match (the second value of the last domino in chain) |
| 42 | target = chain[-1][1] |
| 43 | |
| 44 | # Try each remaining domino |
| 45 | for i in range(len(remaining)): |
| 46 | domino = remaining[i] |
| 47 | rest = remaining[:i] + remaining[i+1:] |
| 48 | |
| 49 | # Try matching in original orientation |
| 50 | if domino[0] == target: |
| 51 | new_chain = chain + [domino] |
| 52 | result = _build_chain(new_chain, rest) |
| 53 | if result is not None: |
| 54 | return result |
| 55 | |
| 56 | # Try matching in flipped orientation |
| 57 | if domino[1] == target: |
| 58 | flipped = (domino[1], domino[0]) |
| 59 | new_chain = chain + [flipped] |
| 60 | result = _build_chain(new_chain, rest) |
| 61 | if result is not None: |
| 62 | return result |
| 63 | |
| 64 | return None |
| 65 | # Handled Edge Cases: empty set of dominoes, single domino, no valid chain exists, dominoes that cannot form a cycle |