| 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 | The function handles the following edge cases: |
| 12 | - Invalid puzzle format (no '==') |
| 13 | - Words with leading zeros |
| 14 | - Repeated letters getting different digit assignments |
| 15 | - No valid solutions |
| 16 | """ |
| 17 | # Edge Case: Invalid puzzle format (no '==') |
| 18 | if "==" not in puzzle: |
| 19 | return None |
| 20 | |
| 21 | # Parse the puzzle |
| 22 | left_side, right_side = puzzle.split("==") |
| 23 | left_parts = [part.strip() for part in left_side.split("+")] |
| 24 | right_part = right_side.strip() |
| 25 | |
| 26 | # Extract all unique letters |
| 27 | letters = set() |
| 28 | for part in left_parts + [right_part]: |
| 29 | letters.update(part) |
| 30 | |
| 31 | # Edge Case: No letters in puzzle |
| 32 | if not letters: |
| 33 | return None |
| 34 | |
| 35 | # Extract first letters (can't be zero) |
| 36 | first_letters = {word[0] for word in left_parts + [right_part]} |
| 37 | |
| 38 | # Convert letters to a list for indexing |
| 39 | letters_list = list(letters) |
| 40 | |
| 41 | # Try all possible digit assignments |
| 42 | from itertools import permutations |
| 43 | |
| 44 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 45 | if len(letters) > 10: |
| 46 | return None |
| 47 | |
| 48 | # Try all permutations of digits for the letters |
| 49 | for perm in permutations(range(10), len(letters)): |
| 50 | mapping = dict(zip(letters_list, perm)) |
| 51 | |
| 52 | # Edge Case: Leading zeros |
| 53 | if any(mapping[first_letter] == 0 for first_letter in first_letters): |
| 54 | continue |
| 55 | |
| 56 | # Calculate values of words |
| 57 | left_values = [] |
| 58 | for word in left_parts: |
| 59 | value = 0 |
| 60 | for char in word: |
| 61 | value = value * 10 + mapping[char] |
| 62 | left_values.append(value) |
| 63 | |
| 64 | right_value = 0 |
| 65 | for char in right_part: |
| 66 | right_value = right_value * 10 + mapping[char] |
| 67 | |
| 68 | # Check if the equation is satisfied |
| 69 | if sum(left_values) == right_value: |
| 70 | return mapping |
| 71 | |
| 72 | # Edge Case: No valid solution found |
| 73 | return None |
| 74 | # Handled Edge Cases: Invalid puzzle format (no '=='), Words with leading zeros, Repeated letters getting different digit assignments, No valid solutions, More than 10 unique letters" |