2769. Find the Maximum Achievable Number

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.

 

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

Solutions

Solution 1: Mathematics

Notice that every time we can decrease \(x\) by \(1\) and increase \(num\) by \(1\), the difference between \(x\) and \(num\) will decrease by \(2\), and we can do this operation at most \(t\) times, so the maximum reachable number is \(num + t \times 2\).

The time complexity is \(O(1)\), and the space complexity is \(O(1)\).

Python3JavaC++GoTypeScript

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

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

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

func theMaximumAchievableX(num int, t int) int {
    return num + t*2
}

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

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