| 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 |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | left_side, right_side = parts[0], parts[1] |
| 27 | |
| 28 | # Extract terms (addends) from the left side |
| 29 | terms = left_side.replace("+", " ").split() |
| 30 | |
| 31 | # Edge Case: No terms on left side |
| 32 | if not terms: |
| 33 | return None |
| 34 | |
| 35 | # Collect all unique letters |
| 36 | letters = set() |
| 37 | for term in terms + [right_side]: |
| 38 | letters.update(term) |
| 39 | |
| 40 | # Edge Case: No letters in puzzle |
| 41 | if not letters: |
| 42 | return None |
| 43 | |
| 44 | # Identify first letters (can't be zero) |
| 45 | first_letters = {term[0] for term in terms + [right_side]} |
| 46 | |
| 47 | # Convert letters to a list for consistent ordering |
| 48 | letters = list(letters) |
| 49 | |
| 50 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 51 | if len(letters) > 10: |
| 52 | return None |
| 53 | |
| 54 | # Helper function to convert a word to a number based on a letter-to-digit mapping |
| 55 | def word_to_number(word, mapping): |
| 56 | return int(''.join(str(mapping[letter]) for letter in word)) |
| 57 | |
| 58 | # Helper function to check if a mapping is valid |
| 59 | def is_valid_mapping(mapping): |
| 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 | # Calculate the sum of the terms |
| 66 | total = 0 |
| 67 | for term in terms: |
| 68 | total += word_to_number(term, mapping) |
| 69 | |
| 70 | # Check if it equals the right side |
| 71 | return total == word_to_number(right_side, mapping) |
| 72 | |
| 73 | # Backtracking function to try digit assignments |
| 74 | def backtrack(index, used_digits, 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 to 9 |
| 84 | for digit in range(10): |
| 85 | # Skip if digit is already used |
| 86 | if digit in used_digits: |
| 87 | continue |
| 88 | |
| 89 | # Assign the digit to the letter |
| 90 | mapping[letter] = digit |
| 91 | used_digits.add(digit) |
| 92 | |
| 93 | # Recurse to the next letter |
| 94 | result = backtrack(index + 1, used_digits, mapping) |
| 95 | if result is not None: |
| 96 | return result |
| 97 | |
| 98 | # Backtrack: remove the assignment |
| 99 | used_digits.remove(digit) |
| 100 | del mapping[letter] |
| 101 | |
| 102 | return None |
| 103 | |
| 104 | # Start the backtracking search |
| 105 | solution = backtrack(0, set(), {}) |
| 106 | return solution |
| 107 | |
| 108 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on left side, No letters in puzzle, More than 10 unique letters |