| 1 | 1 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 2 | """ |
| 3 | Solve an alphametics puzzle. |
| 4 | |
| 5 | Args: |
| 6 | puzzle: A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 7 | |
| 8 | Returns: |
| 9 | A dictionary mapping letters to digits that solves the puzzle, or None if no solution exists. |
| 10 | |
| 11 | Example: |
| 12 | >>> solve("SEND + MORE == MONEY") |
| 13 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 14 | """ |
| 15 | # Edge Case: Empty or None puzzle |
| 16 | if not puzzle: |
| 17 | return None |
| 18 | |
| 19 | # Parse the puzzle |
| 20 | parts = puzzle.replace("==", "=").replace(" ", "").split("=") |
| 21 | |
| 22 | # Edge Case: Invalid puzzle format (no equals sign or too many parts) |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | right_side = parts[1] |
| 27 | left_parts = parts[0].replace("+", " ").split() |
| 28 | |
| 29 | # Edge Case: No terms on the left side |
| 30 | if not left_parts: |
| 31 | return None |
| 32 | |
| 33 | # Extract all unique letters |
| 34 | letters = set() |
| 35 | for part in left_parts + [right_side]: |
| 36 | letters.update(part) |
| 37 | |
| 38 | # Edge Case: No letters in puzzle |
| 39 | if not letters: |
| 40 | return None |
| 41 | |
| 42 | # Extract first letters (can't be zero) |
| 43 | first_letters = {word[0] for word in left_parts + [right_side]} |
| 44 | |
| 45 | letters = list(letters) |
| 46 | |
| 47 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 48 | if len(letters) > 10: |
| 49 | return None |
| 50 | |
| 51 | # Try all possible digit assignments |
| 52 | from itertools import permutations |
| 53 | |
| 54 | for perm in permutations(range(10), len(letters)): |
| 55 | mapping = dict(zip(letters, perm)) |
| 56 | |
| 57 | # Edge Case: Leading zero |
| 58 | if any(mapping[letter] == 0 for letter in first_letters): |
| 59 | continue |
| 60 | |
| 61 | # Calculate left side sum |
| 62 | left_sum = 0 |
| 63 | for word in left_parts: |
| 64 | number = 0 |
| 65 | for letter in word: |
| 66 | number = number * 10 + mapping[letter] |
| 67 | left_sum += number |
| 68 | |
| 69 | # Calculate right side value |
| 70 | right_value = 0 |
| 71 | for letter in right_side: |
| 72 | right_value = right_value * 10 + mapping[letter] |
| 73 | |
| 74 | # Check if equation is satisfied |
| 75 | if left_sum == right_value: |
| 76 | return mapping |
| 77 | |
| 78 | # Edge Case: No solution found |
| 79 | return None |
| 80 | |
| 81 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format (no equals sign or too many parts), No terms on the left side, No letters in puzzle, More than 10 unique letters (impossible to solve), Leading zero, No solution found |