| 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 | left_side, right_side = parts[0], parts[1] |
| 27 | |
| 28 | # Split the left side by '+' to get addends |
| 29 | addends = left_side.split("+") |
| 30 | |
| 31 | # Edge Case: No addends on the left side |
| 32 | if not addends or not all(addends): |
| 33 | return None |
| 34 | |
| 35 | # Edge Case: Empty right side |
| 36 | if not right_side: |
| 37 | return None |
| 38 | |
| 39 | # Extract all unique letters |
| 40 | letters = set() |
| 41 | for part in addends + [right_side]: |
| 42 | letters.update(part) |
| 43 | |
| 44 | # Edge Case: No letters in puzzle |
| 45 | if not letters: |
| 46 | return None |
| 47 | |
| 48 | # Extract first letters (can't be zero) |
| 49 | first_letters = {word[0] for word in addends + [right_side]} |
| 50 | |
| 51 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 52 | if len(letters) > 10: |
| 53 | return None |
| 54 | |
| 55 | # Convert letters to a list for indexing |
| 56 | letters_list = list(letters) |
| 57 | |
| 58 | def is_valid_solution(mapping): |
| 59 | """Check if the current mapping is a valid solution.""" |
| 60 | # Check if any first letter is mapped to 0 |
| 61 | for letter in first_letters: |
| 62 | if mapping[letter] == 0: |
| 63 | return False |
| 64 | |
| 65 | # Convert words to numbers using the mapping |
| 66 | try: |
| 67 | addend_values = [] |
| 68 | for addend in addends: |
| 69 | value = 0 |
| 70 | for char in addend: |
| 71 | value = value * 10 + mapping[char] |
| 72 | addend_values.append(value) |
| 73 | |
| 74 | right_value = 0 |
| 75 | for char in right_side: |
| 76 | right_value = right_value * 10 + mapping[char] |
| 77 | |
| 78 | # Check if the sum of addends equals the right side |
| 79 | return sum(addend_values) == right_value |
| 80 | except KeyError: |
| 81 | # If a letter isn't in mapping, it's not a complete solution yet |
| 82 | return False |
| 83 | |
| 84 | def backtrack(index, mapping, used_digits): |
| 85 | """Backtracking function to find a valid digit assignment.""" |
| 86 | # Base case: all letters have been assigned |
| 87 | if index == len(letters_list): |
| 88 | if is_valid_solution(mapping): |
| 89 | return mapping.copy() |
| 90 | return None |
| 91 | |
| 92 | letter = letters_list[index] |
| 93 | |
| 94 | # Try each digit from 0 to 9 |
| 95 | for digit in range(10): |
| 96 | # Skip if digit is already used |
| 97 | if digit in used_digits: |
| 98 | continue |
| 99 | |
| 100 | # Assign the digit to the letter |
| 101 | mapping[letter] = digit |
| 102 | used_digits.add(digit) |
| 103 | |
| 104 | # Recurse to the next letter |
| 105 | result = backtrack(index + 1, mapping, used_digits) |
| 106 | if result is not None: |
| 107 | return result |
| 108 | |
| 109 | # Backtrack: remove the assignment |
| 110 | used_digits.remove(digit) |
| 111 | |
| 112 | # If we've tried all digits and none worked, remove the letter from mapping |
| 113 | if letter in mapping: |
| 114 | del mapping[letter] |
| 115 | |
| 116 | return None |
| 117 | |
| 118 | # Start backtracking with an empty mapping and used digits set |
| 119 | solution = backtrack(0, {}, set()) |
| 120 | |
| 121 | # Edge Case: No solution found |
| 122 | return solution |
| 123 | |
| 124 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No addends, Empty right side, No letters, More than 10 unique letters |