You are given an integer num. You will apply the following steps exactly two times:
x (0 <= x <= 9).y (0 <= y <= 9). The digit y can be equal to x.x in the decimal representation of num by y.Let a and b be the results of applying the operations to num the first and second times, respectively.
Return the max difference between a and b.
Example 1:
Input: num = 555 Output: 888 Explanation: The first time pick x = 5 and y = 9 and store the new integer in a. The second time pick x = 5 and y = 1 and store the new integer in b. We have now a = 999 and b = 111 and max difference = 888
Example 2:
Input: num = 9 Output: 8 Explanation: The first time pick x = 9 and y = 9 and store the new integer in a. The second time pick x = 9 and y = 1 and store the new integer in b. We have now a = 9 and b = 1 and max difference = 8
Constraints:
1 <= num <= 108To achieve the maximum difference between two numbers obtained by replacing digits, we should try to make one number as large as possible and the other as small as possible. The first operation should replace the highest possible digit with 9s to maximize the number, while the second operation should replace the first non-zero digit with 1 to minimize the number.
The solution involves creating two helper functions: getMax and getMin. The getMax function replaces the first non-9 digit in the integer with 9s to maximize it. The getMin function replaces the first non-zero digit with 1 (or 0 for non-leading digits) to minimize the number. Finally, the difference between these two transformed numbers is returned.
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Time Complexity: O(n), where n is the number of digits in the number.
Space Complexity: O(n) for the character array used to manipulate the digits.
This approach focuses on an alternative systematic strategy for choosing x and y based on simplicity and effectiveness. The main aim is to put more effort on understanding edge cases and trivial replacements rather than directly targeting all possible replacements.
This approach uses simple maximum and minimum replacements as building block logic that focuses on quick target assignments. It also takes into account the prevention of unpleasant replacements like leading zeroes.
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Time Complexity: O(n) for character iteration.
Space Complexity: O(n) due to storage requirements for transformation.
| Approach | Complexity |
|---|---|
| Maximize and Minimize by Digit Replacement | Time Complexity: O(n), where n is the number of digits in the number. |
| Alternative Simple Replacement Strategy | Time Complexity: O(n) for character iteration. |
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