| 1 | from itertools import permutations |
| 2 | |
| 1 | 3 | def solve(puzzle: str) -> dict[str, int] | None: |
| 2 | | pass |
| 4 | """ |
| 5 | Solve an alphametics puzzle. |
| 6 | |
| 7 | Args: |
| 8 | puzzle: A string representing the alphametics puzzle (e.g., "SEND + MORE == MONEY") |
| 9 | |
| 10 | Returns: |
| 11 | A dictionary mapping letters to digits that solves the puzzle, or None if no solution exists. |
| 12 | |
| 13 | Example: |
| 14 | >>> solve("SEND + MORE == MONEY") |
| 15 | {'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2} |
| 16 | """ |
| 17 | # Parse the puzzle |
| 18 | # Edge Case: Invalid puzzle format |
| 19 | if "==" not in puzzle: |
| 20 | return None |
| 21 | |
| 22 | left_side, right_side = puzzle.replace(" ", "").split("==") |
| 23 | |
| 24 | # Edge Case: Empty sides |
| 25 | if not left_side or not right_side: |
| 26 | return None |
| 27 | |
| 28 | # Split the left side by '+' to get the addends |
| 29 | addends = left_side.split("+") |
| 30 | |
| 31 | # Edge Case: No addends |
| 32 | if not addends: |
| 33 | return None |
| 34 | |
| 35 | # Get all unique letters in the puzzle |
| 36 | letters = set("".join(addends) + right_side) |
| 37 | |
| 38 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 39 | if len(letters) > 10: |
| 40 | return None |
| 41 | |
| 42 | # Get the first letter of each word (these can't be zero) |
| 43 | first_letters = {word[0] for word in addends + [right_side]} |
| 44 | |
| 45 | # Try all possible digit assignments |
| 46 | for perm in permutations(range(10), len(letters)): |
| 47 | mapping = dict(zip(letters, perm)) |
| 48 | |
| 49 | # Edge Case: Leading zero |
| 50 | if any(mapping[letter] == 0 for letter in first_letters): |
| 51 | continue |
| 52 | |
| 53 | # Convert words to numbers using the current mapping |
| 54 | try: |
| 55 | addend_values = [int("".join(str(mapping[c]) for c in word)) for word in addends] |
| 56 | result_value = int("".join(str(mapping[c]) for c in right_side)) |
| 57 | except KeyError: |
| 58 | # This shouldn't happen with our approach, but just in case |
| 59 | continue |
| 60 | |
| 61 | # Check if the sum is correct |
| 62 | if sum(addend_values) == result_value: |
| 63 | return mapping |
| 64 | |
| 65 | # Edge Case: No solution found |
| 66 | return None |
| 67 | # Handled Edge Cases: Invalid puzzle format, Empty sides, No addends, More than 10 unique letters, Leading zero, No solution found |