| 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 an alphametics puzzle in the format "A + B == C" |
| 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 |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | left_side, right_side = parts[0], parts[1] |
| 27 | |
| 28 | # Extract all words (addends and result) |
| 29 | addends = left_side.split("+") |
| 30 | result = right_side |
| 31 | |
| 32 | # Edge Case: No addends |
| 33 | if not addends or not result: |
| 34 | return None |
| 35 | |
| 36 | # Get all unique letters |
| 37 | letters = set() |
| 38 | for word in addends + [result]: |
| 39 | letters.update(word) |
| 40 | |
| 41 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 42 | if len(letters) > 10: |
| 43 | return None |
| 44 | |
| 45 | # Get first letters (can't be zero) |
| 46 | first_letters = {word[0] for word in addends + [result]} |
| 47 | |
| 48 | # Convert letters to list for indexing |
| 49 | letters_list = list(letters) |
| 50 | |
| 51 | # Try all permutations of digits for letters |
| 52 | from itertools import permutations |
| 53 | |
| 54 | # Edge Case: Handle puzzles with no letters |
| 55 | if not letters_list: |
| 56 | return None |
| 57 | |
| 58 | for perm in permutations(range(10), len(letters_list)): |
| 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 | # Convert words to numbers |
| 67 | try: |
| 68 | addend_values = [] |
| 69 | for word in addends: |
| 70 | value = 0 |
| 71 | for letter in word: |
| 72 | value = value * 10 + mapping[letter] |
| 73 | addend_values.append(value) |
| 74 | |
| 75 | result_value = 0 |
| 76 | for letter in result: |
| 77 | result_value = result_value * 10 + mapping[letter] |
| 78 | |
| 79 | # Check if equation is satisfied |
| 80 | if sum(addend_values) == result_value: |
| 81 | return mapping |
| 82 | except KeyError: |
| 83 | # This shouldn't happen with proper permutation, but just in case |
| 84 | continue |
| 85 | |
| 86 | # Edge Case: No solution found |
| 87 | return None |
| 88 | |
| 89 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No addends, More than 10 unique letters, No letters, No solution found |