| 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 if a solution exists, None otherwise |
| 10 | """ |
| 11 | # Edge Case: Empty or None puzzle |
| 12 | if not puzzle: |
| 13 | return None |
| 14 | |
| 15 | # Parse the puzzle to identify operators and operands |
| 16 | # First, normalize the equation |
| 17 | normalized = puzzle.replace("==", "=").replace(" ", "") |
| 18 | |
| 19 | # Split by equals sign |
| 20 | parts = normalized.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 | # Parse left side to identify operators and operands |
| 27 | left_side = parts[0] |
| 28 | right_side = parts[1] |
| 29 | |
| 30 | # Identify the operator and split operands |
| 31 | if "*" in left_side: |
| 32 | operands = left_side.split("*") |
| 33 | operator = "*" |
| 34 | elif "-" in left_side: |
| 35 | operands = left_side.split("-") |
| 36 | operator = "-" |
| 37 | else: # Default to addition |
| 38 | operands = left_side.split("+") |
| 39 | operator = "+" |
| 40 | |
| 41 | # Edge Case: No operands |
| 42 | if not operands: |
| 43 | return None |
| 44 | |
| 45 | # Extract all unique letters (only alphabetic characters) |
| 46 | letters = set() |
| 47 | for part in operands + [right_side]: |
| 48 | for char in part: |
| 49 | if char.isalpha(): |
| 50 | letters.add(char) |
| 51 | |
| 52 | # Edge Case: No letters in puzzle |
| 53 | if not letters: |
| 54 | return None |
| 55 | |
| 56 | # Extract first letters of multi-digit words (can't be zero) |
| 57 | first_letters = set() |
| 58 | for part in operands + [right_side]: |
| 59 | if part and part[0].isalpha() and len(part) > 1: |
| 60 | first_letters.add(part[0]) |
| 61 | |
| 62 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 63 | if len(letters) > 10: |
| 64 | return None |
| 65 | |
| 66 | letters = list(letters) |
| 67 | |
| 68 | # Generate all possible digit assignments |
| 69 | from itertools import permutations |
| 70 | |
| 71 | # Try all permutations of digits for the letters |
| 72 | for perm in permutations(range(10), len(letters)): |
| 73 | mapping = dict(zip(letters, perm)) |
| 74 | |
| 75 | # Edge Case: Leading zero in any word |
| 76 | if any(mapping.get(first, 0) == 0 for first in first_letters): |
| 77 | continue |
| 78 | |
| 79 | # Calculate values of operands |
| 80 | operand_values = [] |
| 81 | for operand in operands: |
| 82 | # If operand is a pure number, use it directly |
| 83 | if operand.isdigit(): |
| 84 | operand_values.append(int(operand)) |
| 85 | else: |
| 86 | # Calculate value from letters |
| 87 | value = 0 |
| 88 | for char in operand: |
| 89 | if char.isalpha(): |
| 90 | value = value * 10 + mapping[char] |
| 91 | else: # Handle case where operand might have digits |
| 92 | value = value * 10 + int(char) |
| 93 | operand_values.append(value) |
| 94 | |
| 95 | # Calculate value of right side |
| 96 | if right_side.isdigit(): |
| 97 | right_value = int(right_side) |
| 98 | else: |
| 99 | right_value = 0 |
| 100 | for char in right_side: |
| 101 | if char.isalpha(): |
| 102 | right_value = right_value * 10 + mapping[char] |
| 103 | else: # Handle case where right side might have digits |
| 104 | right_value = right_value * 10 + int(char) |
| 105 | |
| 106 | # Check if equation is satisfied based on operator |
| 107 | if operator == "+": |
| 108 | if sum(operand_values) == right_value: |
| 109 | return mapping |
| 110 | elif operator == "-": |
| 111 | # For subtraction, we assume format like "AB - C == D" |
| 112 | if len(operand_values) == 2 and operand_values[0] - operand_values[1] == right_value: |
| 113 | return mapping |
| 114 | elif operator == "*": |
| 115 | # For multiplication, we assume format like "AB * C == DE" |
| 116 | if len(operand_values) == 2 and operand_values[0] * operand_values[1] == right_value: |
| 117 | return mapping |
| 118 | |
| 119 | # Edge Case: No solution found |
| 120 | return None |
| 121 | # 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 solution found |