Introduction

In this blog post, we will explore how to solve the LeetCode problem "2656" 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 given a 0-indexed integer array nums and an integer k. Your task is to perform the following operation exactly k times in order to maximize your score: Select an element m from nums. Remove the selected element m from the array. Add a new element with a value of m + 1 to the array. Increase your score by m. Return the maximum score you can achieve after performing the operation exactly k times. Example 1: Input: nums = [1,2,3,4,5], k = 3 Output: 18 Explanation: We need to choose exactly 3 elements from nums to maximize the sum. For the first iteration, we choose 5. Then sum is 5 and nums = [1,2,3,4,6] For the second iteration, we choose 6. Then sum is 5 + 6 and nums = [1,2,3,4,7] For the third iteration, we choose 7. Then sum is 5 + 6 + 7 = 18 and nums = [1,2,3,4,8] So, we will return 18. It can be proven, that 18 is the maximum answer that we can achieve. Example 2: Input: nums = [5,5,5], k = 2 Output: 11 Explanation: We need to choose exactly 2 elements from nums to maximize the sum. For the first iteration, we choose 5. Then sum is 5 and nums = [5,5,6] For the second iteration, we choose 6. Then sum is 5 + 6 = 11 and nums = [5,5,7] So, we will return 11. It can be proven, that 11 is the maximum answer that we can achieve. Constraints: 1 <= nums.length <= 100 1 <= nums[i] <= 100 1 <= k <= 100

Explanation

Here's the breakdown of the solution:

• Key Idea: The optimal strategy is to always pick the largest element available at each step. Since after picking an element m, we add m + 1 back, it's effectively like picking the k largest numbers we can obtain from this process. Since we always add +1, we can pick the k largest values without needing to actually simulate the array operations.

• Implementation: Sort the initial array to easily determine the starting largest element. Then, the problem reduces to summing a series of k consecutive numbers starting from the initial largest. This can be done efficiently using a formula for the sum of an arithmetic series.

• Complexity:

  • Runtime: O(n log n) for sorting the array, where n is the number of elements in nums.
  • Storage: O(1) for constant extra space.

Code

    def maximize_score(nums: list[int], k: int) -> int:
    """
    Calculates the maximum score achievable by performing the given operation k times.

    Args:
        nums: A list of integers.
        k: The number of operations to perform.

    Returns:
        The maximum score achievable.
    """
    nums.sort()
    largest = nums[-1]
    return k * largest + k * (k - 1) // 2