| 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 | Example: |
| 12 | >>> solve("SEND + MORE == MONEY") |
| 13 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 14 | """ |
| 15 | # Parse the puzzle |
| 16 | if "==" not in puzzle: |
| 17 | return None |
| 18 | |
| 19 | left_side, right_side = puzzle.split("==") |
| 20 | left_side = left_side.strip() |
| 21 | right_side = right_side.strip() |
| 22 | |
| 23 | # Extract words (remove operators and spaces) |
| 24 | words = [] |
| 25 | for part in left_side.split("+"): |
| 26 | words.append(part.strip()) |
| 27 | words.append(right_side) |
| 28 | |
| 29 | # Edge Case: Empty puzzle or invalid format |
| 30 | if not all(words): |
| 31 | return None |
| 32 | |
| 33 | # Get all unique letters |
| 34 | letters = set() |
| 35 | for word in words: |
| 36 | letters.update(word) |
| 37 | |
| 38 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 39 | if len(letters) > 10: |
| 40 | return None |
| 41 | |
| 42 | first_letters = {word[0] for word in words} |
| 43 | |
| 44 | # Edge Case: Empty letters set |
| 45 | if not letters: |
| 46 | return None |
| 47 | |
| 48 | letters = list(letters) |
| 49 | |
| 50 | # Try all possible digit assignments |
| 51 | from itertools import permutations |
| 52 | |
| 53 | # Edge Case: Not enough digits for letters |
| 54 | for perm in permutations(range(10), len(letters)): |
| 55 | mapping = dict(zip(letters, perm)) |
| 56 | |
| 57 | # Edge Case: Leading zero |
| 58 | if any(mapping[first_letter] == 0 for first_letter in first_letters): |
| 59 | continue |
| 60 | |
| 61 | # Calculate values of words |
| 62 | try: |
| 63 | left_value = 0 |
| 64 | for word in words[:-1]: # All words except the last (result) |
| 65 | num = 0 |
| 66 | for char in word: |
| 67 | num = num * 10 + mapping[char] |
| 68 | left_value += num |
| 69 | |
| 70 | right_value = 0 |
| 71 | for char in words[-1]: # Last word (result) |
| 72 | right_value = right_value * 10 + mapping[char] |
| 73 | |
| 74 | # Edge Case: Valid solution found |
| 75 | if left_value == right_value: |
| 76 | return mapping |
| 77 | except KeyError: |
| 78 | # Edge Case: Invalid mapping (should not happen with proper permutation) |
| 79 | continue |
| 80 | |
| 81 | # Edge Case: No solution found |
| 82 | return None |
| 83 | |
| 84 | # Handled Edge Cases: Empty puzzle or invalid format, more than 10 unique letters, empty letters set, leading zero, not enough digits for letters, invalid mapping, no solution found, valid solution found |