| 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 | # Parse the puzzle - handle both "=" and "==" operators |
| 16 | if "==" in puzzle: |
| 17 | left_side, right_side = puzzle.split("==") |
| 18 | elif "=" in puzzle: |
| 19 | left_side, right_side = puzzle.split("=") |
| 20 | else: |
| 21 | return None |
| 22 | |
| 23 | left_side = left_side.strip() |
| 24 | right_side = right_side.strip() |
| 25 | |
| 26 | # Extract words from left side (remove operators and spaces) |
| 27 | left_words = [] |
| 28 | for part in left_side.split("+"): |
| 29 | word = part.strip() |
| 30 | if word: # Only add non-empty words |
| 31 | left_words.append(word) |
| 32 | |
| 33 | # Right side is the result word |
| 34 | result_word = right_side.strip() |
| 35 | |
| 36 | # Edge Case: Empty puzzle or invalid format |
| 37 | if not left_words or not result_word: |
| 38 | return None |
| 39 | |
| 40 | # All words for letter extraction |
| 41 | all_words = left_words + [result_word] |
| 42 | |
| 43 | # Get all unique letters |
| 44 | letters = set() |
| 45 | for word in all_words: |
| 46 | letters.update(word) |
| 47 | |
| 48 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 49 | if len(letters) > 10: |
| 50 | return None |
| 51 | |
| 52 | # Edge Case: Empty letters set |
| 53 | if not letters: |
| 54 | return None |
| 55 | |
| 56 | letters = list(letters) |
| 57 | |
| 58 | # Generate all possible digit assignments |
| 59 | from itertools import permutations |
| 60 | |
| 61 | # Edge Case: Not enough digits for letters |
| 62 | for perm in permutations(range(10), len(letters)): |
| 63 | mapping = dict(zip(letters, perm)) |
| 64 | |
| 65 | # Edge Case: Leading zero in any word (including result) |
| 66 | if any(mapping[word[0]] == 0 for word in all_words): |
| 67 | continue |
| 68 | |
| 69 | # Calculate values of left side words |
| 70 | left_values = [] |
| 71 | for word in left_words: |
| 72 | value = 0 |
| 73 | for char in word: |
| 74 | value = value * 10 + mapping[char] |
| 75 | left_values.append(value) |
| 76 | |
| 77 | # Calculate value of result word |
| 78 | result_value = 0 |
| 79 | for char in result_word: |
| 80 | result_value = result_value * 10 + mapping[char] |
| 81 | |
| 82 | # Check if the equation holds |
| 83 | if sum(left_values) == result_value: |
| 84 | return mapping |
| 85 | |
| 86 | # Edge Case: No valid solution found |
| 87 | return None |
| 88 | |
| 89 | # Handled Edge Cases: Empty puzzle or invalid format, more than 10 unique letters, empty letters set, leading zero in any word, not enough digits for letters, no valid solution found |