| 1 | from itertools import permutations |
| 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: A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 10 | |
| 11 | Returns: |
| 12 | A dictionary mapping letters to digits that solves the puzzle, or None if no solution exists. |
| 13 | |
| 14 | Example: |
| 15 | >>> solve("SEND + MORE == MONEY") |
| 16 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 17 | """ |
| 18 | # Parse the puzzle into components |
| 19 | # Edge Case: Invalid puzzle format |
| 20 | if "==" not in puzzle: |
| 21 | return None |
| 22 | |
| 23 | left_side, right_side = puzzle.split("==") |
| 24 | left_side = left_side.strip() |
| 25 | right_side = right_side.strip() |
| 26 | |
| 27 | # Extract all words (sequences of uppercase letters) |
| 28 | words = re.findall(r'[A-Z]+', puzzle) |
| 29 | if not words: |
| 30 | return None |
| 31 | |
| 32 | # Edge Case: Empty words or invalid characters |
| 33 | if not all(word.isalpha() and word.isupper() for word in words): |
| 34 | return None |
| 35 | |
| 36 | # Get all unique letters |
| 37 | letters = set(''.join(words)) |
| 38 | |
| 39 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 40 | if len(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 words} |
| 45 | |
| 46 | # Edge Case: Empty puzzle |
| 47 | if not letters: |
| 48 | return None |
| 49 | |
| 50 | # Try all permutations of digits for the letters |
| 51 | digits = range(10) |
| 52 | for perm in permutations(digits, len(letters)): |
| 53 | mapping = dict(zip(letters, perm)) |
| 54 | |
| 55 | # Edge Case: Leading zeros |
| 56 | if any(mapping[letter] == 0 for letter in first_letters): |
| 57 | continue |
| 58 | |
| 59 | # Convert words to numbers using the mapping |
| 60 | def word_to_number(word): |
| 61 | return int(''.join(str(mapping[letter]) for letter in word)) |
| 62 | |
| 63 | # Calculate values of the left side expressions |
| 64 | left_values = [word_to_number(word) for word in re.findall(r'[A-Z]+', left_side)] |
| 65 | |
| 66 | # Edge Case: Empty left side |
| 67 | if not left_values: |
| 68 | continue |
| 69 | |
| 70 | left_sum = sum(left_values) |
| 71 | right_value = word_to_number(right_side) |
| 72 | |
| 73 | # Check if the equation is satisfied |
| 74 | if left_sum == right_value: |
| 75 | return mapping |
| 76 | |
| 77 | # Edge Case: No solution found |
| 78 | return None |
| 79 | # Handled Edge Cases: Invalid puzzle format, empty words or invalid characters, more than 10 unique letters, leading zeros, empty puzzle, no solution found |