Find the Maximum Achievable Number

Problem Description

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

Increase or decrease the number by 1, and simultaneously increase or decrease num by 1. Return the maximum achievable number after applying the operation at most t times.

Example

Example 1:

Input: num = 4, t = 1

Output: 6

Explanation:

Apply the following operation once to make the maximum achievable number equal to num:

Decrease the maximum achievable number by 1, and increase num by 1.

Example 2:

Input: num = 3, t = 2

Output: 7

Explanation:

Apply the following operation twice to make the maximum achievable number equal to num:

Decrease the maximum achievable number by 1, and increase num by 1.

Constraints

• 1 <= num, t <= 50

Solution Approach

Intuition:

To efficiently Find the Maximum Achievable Number

Aproach

1. Define the problem: Determine the maximum achievable X given num and t.
2. Understand the relationship: Recognize that X increases by 2t for every num.
3. Formulate the solution: Return num + 2*t to calculate the maximum achievable X.
4. Implement the solution: Write the code in the desired programming language (JavaScript, TypeScript, Python, or Java).
5. Test and verify: Check the code with various inputs to ensure it produces the correct output.

Solution Implementation

Code In Different Languages:

JavaScript

Written by @Ishitamukherjee2004

class Solution {
theMaximumAchievableX(num, t) {
 return num + 2 * t;
}
}

TypeScript

Written by @Ishitamukherjee2004

class Solution {
theMaximumAchievableX(num: number, t: number): number {
 return num + 2 * t;
}
}

Python

Written by @Ishitamukherjee2004

 
class Solution:
 def theMaximumAchievableX(self, num: int, t: int) -> int:
     return num + 2 * t

Java

Written by @Ishitamukherjee2004

public class Solution {
 public int theMaximumAchievableX(int num, int t) {
     return num + 2 * t;
 }
}

C++

Written by @Ishitamukherjee2004

class Solution {
public:
 int theMaximumAchievableX(int num, int t) {
     return num+2*t;
 }
};

Complexity Analysis

• Time Complexity: $O(1)$, meaning it takes constant time, regardless of the input size. This is because the method performs a simple arithmetic operation that doesn't depend on the size of the input.

• Space Complexity: $O(1)$, meaning the method uses a constant amount of space, regardless of the input size. This is because the method doesn't allocate any new memory that scales with the input size.