| 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 |
| 23 | if len(parts) != 2: |
| 24 | return None |
| 25 | |
| 26 | right_side = parts[1] |
| 27 | left_sides = parts[0].replace("+", " ").split() |
| 28 | |
| 29 | # Edge Case: No terms on the left side |
| 30 | if not left_sides: |
| 31 | return None |
| 32 | |
| 33 | # Extract all unique letters |
| 34 | letters = set() |
| 35 | for part in left_sides + [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_sides + [right_side]} |
| 44 | |
| 45 | # Convert to sorted list for consistent ordering |
| 46 | letters = list(letters) |
| 47 | |
| 48 | # Edge Case: More than 10 unique letters (impossible to solve) |
| 49 | if len(letters) > 10: |
| 50 | return None |
| 51 | |
| 52 | def evaluate(assignment): |
| 53 | """Evaluate if the current assignment satisfies the puzzle.""" |
| 54 | # Convert words to numbers using the assignment |
| 55 | left_values = [] |
| 56 | for word in left_sides: |
| 57 | num = 0 |
| 58 | for char in word: |
| 59 | num = num * 10 + assignment[char] |
| 60 | left_values.append(num) |
| 61 | |
| 62 | right_value = 0 |
| 63 | for char in right_side: |
| 64 | right_value = right_value * 10 + assignment[char] |
| 65 | |
| 66 | return sum(left_values) == right_value |
| 67 | |
| 68 | def is_valid(assignment): |
| 69 | """Check if assignment is valid (no leading zeros).""" |
| 70 | for letter in first_letters: |
| 71 | if assignment[letter] == 0: |
| 72 | return False |
| 73 | return True |
| 74 | |
| 75 | def backtrack(index, assignment, used_digits): |
| 76 | """Backtracking function to find a solution.""" |
| 77 | # Base case: all letters assigned |
| 78 | if index == len(letters): |
| 79 | if is_valid(assignment) and evaluate(assignment): |
| 80 | return assignment.copy() |
| 81 | return None |
| 82 | |
| 83 | letter = letters[index] |
| 84 | |
| 85 | # Try each digit from 0-9 |
| 86 | for digit in range(10): |
| 87 | # Skip if digit already used |
| 88 | if digit in used_digits: |
| 89 | continue |
| 90 | |
| 91 | # Assign digit to letter |
| 92 | assignment[letter] = digit |
| 93 | used_digits.add(digit) |
| 94 | |
| 95 | # Recurse |
| 96 | result = backtrack(index + 1, assignment, used_digits) |
| 97 | if result is not None: |
| 98 | return result |
| 99 | |
| 100 | # Backtrack |
| 101 | used_digits.remove(digit) |
| 102 | del assignment[letter] |
| 103 | |
| 104 | return None |
| 105 | |
| 106 | # Start backtracking |
| 107 | solution = backtrack(0, {}, set()) |
| 108 | return solution |
| 109 | |
| 110 | # Handled Edge Cases: Empty or None puzzle, Invalid puzzle format, No terms on the left side, No letters in puzzle, More than 10 unique letters (impossible to solve) |