| 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 | The function handles the following edge cases: |
| 12 | - Invalid puzzle format (no '==') |
| 13 | - Words with leading zeros |
| 14 | - Repeated letters in the mapping |
| 15 | - No valid solutions |
| 16 | """ |
| 17 | # Edge Case: Invalid puzzle format (no '==') |
| 18 | if "==" not in puzzle: |
| 19 | return None |
| 20 | |
| 21 | # Parse the puzzle |
| 22 | left_side, right_side = puzzle.split("==") |
| 23 | left_side = left_side.strip() |
| 24 | right_side = right_side.strip() |
| 25 | |
| 26 | # Extract words (remove operators like +, -) |
| 27 | import re |
| 28 | addends = re.findall(r'[A-Z]+', left_side) |
| 29 | result_word = right_side |
| 30 | |
| 31 | # Edge Case: No words found |
| 32 | if not addends or not result_word: |
| 33 | return None |
| 34 | |
| 35 | # Get all unique letters |
| 36 | all_words = addends + [result_word] |
| 37 | unique_letters = set(''.join(all_words)) |
| 38 | |
| 39 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 40 | if len(unique_letters) > 10: |
| 41 | return None |
| 42 | |
| 43 | # Get first letters of each word (can't be zero) |
| 44 | first_letters = {word[0] for word in all_words} |
| 45 | |
| 46 | # Generate all possible digit assignments |
| 47 | from itertools import permutations |
| 48 | |
| 49 | # Try all permutations of digits for the unique letters |
| 50 | for perm in permutations(range(10), len(unique_letters)): |
| 51 | mapping = dict(zip(unique_letters, perm)) |
| 52 | |
| 53 | # Edge Case: Leading zero in any word |
| 54 | if any(mapping[word[0]] == 0 for word in all_words): |
| 55 | continue |
| 56 | |
| 57 | # Convert addends to numbers using the mapping |
| 58 | addend_numbers = [] |
| 59 | for word in addends: |
| 60 | num = 0 |
| 61 | for char in word: |
| 62 | num = num * 10 + mapping[char] |
| 63 | addend_numbers.append(num) |
| 64 | |
| 65 | # Convert result to number |
| 66 | result_number = 0 |
| 67 | for char in result_word: |
| 68 | result_number = result_number * 10 + mapping[char] |
| 69 | |
| 70 | # Check if the equation holds |
| 71 | if sum(addend_numbers) == result_number: |
| 72 | return mapping |
| 73 | |
| 74 | # Edge Case: No valid solution found |
| 75 | return None |
| 76 | # Handled Edge Cases: Invalid puzzle format (no '=='), No words found, More than 10 unique letters, Leading zero in any word, No valid solution found |