| 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 with constraint checking to find a valid digit assignment |
| 12 | where each letter represents a unique digit, no leading digit is zero, and the equation holds. |
| 13 | |
| 14 | Handled Edge Cases: |
| 15 | - Invalid puzzle format (no '==') |
| 16 | - Words with invalid characters |
| 17 | - Leading zeros in multi-digit words |
| 18 | - No valid solutions |
| 19 | - Empty or whitespace-only puzzle |
| 20 | """ |
| 21 | # Edge Case: Empty or whitespace-only puzzle |
| 22 | if not puzzle or not puzzle.strip(): |
| 23 | return None |
| 24 | |
| 25 | # Parse the puzzle |
| 26 | # Edge Case: Invalid puzzle format (no '==') |
| 27 | if "==" not in puzzle: |
| 28 | return None |
| 29 | |
| 30 | left_side, right_side = puzzle.split("==") |
| 31 | left_side = left_side.strip() |
| 32 | right_side = right_side.strip() |
| 33 | |
| 34 | # Extract words (remove operators like +, -, etc.) |
| 35 | import re |
| 36 | words = re.findall(r'[A-Z]+', left_side + ' ' + right_side) |
| 37 | |
| 38 | # Edge Case: No words found |
| 39 | if not words: |
| 40 | return None |
| 41 | |
| 42 | # Check for invalid characters |
| 43 | # Edge Case: Words contain non-alphabetic characters |
| 44 | for word in words: |
| 45 | if not word.isalpha(): |
| 46 | return None |
| 47 | |
| 48 | # Get all unique letters |
| 49 | unique_letters = set(''.join(words)) |
| 50 | |
| 51 | # Edge Case: More than 10 unique letters (impossible to assign unique digits) |
| 52 | if len(unique_letters) > 10: |
| 53 | return None |
| 54 | |
| 55 | # Get first letters of each word (can't be zero) |
| 56 | first_letters = {word[0] for word in words} |
| 57 | |
| 58 | # Convert words to expressions for evaluation |
| 59 | left_expr = left_side.replace("+", " + ").replace("-", " - ") |
| 60 | right_expr = right_side |
| 61 | |
| 62 | # Create a list of letters for consistent ordering |
| 63 | letters_list = list(unique_letters) |
| 64 | |
| 65 | def is_valid_solution(assignment): |
| 66 | """Check if the current assignment is valid""" |
| 67 | # Edge Case: Leading zeros |
| 68 | for word in words: |
| 69 | if assignment[word[0]] == 0 and len(word) > 1: |
| 70 | return False |
| 71 | |
| 72 | # Evaluate the expressions |
| 73 | left_val = left_expr |
| 74 | right_val = right_expr |
| 75 | |
| 76 | for letter, digit in assignment.items(): |
| 77 | left_val = left_val.replace(letter, str(digit)) |
| 78 | right_val = right_val.replace(letter, str(digit)) |
| 79 | |
| 80 | try: |
| 81 | return eval(left_val) == eval(right_val) |
| 82 | except: |
| 83 | return False |
| 84 | |
| 85 | def backtrack(index, assignment, used_digits): |
| 86 | """Backtracking function to find a solution""" |
| 87 | # Base case: all letters assigned |
| 88 | if index == len(letters_list): |
| 89 | if is_valid_solution(assignment): |
| 90 | return assignment.copy() |
| 91 | return None |
| 92 | |
| 93 | letter = letters_list[index] |
| 94 | |
| 95 | # Try each digit from 0-9 |
| 96 | for digit in range(10): |
| 97 | # Skip if digit already used |
| 98 | if digit in used_digits: |
| 99 | continue |
| 100 | |
| 101 | # Skip if this is a first letter and digit is 0 |
| 102 | # Edge Case: Leading zero constraint |
| 103 | if letter in first_letters and digit == 0: |
| 104 | continue |
| 105 | |
| 106 | # Make assignment |
| 107 | assignment[letter] = digit |
| 108 | used_digits.add(digit) |
| 109 | |
| 110 | # Recurse |
| 111 | result = backtrack(index + 1, assignment, used_digits) |
| 112 | if result is not None: |
| 113 | return result |
| 114 | |
| 115 | # Backtrack |
| 116 | del assignment[letter] |
| 117 | used_digits.remove(digit) |
| 118 | |
| 119 | return None |
| 120 | |
| 121 | # Start backtracking |
| 122 | solution = backtrack(0, {}, set()) |
| 123 | return solution |
| 124 | |
| 125 | # Handled Edge Cases: Empty puzzle, invalid format, non-alphabetic characters, more than 10 unique letters, leading zeros, no solution |