Problem Description
You are given an integer num. You know that Bob will sneakily remap one of the 10 possible digits (0 to 9) to another digit. Return the difference between the maximum and minimum values Bob can make by remapping exactly one digit in num.
Key Insights
- Bob can choose any digit (0-9) to remap to another digit.
- The maximum value is obtained by replacing the smallest digit with the largest digit (9).
- The minimum value is obtained by replacing the largest digit with the smallest digit (0), except if the digit is the leading digit.
- Bob can choose different digits for maximum and minimum values.
- The number can have leading zeros after remapping.
Space and Time Complexity
Time Complexity: O(1) - The algorithm runs in constant time as it processes a fixed number of digits (at most 8 digits). Space Complexity: O(1) - Only a few variables are used for calculations.
Solution
To solve the problem, we first convert the integer num into a string to easily access each digit. We then iterate through all possible digit pairs (d1, d2) where d1 is the digit to be remapped and d2 is the new digit. For each remapping, we create two new numbers: one for the maximum value by replacing d1 with 9, and another for the minimum value by replacing d1 with 0 (taking care to avoid leading zeros). Finally, we calculate the difference between the maximum and minimum values obtained through all possible remappings.