| 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_parts = parts[0].replace("+", " ").split() |
| 28 | |
| 29 | # Edge Case: No terms on the left side |
| 30 | if not left_parts: |
| 31 | return None |
| 32 | |
| 33 | # Extract all unique letters |
| 34 | letters = set() |
| 35 | for part in left_parts + [right_side]: |
| 36 | letters.update(part) |
| 37 | |
| 38 | # Edge Case: No letters in puzzle |
| 39 | if not letters: |
| 40 | return None |
| 41 | |
| 42 | # Extract first letters (can't be zero) |
| 43 | first_letters = {word[0] for word in left_parts + [right_side]} |
| 44 | |
| 45 | letters = list(letters) |
| 46 | n = len(letters) |
| 47 | |
| 48 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 49 | if n > 10: |
| 50 | return None |
| 51 | |
| 52 | # Create a mapping from letters to indices |
| 53 | letter_to_index = {letter: i for i, letter in enumerate(letters)} |
| 54 | |
| 55 | # Convert words to lists of indices |
| 56 | left_indices = [] |
| 57 | for word in left_parts: |
| 58 | left_indices.append([letter_to_index[letter] for letter in word]) |
| 59 | |
| 60 | right_indices = [letter_to_index[letter] for letter in right_side] |
| 61 | |
| 62 | # Generate all possible digit assignments |
| 63 | from itertools import permutations |
| 64 | |
| 65 | # Try all permutations of digits for the letters |
| 66 | for perm in permutations(range(10), n): |
| 67 | # Edge Case: Leading zero in any number |
| 68 | if any(perm[letter_to_index[letter]] == 0 for letter in first_letters): |
| 69 | continue |
| 70 | |
| 71 | # Calculate left side sum |
| 72 | left_sum = 0 |
| 73 | for word_indices in left_indices: |
| 74 | number = 0 |
| 75 | for idx in word_indices: |
| 76 | number = number * 10 + perm[idx] |
| 77 | left_sum += number |
| 78 | |
| 79 | # Calculate right side value |
| 80 | right_value = 0 |
| 81 | for idx in right_indices: |
| 82 | right_value = right_value * 10 + perm[idx] |
| 83 | |
| 84 | # Check if equation is satisfied |
| 85 | if left_sum == right_value: |
| 86 | # Return the solution as a dictionary |
| 87 | return {letter: perm[letter_to_index[letter]] for letter in letters} |
| 88 | |
| 89 | # Edge Case: No valid solution found |
| 90 | return None |
| 91 | |
| 92 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on left side, No letters in puzzle, More than 10 unique letters, Leading zero in any number, No valid solution found |