| 1 | import itertools |
| 2 | import re |
| 3 | |
| 1 | 4 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 5 | """ |
| 6 | Solve an alphametics puzzle. |
| 7 | |
| 8 | Args: |
| 9 | puzzle (str): A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 10 | |
| 11 | Returns: |
| 12 | dict[str, int] | None: A dictionary mapping letters to digits that solves the puzzle, |
| 13 | or None if no solution exists. |
| 14 | |
| 15 | Example: |
| 16 | >>> solve("SEND + MORE == MONEY") |
| 17 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 18 | """ |
| 19 | # Parse the puzzle into components |
| 20 | # Edge Case: Invalid puzzle format |
| 21 | if "==" not in puzzle: |
| 22 | return None |
| 23 | |
| 24 | left_side, right_side = puzzle.replace(" ", "").split("==") |
| 25 | |
| 26 | # Edge Case: Empty sides in puzzle |
| 27 | if not left_side or not right_side: |
| 28 | return None |
| 29 | |
| 30 | # Extract all words (addends and result) |
| 31 | addends = left_side.split("+") |
| 32 | result_word = right_side |
| 33 | |
| 34 | # Edge Case: Empty addend |
| 35 | if any(not addend for addend in addends): |
| 36 | return None |
| 37 | |
| 38 | # Edge Case: Empty result word |
| 39 | if not result_word: |
| 40 | return None |
| 41 | |
| 42 | # Get all unique letters |
| 43 | all_words = addends + [result_word] |
| 44 | unique_letters = set("".join(all_words)) |
| 45 | |
| 46 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 47 | if len(unique_letters) > 10: |
| 48 | return None |
| 49 | |
| 50 | # Get first letters of each word (can't be zero) |
| 51 | first_letters = {word[0] for word in all_words} |
| 52 | |
| 53 | # Edge Case: First letters contain non-alphabetic characters |
| 54 | if any(not letter.isalpha() for letter in first_letters): |
| 55 | return None |
| 56 | |
| 57 | # Sort letters for consistent ordering |
| 58 | sorted_letters = sorted(unique_letters) |
| 59 | |
| 60 | # Try all digit permutations for the unique letters |
| 61 | digits = range(10) |
| 62 | for perm in itertools.permutations(digits, len(unique_letters)): |
| 63 | # Create mapping from letters to digits |
| 64 | mapping = dict(zip(sorted_letters, perm)) |
| 65 | |
| 66 | # Edge Case: Leading zero in any word |
| 67 | if any(mapping[letter] == 0 for letter in first_letters): |
| 68 | continue |
| 69 | |
| 70 | # Convert words to numbers using the mapping |
| 71 | try: |
| 72 | addend_values = [] |
| 73 | for word in addends: |
| 74 | value = 0 |
| 75 | for letter in word: |
| 76 | value = value * 10 + mapping[letter] |
| 77 | addend_values.append(value) |
| 78 | |
| 79 | result_value = 0 |
| 80 | for letter in result_word: |
| 81 | result_value = result_value * 10 + mapping[letter] |
| 82 | except KeyError: |
| 83 | # Edge Case: Non-alphabetic characters in words |
| 84 | continue |
| 85 | |
| 86 | # Check if the sum is correct |
| 87 | if sum(addend_values) == result_value: |
| 88 | return mapping |
| 89 | |
| 90 | # Edge Case: No valid solution found |
| 91 | return None |
| 92 | |
| 93 | # Handled Edge Cases: Invalid puzzle format, Empty sides in puzzle, Empty addend, Empty result word, More than 10 unique letters, First letters contain non-alphabetic characters, Leading zero in any word, Non-alphabetic characters in words, No valid solution found |