| 1 | from itertools import permutations |
| 2 | import re |
| 3 | |
| 1 | 4 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 5 | """ |
| 6 | Solve an alphametics puzzle. |
| 7 | |
| 8 | Args: |
| 9 | puzzle: A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 10 | |
| 11 | Returns: |
| 12 | A dictionary mapping letters to digits that solves the puzzle, or None if no solution exists. |
| 13 | |
| 14 | Example: |
| 15 | >>> solve("SEND + MORE == MONEY") |
| 16 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 17 | """ |
| 18 | # Edge Case: Empty or None puzzle |
| 19 | if not puzzle: |
| 20 | return None |
| 21 | |
| 22 | # Parse the puzzle - handle both == and =, and extract operators |
| 23 | puzzle = puzzle.replace("==", "=") |
| 24 | parts = puzzle.split("=") |
| 25 | |
| 26 | # Edge Case: Invalid puzzle format |
| 27 | if len(parts) != 2: |
| 28 | return None |
| 29 | |
| 30 | right_side = parts[1].strip() |
| 31 | left_expression = parts[0].strip() |
| 32 | |
| 33 | # Extract terms and operators from left side |
| 34 | # Handle both + and * operators |
| 35 | terms = re.findall(r'[A-Z]+', left_expression) |
| 36 | operators = re.findall(r'[+*]', left_expression) |
| 37 | |
| 38 | # Edge Case: No terms on the left side |
| 39 | if not terms: |
| 40 | return None |
| 41 | |
| 42 | # Get all unique letters |
| 43 | all_words = terms + [right_side] |
| 44 | letters = set("".join(all_words)) |
| 45 | |
| 46 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 47 | if len(letters) > 10: |
| 48 | return None |
| 49 | |
| 50 | # Get first letters (can't be zero) |
| 51 | first_letters = {word[0] for word in all_words if len(word) > 1} |
| 52 | |
| 53 | # Get all letters as a list for consistent ordering |
| 54 | all_letters = list(letters) |
| 55 | |
| 56 | # Try all digit permutations |
| 57 | for perm in permutations(range(10), len(letters)): |
| 58 | mapping = dict(zip(all_letters, perm)) |
| 59 | |
| 60 | # Edge Case: Leading zero |
| 61 | if any(mapping[letter] == 0 for letter in first_letters): |
| 62 | continue |
| 63 | |
| 64 | # Convert words to numbers using the mapping |
| 65 | term_values = [] |
| 66 | for term in terms: |
| 67 | number = 0 |
| 68 | for letter in term: |
| 69 | number = number * 10 + mapping[letter] |
| 70 | term_values.append(number) |
| 71 | |
| 72 | # Calculate right side value |
| 73 | right_value = 0 |
| 74 | for letter in right_side: |
| 75 | right_value = right_value * 10 + mapping[letter] |
| 76 | |
| 77 | # Calculate left side result based on operators |
| 78 | if not operators: |
| 79 | # Single term on left side |
| 80 | left_result = term_values[0] |
| 81 | else: |
| 82 | # Apply operations in order (left to right) |
| 83 | left_result = term_values[0] |
| 84 | for i, op in enumerate(operators): |
| 85 | if op == '+': |
| 86 | left_result += term_values[i + 1] |
| 87 | elif op == '*': |
| 88 | left_result *= term_values[i + 1] |
| 89 | |
| 90 | # Check if equation is satisfied |
| 91 | if left_result == right_value: |
| 92 | return mapping |
| 93 | |
| 94 | # Edge Case: No solution found |
| 95 | return None |
| 96 | |
| 97 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on the left side, More than 10 unique letters, Leading zero, No solution found |