| 1 | 1 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 2 | # Parse the puzzle |
| 3 | parts = puzzle.replace("==", "=").replace(" ", "").split("=") |
| 4 | if len(parts) != 2: |
| 5 | return None |
| 6 | |
| 7 | right_side = parts[1] |
| 8 | left_sides = parts[0].replace("+", " ").split() |
| 9 | |
| 10 | # Edge Case: Invalid puzzle format |
| 11 | if not left_sides: |
| 12 | return None |
| 13 | |
| 14 | # Collect all unique letters |
| 15 | letters = set() |
| 16 | for part in left_sides + [right_side]: |
| 17 | letters.update(part) |
| 18 | |
| 19 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 20 | if len(letters) > 10: |
| 21 | return None |
| 22 | |
| 23 | # Collect first letters (can't be zero) |
| 24 | first_letters = {word[0] for word in left_sides + [right_side]} |
| 25 | |
| 26 | # Edge Case: Single letter words that are first letters |
| 27 | # This is handled by the constraint that first letters can't be zero |
| 28 | |
| 29 | letters = list(letters) |
| 30 | |
| 31 | # Generate all possible digit assignments |
| 32 | def permute_digits(available_digits, letter_index): |
| 33 | if letter_index == len(letters): |
| 34 | # Check if this assignment works |
| 35 | return check_solution({letters[i]: available_digits[i] for i in range(len(letters))}) |
| 36 | |
| 37 | for i in range(len(available_digits)): |
| 38 | # Try assigning available_digits[i] to letters[letter_index] |
| 39 | result = permute_digits(available_digits[:i] + available_digits[i+1:], letter_index + 1) |
| 40 | if result: |
| 41 | return result |
| 42 | return None |
| 43 | |
| 44 | def check_solution(mapping): |
| 45 | # Edge Case: Leading zeros |
| 46 | for letter in first_letters: |
| 47 | if mapping[letter] == 0: |
| 48 | return None |
| 49 | |
| 50 | # Calculate left side sum |
| 51 | left_sum = 0 |
| 52 | for word in left_sides: |
| 53 | num = 0 |
| 54 | for char in word: |
| 55 | num = num * 10 + mapping[char] |
| 56 | left_sum += num |
| 57 | |
| 58 | # Calculate right side value |
| 59 | right_num = 0 |
| 60 | for char in right_side: |
| 61 | right_num = right_num * 10 + mapping[char] |
| 62 | |
| 63 | # Edge Case: Check if equation is satisfied |
| 64 | if left_sum == right_num: |
| 65 | return mapping |
| 66 | return None |
| 67 | |
| 68 | # Edge Case: No solution exists |
| 69 | # This is handled by returning None if no valid permutation is found |
| 70 | |
| 71 | # Start permutation with digits 0-9 |
| 72 | import itertools |
| 73 | for perm in itertools.permutations(range(10), len(letters)): |
| 74 | mapping = {letters[i]: perm[i] for i in range(len(letters))} |
| 75 | # Check leading zeros first for efficiency |
| 76 | if any(mapping[letter] == 0 for letter in first_letters): |
| 77 | continue |
| 78 | result = check_solution(mapping) |
| 79 | if result: |
| 80 | return result |
| 81 | |
| 82 | return None |
| 83 | # Handled Edge Cases: Invalid puzzle format, more than 10 unique letters, leading zeros, no solution exists |