| 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 | Edge Cases Handled: |
| 15 | - Invalid puzzle format (no '==') |
| 16 | - Empty puzzle |
| 17 | - Words with no letters |
| 18 | - Single word equations |
| 19 | - Leading zeros in results |
| 20 | """ |
| 21 | # Edge Case: Empty puzzle |
| 22 | if not puzzle: |
| 23 | return None |
| 24 | |
| 25 | # Parse the puzzle |
| 26 | # Edge Case: Invalid puzzle format (no '==') |
| 27 | if "==" not in puzzle: |
| 28 | return None |
| 29 | |
| 30 | left_side, right_side = puzzle.split("==") |
| 31 | left_words = [word.strip() for word in left_side.split("+")] |
| 32 | right_word = right_side.strip() |
| 33 | |
| 34 | # Edge Case: No words in equation |
| 35 | if not left_words or not right_word: |
| 36 | return None |
| 37 | |
| 38 | # Extract all unique letters |
| 39 | letters = set() |
| 40 | for word in left_words + [right_word]: |
| 41 | letters.update(word) |
| 42 | |
| 43 | # Edge Case: No letters in puzzle |
| 44 | if not letters: |
| 45 | return None |
| 46 | |
| 47 | # Identify first letters (can't be zero) |
| 48 | first_letters = {word[0] for word in left_words + [right_word]} |
| 49 | |
| 50 | # Convert to lists for indexing |
| 51 | letters = list(letters) |
| 52 | |
| 53 | def evaluate(assignment): |
| 54 | """Evaluate if current assignment satisfies the equation""" |
| 55 | # Edge Case: Not all letters assigned |
| 56 | for letter in letters: |
| 57 | if letter not in assignment: |
| 58 | return False |
| 59 | |
| 60 | left_sum = 0 |
| 61 | for word in left_words: |
| 62 | # Edge Case: Empty word |
| 63 | if not word: |
| 64 | continue |
| 65 | num = 0 |
| 66 | for char in word: |
| 67 | # Edge Case: Character not in assignment (should not happen in valid paths) |
| 68 | if char not in assignment: |
| 69 | return False |
| 70 | num = num * 10 + assignment[char] |
| 71 | left_sum += num |
| 72 | |
| 73 | right_num = 0 |
| 74 | for char in right_word: |
| 75 | # Edge Case: Character not in assignment (should not happen in valid paths) |
| 76 | if char not in assignment: |
| 77 | return False |
| 78 | right_num = right_num * 10 + assignment[char] |
| 79 | |
| 80 | return left_sum == right_num |
| 81 | |
| 82 | def is_valid_partial(assignment): |
| 83 | """Check if partial assignment could lead to valid solution""" |
| 84 | # Check leading zeros |
| 85 | for letter in first_letters: |
| 86 | if letter in assignment and assignment[letter] == 0: |
| 87 | return False |
| 88 | |
| 89 | # Check for duplicate digits |
| 90 | used_digits = set(assignment.values()) |
| 91 | if len(used_digits) != len(assignment): |
| 92 | return False |
| 93 | |
| 94 | return True |
| 95 | |
| 96 | def backtrack(assignment): |
| 97 | """Backtracking search for solution""" |
| 98 | # If we've assigned all letters, check if it's a solution |
| 99 | if len(assignment) == len(letters): |
| 100 | if evaluate(assignment): |
| 101 | return assignment.copy() |
| 102 | return None |
| 103 | |
| 104 | # Choose next unassigned letter |
| 105 | for letter in letters: |
| 106 | if letter not in assignment: |
| 107 | break |
| 108 | |
| 109 | # Try each digit for this letter |
| 110 | for digit in range(10): |
| 111 | # Make assignment |
| 112 | assignment[letter] = digit |
| 113 | |
| 114 | # If partial assignment is valid, continue |
| 115 | if is_valid_partial(assignment): |
| 116 | result = backtrack(assignment) |
| 117 | if result is not None: |
| 118 | return result |
| 119 | |
| 120 | # Backtrack |
| 121 | del assignment[letter] |
| 122 | |
| 123 | return None |
| 124 | |
| 125 | # Start backtracking with empty assignment |
| 126 | solution = backtrack({}) |
| 127 | return solution |
| 128 | |
| 129 | # Handled Edge Cases: Empty puzzle, invalid format, no words, no letters, empty words, |
| 130 | # characters not in assignment, leading zeros, duplicate digits |