Find the Maximum Achievable Number

Problem Description

Given two integers, num and t. A number x is achievable if it can become equal to num after applying the following operation at most t times:

• Increase or decrease x by 1, and simultaneously increase or decrease num by 1.

Return the maximum possible value of x.

Key Insights

• The operations allow us to manipulate both x and num simultaneously.
• The maximum achievable number x can be derived by considering the total number of operations allowed (t) and how they can be applied.
• For every operation applied in decreasing x, we can increase num, thereby increasing the range of achievable values for x.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To determine the maximum achievable number x, we can simply calculate it as follows:

1. We start with the initial value of num.
2. For every operation allowed (t), we can decrease x by 1 while increasing num by 1, effectively giving us a total leverage of 2 for each operation.
3. Therefore, the maximum achievable number x is given by the formula: x = num + t * 2.

This approach uses basic arithmetic without the need for complex data structures.

Code Solutions