Maximum Difference by Remapping a Digit

Maximum Difference by Remapping a Digit - Problem

Math Greedy Easy

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.

Notes:

When Bob remaps a digit d1 to another digit d2, Bob replaces all occurrences of d1 in num with d2.
Bob can remap a digit to itself, in which case num does not change.
Bob can remap different digits for obtaining minimum and maximum values respectively.
The resulting number after remapping can contain leading zeroes.

Input & Output

Example 1 — Basic Case

$ Input: num = 123

› Output: 900

💡 Note: For maximum: replace 1→9 to get 923. For minimum: replace 1→0 to get 023 (which is 23). Difference is 923 - 23 = 900.

Example 2 — All Same Digits

$ Input: num = 555

› Output: 888

💡 Note: For maximum: replace 5→9 to get 999. For minimum: replace 5→1 to get 111. Difference is 999 - 111 = 888.

Example 3 — Already Has 9

$ Input: num = 9321

› Output: 8600

💡 Note: For maximum: replace 3→9 to get 9921. For minimum: replace 9→1 to get 1321. Difference is 9921 - 1321 = 8600.

Constraints

1 ≤ num ≤ 10⁸

Visualization

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Asked in

G Google 15 M Microsoft 12 A Amazon 8

The key insight is that leftmost digits have the biggest impact on a number's value. For maximum, replace the first non-9 digit with 9. For minimum, if the first digit is greater than 1, replace it with 1; otherwise find the first digit that's not 0 or 1 and replace with 0. Best approach is Greedy with Time: O(n), Space: O(1).

Common Approaches

✓ Memoization

⏱️ Time: N/A Space: N/A

Brute Force - Try All Digit Replacements

⏱️ Time: O(1) Space: O(1)

Convert number to string, try all 10×10 = 100 possible digit replacements, calculate resulting values and track minimum and maximum.

Greedy - Smart Digit Selection

⏱️ Time: O(n) Space: O(1)

For maximum: find first non-9 digit and replace with 9. For minimum: if first digit is not 1, replace with 1; otherwise find first non-0,1 digit and replace with 0.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Medium Frequency

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Smart Actions

💡 Explanation

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