Maximize Your Card Collection Score

Imagine you're at a fun fair, playing a game where you collect cards from a long row. Each card has a certain number of points. The rule is you must pick exactly k cards, but you can only take them from either the very beginning or the very end of the row. Your challenge is to devise a strategy to pick your cards such that your total score is maximized.

Problem Description

You are given an integer array cardPoints, where cardPoints[i] represents the points of the i-th card in a row. You are also given an integer k, which is the exact number of cards you must take.

In each step, you can take a card from the leftmost available position or the rightmost available position. You must perform exactly k such steps. Your objective is to find and return the maximum total score you can obtain.

• What needs to be achieved: Calculate the highest possible sum of points from k cards, where these cards are chosen exclusively from the ends of the given cardPoints array.
• Key requirements: You must select precisely k cards. Selections are restricted to the outermost available cards (either the current leftmost or the current rightmost).
• Expected behavior: The function should identify the optimal combination of i cards from the left and k-i cards from the right to yield the highest total score.
• Important edge cases to consider:
  • When k is equal to the total number of cards (cardPoints.length), you must take all cards.
  • When k is 1, you simply choose the maximum between the first and last card.
  • The cardPoints array might contain only one element.

Examples

Example 1:

Input:
cardPoints = [1,2,3,4,5,6,1]
k = 3
Output: 12
Explanation:
You can take cards in various combinations:
- Take 3 cards from the left: [1,2,3]. Sum = 6.
- Take 2 cards from the left and 1 from the right: [1,2] + [1]. Sum = 4.
- Take 1 card from the left and 2 from the right: [1] + [6,1]. Sum = 8.
- Take 0 cards from the left and 3 from the right: [5,6,1]. Sum = 12.
The maximum score you can obtain is 12.

Example 2:

Input:
cardPoints = [2,2,2]
k = 2
Output: 4
Explanation:
Possible combinations:
- Take 2 cards from the left: [2,2]. Sum = 4.
- Take 1 card from the left and 1 from the right: [2] + [2]. Sum = 4.
- Take 0 cards from the left and 2 from the right: [2,2]. Sum = 4.
In all valid cases, the total score is 4. The maximum score is 4.

Example 3:

Input:
cardPoints = [9,7,7,9,7,7,9]
k = 7
Output: 49
Explanation:
Since k (7) is equal to the total number of cards (7), you must take all cards. The sum of all cards is 9 + 7 + 7 + 9 + 7 + 7 + 9 = 49.

Constraints

• 1 <= cardPoints.length <= 10^5
• 1 <= cardPoints[i] <= 10^4
• 1 <= k <= cardPoints.length

Notes

• Consider the various ways you can choose k cards: you can pick i cards from the left end and k - i cards from the right end, where i can range from 0 to k.
• Think about how to efficiently calculate the sum for each of these k+1 possible combinations without redundant calculations. Pre-calculating prefix sums or suffix sums might be a helpful approach.
• The total sum of points for k cards can be large, so ensure your chosen data types can handle potentially large integer values (up to 10^5 * 10^4 = 10^9).
• This problem can also be thought of as finding a subarray of size cardPoints.length - k in the middle of the array such that its sum is minimized. Once you find this minimum sum, subtract it from the total sum of all cards to get the maximum points from the ends.