Introduction

In this blog post, we will explore how to solve the LeetCode problem "1753" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are playing a solitaire game with three piles of stones of sizes a​​​​​​, b,​​​​​​ and c​​​​​​ respectively. Each turn you choose two different non-empty piles, take one stone from each, and add 1 point to your score. The game stops when there are fewer than two non-empty piles (meaning there are no more available moves). Given three integers a​​​​​, b,​​​​​ and c​​​​​, return the maximum score you can get. Example 1: Input: a = 2, b = 4, c = 6 Output: 6 Explanation: The starting state is (2, 4, 6). One optimal set of moves is: - Take from 1st and 3rd piles, state is now (1, 4, 5) - Take from 1st and 3rd piles, state is now (0, 4, 4) - Take from 2nd and 3rd piles, state is now (0, 3, 3) - Take from 2nd and 3rd piles, state is now (0, 2, 2) - Take from 2nd and 3rd piles, state is now (0, 1, 1) - Take from 2nd and 3rd piles, state is now (0, 0, 0) There are fewer than two non-empty piles, so the game ends. Total: 6 points. Example 2: Input: a = 4, b = 4, c = 6 Output: 7 Explanation: The starting state is (4, 4, 6). One optimal set of moves is: - Take from 1st and 2nd piles, state is now (3, 3, 6) - Take from 1st and 3rd piles, state is now (2, 3, 5) - Take from 1st and 3rd piles, state is now (1, 3, 4) - Take from 1st and 3rd piles, state is now (0, 3, 3) - Take from 2nd and 3rd piles, state is now (0, 2, 2) - Take from 2nd and 3rd piles, state is now (0, 1, 1) - Take from 2nd and 3rd piles, state is now (0, 0, 0) There are fewer than two non-empty piles, so the game ends. Total: 7 points. Example 3: Input: a = 1, b = 8, c = 8 Output: 8 Explanation: One optimal set of moves is to take from the 2nd and 3rd piles for 8 turns until they are empty. After that, there are fewer than two non-empty piles, so the game ends. Constraints: 1 <= a, b, c <= 105

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• Approach: The optimal strategy is to always reduce the two largest piles. The maximum score is limited by the sum of the piles and twice the value of the smallest pile. We calculate the total sum and find the largest pile, then apply the formula to determine the maximum score.
• Complexity:
  • Runtime Complexity: O(1)
  • Storage Complexity: O(1)

Code

    def maximum_score(a: int, b: int, c: int) -> int:
    """
    Given three integers a, b, and c, return the maximum score you can get.
    """
    total_sum = a + b + c
    largest = max(a, b, c)
    remaining_sum = total_sum - largest

    if largest > remaining_sum:
        return remaining_sum
    else:
        return total_sum // 2