| 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 to try different digit assignments for letters, respecting: |
| 12 | - Each letter maps to a unique digit |
| 13 | - Leading digits cannot be zero |
| 14 | - The mathematical equation must be satisfied |
| 15 | """ |
| 16 | # Edge Case: Empty or None puzzle |
| 17 | if not puzzle: |
| 18 | return None |
| 19 | |
| 20 | # Parse the puzzle |
| 21 | parts = puzzle.replace("==", "=").replace(" ", "").split("=") |
| 22 | |
| 23 | # Edge Case: Invalid puzzle format (no equals sign or too many parts) |
| 24 | if len(parts) != 2: |
| 25 | return None |
| 26 | |
| 27 | left_side, right_side = parts[0], parts[1] |
| 28 | |
| 29 | # Extract all words (addition terms and result) |
| 30 | addition_terms = left_side.split("+") |
| 31 | result_term = right_side |
| 32 | |
| 33 | # Edge Case: No addition terms |
| 34 | if not addition_terms or not result_term: |
| 35 | return None |
| 36 | |
| 37 | # Get all unique letters |
| 38 | all_letters = set() |
| 39 | for term in addition_terms + [result_term]: |
| 40 | all_letters.update(term) |
| 41 | |
| 42 | # Edge Case: Too many unique letters (more than 10) |
| 43 | if len(all_letters) > 10: |
| 44 | return None |
| 45 | |
| 46 | # Get leading letters (first letter of each word) |
| 47 | leading_letters = {word[0] for word in addition_terms + [result_term]} |
| 48 | |
| 49 | # Convert to lists for indexing |
| 50 | letters_list = list(all_letters) |
| 51 | |
| 52 | def word_to_number(word: str, mapping: dict) -> int: |
| 53 | """Convert a word to a number using the given letter-to-digit mapping.""" |
| 54 | return int(''.join(str(mapping[char]) for char in word)) |
| 55 | |
| 56 | def is_valid_solution(mapping: dict) -> bool: |
| 57 | """Check if the current mapping satisfies the puzzle equation.""" |
| 58 | # Check if all letters are mapped |
| 59 | for letter in all_letters: |
| 60 | if letter not in mapping: |
| 61 | return False |
| 62 | |
| 63 | # Check leading digit constraint |
| 64 | for letter in leading_letters: |
| 65 | if mapping[letter] == 0: |
| 66 | return False |
| 67 | |
| 68 | # Calculate sum of addition terms |
| 69 | total = 0 |
| 70 | for term in addition_terms: |
| 71 | total += word_to_number(term, mapping) |
| 72 | |
| 73 | # Check if it equals the result |
| 74 | return total == word_to_number(result_term, mapping) |
| 75 | |
| 76 | def backtrack(index: int, mapping: dict, used_digits: set) -> dict | None: |
| 77 | """ |
| 78 | Recursively try digit assignments for letters. |
| 79 | |
| 80 | Args: |
| 81 | index: Current index in letters_list |
| 82 | mapping: Current letter-to-digit mapping |
| 83 | used_digits: Set of digits already used |
| 84 | |
| 85 | Returns: |
| 86 | A valid mapping if found, otherwise None |
| 87 | """ |
| 88 | # Base case: all letters have been assigned |
| 89 | if index == len(letters_list): |
| 90 | if is_valid_solution(mapping): |
| 91 | return mapping.copy() |
| 92 | return None |
| 93 | |
| 94 | letter = letters_list[index] |
| 95 | |
| 96 | # Try each digit from 0 to 9 |
| 97 | for digit in range(10): |
| 98 | # Skip if digit is already used |
| 99 | if digit in used_digits: |
| 100 | continue |
| 101 | |
| 102 | # Skip if this is a leading letter and digit is 0 |
| 103 | if letter in leading_letters and digit == 0: |
| 104 | continue |
| 105 | |
| 106 | # Try this digit assignment |
| 107 | mapping[letter] = digit |
| 108 | used_digits.add(digit) |
| 109 | |
| 110 | # Recurse to next letter |
| 111 | result = backtrack(index + 1, mapping, used_digits) |
| 112 | if result is not None: |
| 113 | return result |
| 114 | |
| 115 | # Backtrack |
| 116 | del mapping[letter] |
| 117 | used_digits.remove(digit) |
| 118 | |
| 119 | return None |
| 120 | |
| 121 | # Start backtracking |
| 122 | solution = backtrack(0, {}, set()) |
| 123 | return solution |
| 124 | |
| 125 | # Handled Edge Cases: Empty/None puzzle, invalid format, no addition terms, too many unique letters (>10) |