| 1 | 1 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 2 | """ |
| 3 | Solve an alphametics puzzle. |
| 4 | |
| 5 | Args: |
| 6 | puzzle (str): A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 7 | |
| 8 | Returns: |
| 9 | dict[str, int] | None: A dictionary mapping letters to digits that solves the puzzle, |
| 10 | or None if no solution exists |
| 11 | |
| 12 | The function uses backtracking to try different digit assignments to letters, |
| 13 | respecting the constraints that each letter maps to a unique digit and no |
| 14 | leading digit can be zero. |
| 15 | |
| 16 | Handled Edge Cases: Empty puzzle string, puzzle with no alphabetic characters, |
| 17 | puzzle with too many unique letters (>10), invalid puzzle format |
| 18 | """ |
| 19 | # Edge Case: Empty puzzle string |
| 20 | if not puzzle: |
| 21 | return None |
| 22 | |
| 23 | # Parse the puzzle into words |
| 24 | # Remove spaces and split by '==' to separate left and right sides |
| 25 | parts = puzzle.replace(" ", "").split("==") |
| 26 | |
| 27 | # Edge Case: Invalid puzzle format (no '==' or more than one '==') |
| 28 | if len(parts) != 2: |
| 29 | return None |
| 30 | |
| 31 | left_side, right_side = parts[0], parts[1] |
| 32 | |
| 33 | # Split left side by '+' to get addends |
| 34 | addends = left_side.split("+") |
| 35 | |
| 36 | # Edge Case: No addends on left side |
| 37 | if not addends or not all(addends): |
| 38 | return None |
| 39 | |
| 40 | # Edge Case: Empty right side |
| 41 | if not right_side: |
| 42 | return None |
| 43 | |
| 44 | # Collect all unique letters |
| 45 | letters = set() |
| 46 | for part in addends + [right_side]: |
| 47 | for char in part: |
| 48 | if char.isalpha(): |
| 49 | letters.add(char) |
| 50 | |
| 51 | # Edge Case: No letters in puzzle |
| 52 | if not letters: |
| 53 | return None |
| 54 | |
| 55 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 56 | if len(letters) > 10: |
| 57 | return None |
| 58 | |
| 59 | # Identify first letters (can't be zero) |
| 60 | first_letters = {word[0] for word in addends + [right_side] if word} |
| 61 | |
| 62 | # Convert set to list for indexing |
| 63 | letters_list = list(letters) |
| 64 | |
| 65 | def is_valid_solution(mapping): |
| 66 | """Check if the current mapping is a valid solution to the puzzle.""" |
| 67 | # Check for leading zeros |
| 68 | for word in addends + [right_side]: |
| 69 | if len(word) > 1 and mapping[word[0]] == 0: |
| 70 | return False |
| 71 | |
| 72 | # Calculate left side sum |
| 73 | left_sum = 0 |
| 74 | for word in addends: |
| 75 | num = 0 |
| 76 | for char in word: |
| 77 | num = num * 10 + mapping[char] |
| 78 | left_sum += num |
| 79 | |
| 80 | # Calculate right side value |
| 81 | right_num = 0 |
| 82 | for char in right_side: |
| 83 | right_num = right_num * 10 + mapping[char] |
| 84 | |
| 85 | return left_sum == right_num |
| 86 | |
| 87 | def backtrack(index, mapping, used_digits): |
| 88 | """Backtracking function to try digit assignments.""" |
| 89 | # Base case: all letters have been assigned |
| 90 | if index == len(letters_list): |
| 91 | if is_valid_solution(mapping): |
| 92 | return mapping.copy() |
| 93 | return None |
| 94 | |
| 95 | letter = letters_list[index] |
| 96 | |
| 97 | # Try each digit from 0-9 |
| 98 | for digit in range(10): |
| 99 | # Skip if digit already used |
| 100 | if digit in used_digits: |
| 101 | continue |
| 102 | |
| 103 | # Skip if this is a first letter and digit is 0 |
| 104 | if letter in first_letters and digit == 0: |
| 105 | continue |
| 106 | |
| 107 | # Try this digit assignment |
| 108 | mapping[letter] = digit |
| 109 | used_digits.add(digit) |
| 110 | |
| 111 | # Recurse to next letter |
| 112 | result = backtrack(index + 1, mapping, used_digits) |
| 113 | if result is not None: |
| 114 | return result |
| 115 | |
| 116 | # Backtrack |
| 117 | del mapping[letter] |
| 118 | used_digits.remove(digit) |
| 119 | |
| 120 | return None |
| 121 | |
| 122 | # Start backtracking with empty mapping |
| 123 | solution = backtrack(0, {}, set()) |
| 124 | return solution |
| 125 | |
| 126 | # Handled Edge Cases: Empty puzzle string, puzzle with no alphabetic characters, |
| 127 | # puzzle with too many unique letters (>10), invalid puzzle format, |
| 128 | # no addends on left side, empty right side |