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Leetcode 2566. Maximum Difference by Remapping a Digit

Problem Statement

  1. Maximum Difference by Remapping a Digit

You are given an integer num. You will choose exactly two different digits a and b from the decimal representation of num, and replace all occurrences of the digit a with b and all occurrences of the digit b with a. Your goal is to maximize the difference between the transformed integer and num. Return the maximum difference you can achieve.

Example

Input: num = 123456 Output: 619836

Note: For num = 123456, you can choose a = 1 and b = 6, then swap them resulting in 623451. The difference between 623451 and 123456 is 499995.

Strategy

To solve this problem, we can follow these steps:

  1. Convert the integer num into its string representation.
  2. Iterate over each pair of digits a and b in the string.
  3. For each pair, create a new string where all occurrences of a are replaced with b and all occurrences of b are replaced with a.
  4. Convert the new string back to an integer.
  5. Calculate the difference between this new integer and the original num.
  6. Track the maximum difference encountered during the process.
  7. Return the maximum difference.

Clarifying Questions

  1. Are a and b guaranteed to be different digits?
    • Yes, a and b must be different digits.
  2. Can num have leading zeros after digit replacement?
    • No, converting back to integer will handle any leading zeros automatically.

Code

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>

int getMaxDifferenceByRemapping(int num) {
    std::string numStr = std::to_string(num);
    int n = numStr.size();
    int maxDifference = 0;
    
    for (char a = '0'; a <= '9'; ++a) {
        for (char b = '0'; b <= '9'; ++b) {
            if (a != b) {
                std::string transformed = numStr;
                for (int i = 0; i < n; ++i) {
                    if (transformed[i] == a) {
                        transformed[i] = b;
                    } else if (transformed[i] == b) {
                        transformed[i] = a;
                    }
                }
                int transformedNum = std::stoi(transformed);
                int currentDifference = std::abs(transformedNum - num);
                maxDifference = std::max(maxDifference, currentDifference);
            }
        }
    }
    return maxDifference;
}

int main() {
    int num = 123456;
    std::cout << "Maximum Difference: " << getMaxDifferenceByRemapping(num) << std::endl;
    return 0;
}

Time Complexity

The time complexity of this algorithm is O(n * 10 * 10), where:

Thus, the time complexity simplifies to O(n), which is efficient for typical input sizes.

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