| 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 | # Edge Case: Empty or None puzzle |
| 16 | if not puzzle: |
| 17 | return None |
| 18 | |
| 19 | # Parse the puzzle |
| 20 | parts = puzzle.replace("==", "=").replace(" ", "").split("=") |
| 21 | |
| 22 | # Edge Case: Invalid puzzle format (no equals sign or too many parts) |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | right_side = parts[1] |
| 27 | left_sides = parts[0].split("+") |
| 28 | |
| 29 | # Edge Case: No addends on left side |
| 30 | if not left_sides or len(left_sides) == 0: |
| 31 | return None |
| 32 | |
| 33 | # Get all unique letters |
| 34 | letters = set() |
| 35 | for part in left_sides + [right_side]: |
| 36 | letters.update(part) |
| 37 | |
| 38 | # Edge Case: No letters in puzzle |
| 39 | if not letters: |
| 40 | return None |
| 41 | |
| 42 | # Get first letters (can't be zero) |
| 43 | first_letters = {word[0] for word in left_sides + [right_side]} |
| 44 | |
| 45 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 46 | if len(letters) > 10: |
| 47 | return None |
| 48 | |
| 49 | # Convert letters to list for indexing |
| 50 | letters_list = list(letters) |
| 51 | |
| 52 | # Try all permutations of digits for the letters |
| 53 | from itertools import permutations |
| 54 | |
| 55 | # Edge Case: Handle permutations of digits 0-9 for the letters |
| 56 | for perm in permutations(range(10), len(letters)): |
| 57 | mapping = dict(zip(letters_list, perm)) |
| 58 | |
| 59 | # Check if any first letter is assigned zero |
| 60 | if any(mapping[letter] == 0 for letter in first_letters): |
| 61 | continue |
| 62 | |
| 63 | # Calculate left side sum |
| 64 | left_sum = 0 |
| 65 | for word in left_sides: |
| 66 | num = 0 |
| 67 | for letter in word: |
| 68 | num = num * 10 + mapping[letter] |
| 69 | left_sum += num |
| 70 | |
| 71 | # Calculate right side value |
| 72 | right_num = 0 |
| 73 | for letter in right_side: |
| 74 | right_num = right_num * 10 + mapping[letter] |
| 75 | |
| 76 | # Check if equation is satisfied |
| 77 | if left_sum == right_num: |
| 78 | return mapping |
| 79 | |
| 80 | # Edge Case: No valid solution found |
| 81 | return None |
| 82 | |
| 83 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No addends on left side, No letters in puzzle, More than 10 unique letters, Permutations of digits, First letter assigned zero, No valid solution found |