Description

There are several cards arranged in a row, and each card has an associated number of points The points are given in the integer array cardPoints.

In one step, you can take one card from the beginning or from the end of the row. You have to take exactly k cards.

Your score is the sum of the points of the cards you have taken.

Given the integer array cardPoints and the integer k, return the maximum score you can obtain.

Example 1:

Input: cardPoints = [1,2,3,4,5,6,1], k = 3
Output: 12
Explanation: After the first step, your score will always be 1. However, choosing the rightmost card first will maximize your total score. The optimal strategy is to take the three cards on the right, giving a final score of 1 + 6 + 5 = 12.

Example 2:

Input: cardPoints = [2,2,2], k = 2
Output: 4
Explanation: Regardless of which two cards you take, your score will always be 4.

Example 3:

Input: cardPoints = [9,7,7,9,7,7,9], k = 7
Output: 55
Explanation: You have to take all the cards. Your score is the sum of points of all cards.

Example 4:

Input: cardPoints = [1,1000,1], k = 1
Output: 1
Explanation: You cannot take the card in the middle. Your best score is 1.

Example 5:

Input: cardPoints = [1,79,80,1,1,1,200,1], k = 3
Output: 202

Constraints:

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

分析

题目的意思是：给你一个数组，从左向右或者从右向左选K个数，也可以加起来选K个数，使得组成的数是所选取的组合中最大的。我的思路也很直接，先用一个求和数组，求出前i个数的和。然后构造符合条件的数组，取和的最大值就行了。

代码

class Solution:
    def maxScore(self, cardPoints: List[int], k: int) -> int:
        maxVal=0
        n=len(cardPoints)
        res=[0]*(n+1)
        for i in range(len(cardPoints)):
            res[i+1]=res[i]+cardPoints[i]
        if(k>n):
            return res[n]
        for i in range(k+1):
            maxVal=max(res[i]+res[n]-res[n-k+i],maxVal)
        return maxVal