| 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 to find a valid assignment of digits to letters such that: |
| 12 | 1. Each letter represents a unique digit |
| 13 | 2. No leading digit is zero |
| 14 | 3. The mathematical equation holds true |
| 15 | """ |
| 16 | # Edge Case: Empty or None puzzle |
| 17 | if not puzzle: |
| 18 | return None |
| 19 | |
| 20 | # Parse the puzzle |
| 21 | parts = puzzle.replace("==", "=").replace(" ", "").split("=") |
| 22 | |
| 23 | # Edge Case: Invalid puzzle format (no equals sign or too many parts) |
| 24 | if len(parts) != 2: |
| 25 | return None |
| 26 | |
| 27 | left_side, right_side = parts[0], parts[1] |
| 28 | |
| 29 | # Split the left side by '+' to get addends |
| 30 | addends = left_side.split("+") |
| 31 | |
| 32 | # Edge Case: No addends on the left side |
| 33 | if not addends or not all(addends): |
| 34 | return None |
| 35 | |
| 36 | # Edge Case: Empty right side |
| 37 | if not right_side: |
| 38 | return None |
| 39 | |
| 40 | # Extract all unique letters |
| 41 | letters = set() |
| 42 | for part in addends + [right_side]: |
| 43 | letters.update(part) |
| 44 | |
| 45 | # Edge Case: No letters in puzzle |
| 46 | if not letters: |
| 47 | return None |
| 48 | |
| 49 | # Extract first letters (can't be zero) |
| 50 | first_letters = {word[0] for word in addends + [right_side]} |
| 51 | |
| 52 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 53 | if len(letters) > 10: |
| 54 | return None |
| 55 | |
| 56 | letters = list(letters) |
| 57 | |
| 58 | def evaluate_word(word, assignment): |
| 59 | """Convert a word to a number based on the current assignment""" |
| 60 | result = 0 |
| 61 | for char in word: |
| 62 | result = result * 10 + assignment[char] |
| 63 | return result |
| 64 | |
| 65 | def is_valid_assignment(assignment): |
| 66 | """Check if the current assignment satisfies the equation""" |
| 67 | # Check for leading zeros |
| 68 | for word in addends + [right_side]: |
| 69 | if assignment[word[0]] == 0 and len(word) > 1: |
| 70 | return False |
| 71 | |
| 72 | # Check if equation holds |
| 73 | left_sum = sum(evaluate_word(addend, assignment) for addend in addends) |
| 74 | right_value = evaluate_word(right_side, assignment) |
| 75 | return left_sum == right_value |
| 76 | |
| 77 | def backtrack(index, assignment, used_digits): |
| 78 | """Recursively try digit assignments using backtracking""" |
| 79 | # Base case: all letters assigned |
| 80 | if index == len(letters): |
| 81 | if is_valid_assignment(assignment): |
| 82 | return assignment.copy() |
| 83 | return None |
| 84 | |
| 85 | letter = letters[index] |
| 86 | |
| 87 | # Try each digit from 0-9 |
| 88 | for digit in range(10): |
| 89 | # Skip if digit already used |
| 90 | if digit in used_digits: |
| 91 | continue |
| 92 | |
| 93 | # Skip if this is a first letter and digit is 0 |
| 94 | if letter in first_letters and digit == 0: |
| 95 | continue |
| 96 | |
| 97 | # Make assignment |
| 98 | assignment[letter] = digit |
| 99 | used_digits.add(digit) |
| 100 | |
| 101 | # Recurse |
| 102 | result = backtrack(index + 1, assignment, used_digits) |
| 103 | if result is not None: |
| 104 | return result |
| 105 | |
| 106 | # Backtrack |
| 107 | del assignment[letter] |
| 108 | used_digits.remove(digit) |
| 109 | |
| 110 | return None |
| 111 | |
| 112 | # Start backtracking |
| 113 | result = backtrack(0, {}, set()) |
| 114 | return result |
| 115 | |
| 116 | # Handled Edge Cases: Empty/None puzzle, Invalid puzzle format, No addends, Empty right side, No letters, More than 10 unique letters, Leading zeros, Equation validation |