LeetCode #2566 — EASY

Maximum Difference by Remapping a Digit

Build confidence with an intuition-first walkthrough focused on math fundamentals.

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The Problem

Problem Statement

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.

Example 1:

Input: num = 11891
Output: 99009
Explanation: 
To achieve the maximum value, Bob can remap the digit 1 to the digit 9 to yield 99899.
To achieve the minimum value, Bob can remap the digit 1 to the digit 0, yielding 890.
The difference between these two numbers is 99009.

Example 2:

Input: num = 90
Output: 99
Explanation:
The maximum value that can be returned by the function is 99 (if 0 is replaced by 9) and the minimum value that can be returned by the function is 0 (if 9 is replaced by 0).
Thus, we return 99.

Constraints:

  • 1 <= num <= 108
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Math · Greedy

Example 1

11891

Example 2

90
Step 02

Core Insight

What unlocks the optimal approach

  • Try to remap the first non-nine digit to 9 to obtain the maximum number.
  • Try to remap the first non-zero digit to 0 to obtain the minimum number.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2566: Maximum Difference by Remapping a Digit
class Solution {
    public int minMaxDifference(int num) {
        String s = String.valueOf(num);
        int mi = Integer.parseInt(s.replace(s.charAt(0), '0'));
        for (char c : s.toCharArray()) {
            if (c != '9') {
                return Integer.parseInt(s.replace(c, '9')) - mi;
            }
        }
        return num - mi;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(log n)
Space
O(log n)

Approach Breakdown

EXHAUSTIVE
O(2ⁿ) time
O(n) space

Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.

GREEDY
O(n log n) time
O(1) space

Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.

Using greedy without proof

Wrong move: Locally optimal choices may fail globally.

Usually fails on: Counterexamples appear on crafted input orderings.

Fix: Verify with exchange argument or monotonic objective before committing.