| 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 (str): A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 9 | |
| 10 | Returns: |
| 11 | dict[str, int] | None: A dictionary mapping letters to digits that solves the puzzle, |
| 12 | 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 |
| 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 | # Edge Case: Empty sides |
| 28 | if not left_side or not right_side: |
| 29 | return None |
| 30 | |
| 31 | # Extract all words (terms) |
| 32 | terms = [word.strip() for word in left_side.replace("+", " ").split()] |
| 33 | result = right_side |
| 34 | |
| 35 | # Edge Case: No terms on left side |
| 36 | if not terms: |
| 37 | return None |
| 38 | |
| 39 | # Collect all unique letters |
| 40 | letters = set() |
| 41 | for term in terms + [result]: |
| 42 | letters.update(term) |
| 43 | |
| 44 | # Edge Case: No letters in puzzle |
| 45 | if not letters: |
| 46 | return None |
| 47 | |
| 48 | # Collect first letters (can't be zero) |
| 49 | first_letters = {word[0] for word in terms + [result]} |
| 50 | |
| 51 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 52 | if len(letters) > 10: |
| 53 | return None |
| 54 | |
| 55 | # Try all digit permutations for the letters |
| 56 | digits = range(10) |
| 57 | for perm in permutations(digits, len(letters)): |
| 58 | mapping = dict(zip(letters, perm)) |
| 59 | |
| 60 | # Edge Case: Leading zero |
| 61 | if any(mapping[letter] == 0 for letter in first_letters): |
| 62 | continue |
| 63 | |
| 64 | # Convert words to numbers |
| 65 | term_values = [] |
| 66 | for term in terms: |
| 67 | value = 0 |
| 68 | for char in term: |
| 69 | value = value * 10 + mapping[char] |
| 70 | term_values.append(value) |
| 71 | |
| 72 | result_value = 0 |
| 73 | for char in result: |
| 74 | result_value = result_value * 10 + mapping[char] |
| 75 | |
| 76 | # Check if the equation is satisfied |
| 77 | if sum(term_values) == result_value: |
| 78 | return mapping |
| 79 | |
| 80 | # Edge Case: No solution found |
| 81 | return None |
| 82 | |
| 83 | # Handled Edge Cases: Invalid puzzle format, Empty sides, No terms on left side, No letters in puzzle, More than 10 unique letters, Leading zero, No solution found |