| 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 (no equals sign or too many parts) |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | right_side = parts[1] |
| 27 | left_expression = parts[0] |
| 28 | |
| 29 | # Edge Case: No terms on the left side |
| 30 | if not left_expression: |
| 31 | return None |
| 32 | |
| 33 | # Extract all unique letters |
| 34 | letters = set() |
| 35 | for char in left_expression + right_side: |
| 36 | if char.isalpha(): |
| 37 | letters.add(char) |
| 38 | |
| 39 | # Edge Case: No letters in puzzle |
| 40 | if not letters: |
| 41 | return None |
| 42 | |
| 43 | # Extract first letters (can't be zero) |
| 44 | # We need to parse the expression to find all terms |
| 45 | first_letters = set() |
| 46 | |
| 47 | # Find all words in the expression |
| 48 | import re |
| 49 | words = re.findall(r'[A-Z]+', left_expression + "=" + right_side) |
| 50 | for word in words: |
| 51 | if word: # Non-empty word |
| 52 | first_letters.add(word[0]) |
| 53 | |
| 54 | # Convert letters to a list for indexing |
| 55 | letters_list = list(letters) |
| 56 | |
| 57 | # Try all permutations of digits for the letters |
| 58 | from itertools import permutations |
| 59 | |
| 60 | # Edge Case: More letters than digits (0-9) |
| 61 | if len(letters_list) > 10: |
| 62 | return None |
| 63 | |
| 64 | for perm in permutations(range(10), len(letters_list)): |
| 65 | mapping = dict(zip(letters_list, perm)) |
| 66 | |
| 67 | # Edge Case: Leading zero |
| 68 | if any(mapping[letter] == 0 for letter in first_letters): |
| 69 | continue |
| 70 | |
| 71 | # Evaluate the left side expression |
| 72 | try: |
| 73 | # Replace letters with digits in the expression |
| 74 | left_expr_eval = left_expression |
| 75 | for letter, digit in mapping.items(): |
| 76 | left_expr_eval = left_expr_eval.replace(letter, str(digit)) |
| 77 | |
| 78 | # Evaluate the expression |
| 79 | left_value = eval(left_expr_eval) |
| 80 | |
| 81 | # Calculate right side value |
| 82 | right_number = 0 |
| 83 | for letter in right_side: |
| 84 | right_number = right_number * 10 + mapping[letter] |
| 85 | |
| 86 | # Check if equation is satisfied |
| 87 | if left_value == right_number: |
| 88 | return mapping |
| 89 | except: |
| 90 | # If evaluation fails, continue to next permutation |
| 91 | continue |
| 92 | |
| 93 | # Edge Case: No solution found |
| 94 | return None |
| 95 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on left side, No letters in puzzle, More letters than digits, Leading zero, No solution found |