Leetcode #2769: Find the Maximum Achievable Number

In this guide, we solve Leetcode #2769 Find the Maximum Achievable Number in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

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.

Quick Facts

• Difficulty: Easy
• Premium: No
• Tags: Math

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

• Identify the math relationship.
• Compute the result with a loop or formula.
• Handle edge cases.

Python Solution

Complexity

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

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.