| 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 | The function uses backtracking with constraint propagation to find a valid digit assignment |
| 12 | where each letter represents a unique digit, no leading digit is zero, and the equation holds. |
| 13 | |
| 14 | Handled Edge Cases: |
| 15 | - Invalid puzzle format (no '==') |
| 16 | - Empty puzzle string |
| 17 | - Words with no letters |
| 18 | - Single word equations |
| 19 | - Leading zero constraints |
| 20 | - No valid solutions |
| 21 | """ |
| 22 | # Edge Case: Empty puzzle string |
| 23 | if not puzzle: |
| 24 | return None |
| 25 | |
| 26 | # Parse the puzzle |
| 27 | # Edge Case: Invalid puzzle format (no '==') |
| 28 | if "==" not in puzzle: |
| 29 | return None |
| 30 | |
| 31 | left_side, right_side = puzzle.split("==") |
| 32 | left_words = [word.strip() for word in left_side.split("+")] |
| 33 | right_word = right_side.strip() |
| 34 | |
| 35 | # Edge Case: No words in equation |
| 36 | if not left_words or not right_word: |
| 37 | return None |
| 38 | |
| 39 | # Extract all unique letters |
| 40 | letters = set() |
| 41 | for word in left_words + [right_word]: |
| 42 | letters.update(word) |
| 43 | |
| 44 | # Edge Case: No letters in puzzle |
| 45 | if not letters: |
| 46 | return None |
| 47 | |
| 48 | letters = list(letters) |
| 49 | |
| 50 | # Identify first letters (can't be zero) |
| 51 | first_letters = {word[0] for word in left_words + [right_word]} |
| 52 | |
| 53 | # Edge Case: Single word on left side |
| 54 | if len(left_words) == 1 and left_words[0] == right_word: |
| 55 | # This would mean A == A, which is trivially true but not a valid puzzle |
| 56 | return None |
| 57 | |
| 58 | def word_to_number(word, mapping): |
| 59 | """Convert a word to a number using the given mapping.""" |
| 60 | return int(''.join(str(mapping[char]) for char in word)) |
| 61 | |
| 62 | def is_valid_mapping(mapping): |
| 63 | """Check if the current mapping satisfies the equation.""" |
| 64 | # Check for leading zeros |
| 65 | for word in left_words + [right_word]: |
| 66 | if len(word) > 1 and mapping[word[0]] == 0: |
| 67 | return False |
| 68 | |
| 69 | left_sum = sum(word_to_number(word, mapping) for word in left_words) |
| 70 | right_value = word_to_number(right_word, mapping) |
| 71 | return left_sum == right_value |
| 72 | |
| 73 | def backtrack(index, mapping, used_digits): |
| 74 | """Backtracking function to find a valid mapping.""" |
| 75 | # Base case: all letters have been assigned |
| 76 | if index == len(letters): |
| 77 | if is_valid_mapping(mapping): |
| 78 | return mapping.copy() |
| 79 | return None |
| 80 | |
| 81 | letter = letters[index] |
| 82 | |
| 83 | # Try each digit from 0-9 |
| 84 | for digit in range(10): |
| 85 | # Skip if digit is already used |
| 86 | if digit in used_digits: |
| 87 | continue |
| 88 | |
| 89 | # Skip if this is a first letter and digit is 0 |
| 90 | if letter in first_letters and digit == 0: |
| 91 | continue |
| 92 | |
| 93 | # Assign the digit |
| 94 | mapping[letter] = digit |
| 95 | used_digits.add(digit) |
| 96 | |
| 97 | # Recurse |
| 98 | result = backtrack(index + 1, mapping, used_digits) |
| 99 | if result is not None: |
| 100 | return result |
| 101 | |
| 102 | # Backtrack |
| 103 | del mapping[letter] |
| 104 | used_digits.remove(digit) |
| 105 | |
| 106 | return None |
| 107 | |
| 108 | # Start backtracking |
| 109 | result = backtrack(0, {}, set()) |
| 110 | return result |
| 111 | |
| 112 | # Handled Edge Cases: |
| 113 | # - Invalid puzzle format (no '==') |
| 114 | # - Empty puzzle string |
| 115 | # - Words with no letters |
| 116 | # - Single word equations |
| 117 | # - Leading zero constraints |
| 118 | # - No valid solutions |