1423. Maximum Points You Can Obtain from Cards

Problem

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

Problem Summary

Several cards are arranged in a row, and each card has a corresponding number of points. The points are given by the integer array cardPoints. In one move, you can take one card from the beginning or the end of the row, and in the end you must take exactly k cards. Your score is the sum of the points of all the cards you have taken. Given an integer array cardPoints and an integer k, return the maximum number of points you can obtain.

Solution Approach

• This problem is a simplified sliding window problem. Taking K cards from both ends of the cards can be transformed into taking a contiguous segment of n-K cards from the middle. Maximizing the points from taking cards from both ends means minimizing the points of the remaining middle cards. Scan the array once, calculate the cumulative sum within each window of size n-K, and record the minimum cumulative sum. The maximum number of points requested by the problem is equal to the total sum of all cards minus the minimum cumulative sum in the middle.

Code

package leetcode

func maxScore(cardPoints []int, k int) int {
	windowSize, sum := len(cardPoints)-k, 0
	for _, val := range cardPoints[:windowSize] {
		sum += val
	}
	minSum := sum
	for i := windowSize; i < len(cardPoints); i++ {
		sum += cardPoints[i] - cardPoints[i-windowSize]
		if sum < minSum {
			minSum = sum
		}
	}
	total := 0
	for _, pt := range cardPoints {
		total += pt
	}
	return total - minSum
}