This problem asks you to take an integer and perform exactly one digit remapping to maximize the difference between the resulting maximum and minimum possible values. Remapping a digit means choosing one digit (0-9) and replacing all its occurrences in the number with another digit (0-9). The goal is to find one remapping that creates the largest possible number and another (potentially different) remapping that creates the smallest possible number, then calculate their difference.
The Maximum Difference by Remapping a Digit interview question is a great test of Greedy algorithmic thinking and basic Math skills. It requires candidates to identify the most significant digits in a number and understand how changing them affects the overall value. Since it involves string manipulation or digit-by-digit processing, it assesses how comfortably a developer can switch between numerical and string representations to solve a logic puzzle.
This follows a Greedy interview pattern combined with Math. To maximize the number, you want to change the most significant digit (the first one from the left) that is not already a '9' into a '9'. To minimize the number, you want to change the very first digit of the number into a '0'. Because the first digit carries the most weight, changing it has the largest impact on the final value.
Take the number 454.
One common mistake is only remapping the first occurrence of a digit rather than all occurrences. Another is not correctly identifying which digit to change to maximize the value (e.g., trying to change a digit that is already 9). Some candidates also forget that leading zeros are allowed in the intermediate step of remapping for minimization, which simplifies to a smaller integer.
When tackling the Maximum Difference by Remapping a Digit coding problem, think about 'weight'. In decimal numbers, digits on the left are much more 'heavy' than those on the right. Always prioritize changes to the leftmost possible position. Practice converting integers to strings and back, as this is often the easiest way to handle digit remapping in languages like Python or Java.
