| 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 | # Split the left side by '+' to get the addends |
| 24 | addends = [term.strip() for term in left_side.split("+")] |
| 25 | |
| 26 | # Edge Case: Empty puzzle or missing components |
| 27 | if not addends or not right_side: |
| 28 | return None |
| 29 | |
| 30 | # Get all unique letters in the puzzle |
| 31 | letters = set() |
| 32 | for term in addends + [right_side]: |
| 33 | letters.update(term) |
| 34 | |
| 35 | # Edge Case: No letters in puzzle |
| 36 | if not letters: |
| 37 | return None |
| 38 | |
| 39 | # Get the first letter of each term (can't be zero) |
| 40 | first_letters = {term[0] for term in addends + [right_side]} |
| 41 | |
| 42 | # Edge Case: Invalid characters in puzzle (non-alphabetic) |
| 43 | if not all(c.isalpha() for c in letters): |
| 44 | return None |
| 45 | |
| 46 | # Convert letters to a list for indexing |
| 47 | letters_list = list(letters) |
| 48 | n = len(letters_list) |
| 49 | |
| 50 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 51 | if n > 10: |
| 52 | return None |
| 53 | |
| 54 | # Try all permutations of digits for the letters |
| 55 | from itertools import permutations |
| 56 | |
| 57 | # Edge Case: Handle single letter terms |
| 58 | for perm in permutations(range(10), n): |
| 59 | # Create a mapping from letters to digits |
| 60 | mapping = dict(zip(letters_list, perm)) |
| 61 | |
| 62 | # Check if any first letter is assigned zero |
| 63 | if any(mapping[letter] == 0 for letter in first_letters): |
| 64 | continue |
| 65 | |
| 66 | # Convert words to numbers using the mapping |
| 67 | try: |
| 68 | addend_values = [] |
| 69 | for addend in addends: |
| 70 | value = 0 |
| 71 | for char in addend: |
| 72 | value = value * 10 + mapping[char] |
| 73 | addend_values.append(value) |
| 74 | |
| 75 | right_value = 0 |
| 76 | for char in right_side: |
| 77 | right_value = right_value * 10 + mapping[char] |
| 78 | |
| 79 | # Check if the sum is correct |
| 80 | if sum(addend_values) == right_value: |
| 81 | return mapping |
| 82 | except KeyError: |
| 83 | # Edge Case: Mapping is incomplete (shouldn't happen with proper permutation) |
| 84 | continue |
| 85 | |
| 86 | # Edge Case: No valid solution found |
| 87 | return None |
| 88 | |
| 89 | # Handled Edge Cases: Empty puzzle or missing components, No letters in puzzle, Invalid characters in puzzle (non-alphabetic), More than 10 unique letters (impossible to assign unique digits), Mapping is incomplete, No valid solution found |