| 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_expression = parts[0] |
| 28 | |
| 29 | # Extract operators and operands from the left side |
| 30 | import re |
| 31 | # Find all operators (+, *, -) |
| 32 | operators = re.findall(r'[+*-]', left_expression) |
| 33 | # Split by operators to get operands |
| 34 | operands = re.split(r'[+*-]', left_expression) |
| 35 | |
| 36 | # Edge Case: No terms on the left side |
| 37 | if not operands or not operands[0]: |
| 38 | return None |
| 39 | |
| 40 | left_parts = operands |
| 41 | |
| 42 | # Extract all unique letters |
| 43 | letters = set() |
| 44 | for part in left_parts + [right_side]: |
| 45 | letters.update(part) |
| 46 | |
| 47 | # Edge Case: No letters in puzzle |
| 48 | if not letters: |
| 49 | return None |
| 50 | |
| 51 | # Extract first letters (can't be zero) |
| 52 | first_letters = {word[0] for word in left_parts + [right_side]} |
| 53 | |
| 54 | # Convert letters to a list for indexing |
| 55 | letters_list = list(letters) |
| 56 | |
| 57 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 58 | if len(letters_list) > 10: |
| 59 | return None |
| 60 | |
| 61 | # Try all permutations of digits for the letters |
| 62 | from itertools import permutations |
| 63 | |
| 64 | # Edge Case: Handle permutation generation for different numbers of letters |
| 65 | for perm in permutations(range(10), len(letters_list)): |
| 66 | mapping = dict(zip(letters_list, perm)) |
| 67 | |
| 68 | # Check if any first letter is assigned zero |
| 69 | if any(mapping[letter] == 0 for letter in first_letters): |
| 70 | continue |
| 71 | |
| 72 | # Calculate the value of the left side based on operators |
| 73 | if not operators: |
| 74 | # Single term on left side |
| 75 | left_value = 0 |
| 76 | for letter in left_parts[0]: |
| 77 | left_value = left_value * 10 + mapping[letter] |
| 78 | else: |
| 79 | # Multiple terms with operators |
| 80 | # Convert each word to number |
| 81 | numbers = [] |
| 82 | for word in left_parts: |
| 83 | number = 0 |
| 84 | for letter in word: |
| 85 | number = number * 10 + mapping[letter] |
| 86 | numbers.append(number) |
| 87 | |
| 88 | # Apply operators in order (left to right) |
| 89 | left_value = numbers[0] |
| 90 | for i, op in enumerate(operators): |
| 91 | if op == '+': |
| 92 | left_value += numbers[i + 1] |
| 93 | elif op == '*': |
| 94 | left_value *= numbers[i + 1] |
| 95 | elif op == '-': |
| 96 | left_value -= numbers[i + 1] |
| 97 | |
| 98 | # Calculate the right side value |
| 99 | right_value = 0 |
| 100 | for letter in right_side: |
| 101 | right_value = right_value * 10 + mapping[letter] |
| 102 | |
| 103 | # Check if the equation is satisfied |
| 104 | if left_value == right_value: |
| 105 | return mapping |
| 106 | |
| 107 | # Edge Case: No valid solution found |
| 108 | return None |
| 109 | |
| 110 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on left side, No letters in puzzle, More than 10 unique letters, First letters assigned zero, No valid solution found |