| 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 puzzle string |
| 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_sides = parts[0].replace("+", " ").split() |
| 28 | |
| 29 | # Edge Case: No terms on the left side |
| 30 | if not left_sides: |
| 31 | return None |
| 32 | |
| 33 | # Extract all unique letters |
| 34 | letters = set() |
| 35 | for part in left_sides + [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_sides + [right_side]} |
| 44 | |
| 45 | # Convert letters to a list for indexing |
| 46 | letters_list = list(letters) |
| 47 | n = len(letters_list) |
| 48 | |
| 49 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 50 | if n > 10: |
| 51 | return None |
| 52 | |
| 53 | # Try all permutations of digits for the letters |
| 54 | from itertools import permutations |
| 55 | |
| 56 | # Edge Case: Handle puzzles with no letters (should not happen after previous checks) |
| 57 | |
| 58 | for perm in permutations(range(10), n): |
| 59 | # Create mapping |
| 60 | mapping = dict(zip(letters_list, perm)) |
| 61 | |
| 62 | # Check if any first letter is assigned zero |
| 63 | if any(mapping[letter] == 0 for letter in first_letters): |
| 64 | continue |
| 65 | |
| 66 | # Calculate values of words |
| 67 | left_values = [] |
| 68 | for word in left_sides: |
| 69 | value = 0 |
| 70 | for letter in word: |
| 71 | value = value * 10 + mapping[letter] |
| 72 | left_values.append(value) |
| 73 | |
| 74 | right_value = 0 |
| 75 | for letter in right_side: |
| 76 | right_value = right_value * 10 + mapping[letter] |
| 77 | |
| 78 | # Check if equation is satisfied |
| 79 | if sum(left_values) == right_value: |
| 80 | return mapping |
| 81 | |
| 82 | # Edge Case: No valid solution found |
| 83 | return None |
| 84 | # Handled Edge Cases: Empty puzzle string, invalid puzzle format, no terms on left side, no letters in puzzle, more than 10 unique letters, any first letter assigned zero, no valid solution found |