How do you solve Find the Maximum Achievable Number on LeetCode?

Find the Maximum Achievable Number (LeetCode #2769) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: Always aim to maximize x by decreasing it and increasing num.

What is the brute force solution for Find the Maximum Achievable Number?

The brute force approach for Find the Maximum Achievable Number is Brute Force, with O(t) time complexity and O(1) space complexity. The brute force approach attempts to calculate all possible values of x by simulating the operations up to t times. This means we will explore all combinations of increasing and decreasing operations on both x and num. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Find the Maximum Achievable Number?

Find the Maximum Achievable Number uses the following concepts: Math. The recommended patterns to study are: Mathematical Operations, Greedy Algorithms.

What are the interview tips for Find the Maximum Achievable Number?

Clearly explain your thought process while arriving at the solution. Consider edge cases and how they might affect your solution. Practice simplifying problems to find optimal solutions.

What are common mistakes when solving Find the Maximum Achievable Number?

Overcomplicating the problem with unnecessary loops. Not recognizing the linear relationship between num and t.

#2769

Find the Maximum Achievable Number

Easy

MathMathematical OperationsGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(t)	O(1)
Space	O(1)	O(1)

💡

Intuition

Time O(1)Space O(1)

The optimal approach recognizes that to maximize x, we should always decrease x and increase num. This leads to a straightforward calculation of the maximum achievable number as num + 2 * t.

⚙️

Algorithm

2 steps

1Step 1: Calculate the maximum achievable number using the formula: max_x = num + 2 * t.
2Step 2: Return max_x.

solution.py2 lines

1def maxAchievable(num, t):
2    return num + 2 * t

ℹ

Complexity note: The time complexity is O(1) because we perform a constant number of operations, and the space complexity is O(1) since we only use a single variable to store the result.

1Always aim to maximize x by decreasing it and increasing num.
2The relationship between num and t is linear, allowing for a direct calculation.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.