| 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(" ", "") |
| 21 | |
| 22 | # Edge Case: Invalid puzzle format (no equals sign) |
| 23 | if "=" not in parts: |
| 24 | return None |
| 25 | |
| 26 | left_part, right_side = parts.split("=", 1) |
| 27 | |
| 28 | # Determine the operator |
| 29 | if "+" in left_part: |
| 30 | operator = "+" |
| 31 | left_sides = left_part.split("+") |
| 32 | elif "-" in left_part: |
| 33 | operator = "-" |
| 34 | left_sides = left_part.split("-") |
| 35 | elif "*" in left_part: |
| 36 | operator = "*" |
| 37 | left_sides = left_part.split("*") |
| 38 | else: |
| 39 | # Single term on left side |
| 40 | operator = None |
| 41 | left_sides = [left_part] |
| 42 | |
| 43 | # Edge Case: No terms on the left side |
| 44 | if not left_sides: |
| 45 | return None |
| 46 | |
| 47 | # Extract all unique letters |
| 48 | letters = set() |
| 49 | for part in left_sides + [right_side]: |
| 50 | letters.update(part) |
| 51 | |
| 52 | # Edge Case: No letters in puzzle |
| 53 | if not letters: |
| 54 | return None |
| 55 | |
| 56 | # Extract first letters (can't be zero) |
| 57 | first_letters = {word[0] for word in left_sides + [right_side]} |
| 58 | |
| 59 | # Convert to sorted list for consistent ordering |
| 60 | letters = list(letters) |
| 61 | |
| 62 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 63 | if len(letters) > 10: |
| 64 | return None |
| 65 | |
| 66 | # Try all possible digit assignments |
| 67 | from itertools import permutations |
| 68 | |
| 69 | # Generate all possible digit permutations for the letters |
| 70 | for perm in permutations(range(10), len(letters)): |
| 71 | mapping = dict(zip(letters, perm)) |
| 72 | |
| 73 | # Edge Case: Leading zero in any number |
| 74 | if any(mapping[first_letter] == 0 for first_letter in first_letters): |
| 75 | continue |
| 76 | |
| 77 | # Calculate values of left side terms |
| 78 | left_values = [] |
| 79 | for word in left_sides: |
| 80 | value = 0 |
| 81 | for char in word: |
| 82 | value = value * 10 + mapping[char] |
| 83 | left_values.append(value) |
| 84 | |
| 85 | # Calculate value of right side |
| 86 | right_value = 0 |
| 87 | for char in right_side: |
| 88 | right_value = right_value * 10 + mapping[char] |
| 89 | |
| 90 | # Check if the equation is satisfied based on operator |
| 91 | if operator == "+": |
| 92 | if sum(left_values) == right_value: |
| 93 | return mapping |
| 94 | elif operator == "-": |
| 95 | # For subtraction, we assume the format is "A - B == C" meaning A - B = C |
| 96 | if len(left_values) == 2 and left_values[0] - left_values[1] == right_value: |
| 97 | return mapping |
| 98 | elif operator == "*": |
| 99 | # For multiplication, we assume the format is "A * B == C" meaning A * B = C |
| 100 | if len(left_values) == 2 and left_values[0] * left_values[1] == right_value: |
| 101 | return mapping |
| 102 | else: |
| 103 | # Single term on left side, should equal right side |
| 104 | if len(left_values) == 1 and left_values[0] == 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, Leading zero in any number, No valid solution found |