| 1 | from itertools import permutations |
| 2 | |
| 1 | 3 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 4 | """ |
| 5 | Solve an alphametics puzzle. |
| 6 | |
| 7 | Args: |
| 8 | puzzle: A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 9 | |
| 10 | Returns: |
| 11 | A dictionary mapping letters to digits that solves the puzzle, or None if no solution exists. |
| 12 | |
| 13 | The function handles the following edge cases: |
| 14 | - Invalid puzzle format (no '==') |
| 15 | - Words with leading zeros |
| 16 | - No valid solutions |
| 17 | """ |
| 18 | # Edge Case: Invalid puzzle format (no '==') |
| 19 | if "==" not in puzzle: |
| 20 | return None |
| 21 | |
| 22 | # Split the puzzle into left and right sides |
| 23 | left_side, right_side = puzzle.split("==") |
| 24 | left_side = left_side.strip() |
| 25 | right_side = right_side.strip() |
| 26 | |
| 27 | # Extract all words (alphanumeric sequences) |
| 28 | words = [] |
| 29 | for part in left_side.split("+"): |
| 30 | words.append(part.strip()) |
| 31 | words.append(right_side) |
| 32 | |
| 33 | # Get all unique letters |
| 34 | letters = set() |
| 35 | for word in words: |
| 36 | for char in word: |
| 37 | if char.isalpha(): |
| 38 | letters.add(char) |
| 39 | |
| 40 | # Edge Case: Too many unique letters (more than 10) |
| 41 | if len(letters) > 10: |
| 42 | return None |
| 43 | |
| 44 | # Get first letters of each word (can't be zero) |
| 45 | first_letters = {word[0] for word in words if word and word[0].isalpha()} |
| 46 | |
| 47 | # Convert letters to a list for indexing |
| 48 | letters_list = list(letters) |
| 49 | |
| 50 | # Try all digit permutations for the letters |
| 51 | for perm in permutations(range(10), len(letters)): |
| 52 | mapping = dict(zip(letters_list, perm)) |
| 53 | |
| 54 | # Edge Case: Leading zeros in any word |
| 55 | if any(mapping.get(word[0], 0) == 0 for word in words if len(word) > 1 and word[0].isalpha()): |
| 56 | continue |
| 57 | |
| 58 | # Convert words to numbers |
| 59 | numbers = [] |
| 60 | for word in words: |
| 61 | num_str = "" |
| 62 | for char in word: |
| 63 | if char.isalpha(): |
| 64 | if char in mapping: |
| 65 | num_str += str(mapping[char]) |
| 66 | else: |
| 67 | # This shouldn't happen, but just in case |
| 68 | num_str += char |
| 69 | else: |
| 70 | num_str += char |
| 71 | |
| 72 | # Edge Case: Non-alphabetic characters in word that aren't digits |
| 73 | try: |
| 74 | numbers.append(int(num_str)) |
| 75 | except ValueError: |
| 76 | # Invalid character in word |
| 77 | break |
| 78 | |
| 79 | # Edge Case: Not all words were converted successfully |
| 80 | if len(numbers) != len(words): |
| 81 | continue |
| 82 | |
| 83 | # Check if the sum of left side equals the right side |
| 84 | if sum(numbers[:-1]) == numbers[-1]: |
| 85 | return mapping |
| 86 | |
| 87 | # Edge Case: No valid solution found |
| 88 | return None |
| 89 | # Handled Edge Cases: Invalid puzzle format (no '=='), Words with leading zeros, No valid solutions, Too many unique letters (more than 10), Non-alphabetic characters in word that aren't digits, Not all words were converted successfully |