Question

1423. Maximum Points You Can Obtain from Cards

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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.

 

Constraints:

• 1 <= cardPoints.length <= 105
• 1 <= cardPoints[i] <= 104
• 1 <= k <= cardPoints.length

Solutions

Solution 1: Sliding Window

We can use a sliding window of length $k$ to simulate this process.

Initially, we place the window at the end of the array, i.e., the $k$ positions from index $n-k$ to index $n-1$. The sum of the points of the cards in the window is denoted as $s$, and the initial value of the answer $ans$ is also $s$.

Next, we consider the situation where we take $1, 2, …, k$ cards from the beginning of the array in turn. Suppose the card taken is $cardPoints[i]$. Then we add it to $s$. Due to the length limit of the window is $k$, we need to subtract $cardPoints[n-k+i]$ from $s$. In this way, we can calculate the sum of the points of the $k$ cards taken and update the answer $ans$.

The time complexity is $O(k)$, where $k$ is the integer given in the problem. The space complexity is $O(1)$.

class Solution:
  def maxScore(self, cardPoints: List[int], k: int) -> int:
    ans = s = sum(cardPoints[-k:])
    for i, x in enumerate(cardPoints[:k]):
      s += x - cardPoints[-k + i]
      ans = max(ans, s)
    return ans

class Solution {
  public int maxScore(int[] cardPoints, int k) {
    int s = 0, n = cardPoints.length;
    for (int i = n - k; i < n; ++i) {
      s += cardPoints[i];
    }
    int ans = s;
    for (int i = 0; i < k; ++i) {
      s += cardPoints[i] - cardPoints[n - k + i];
      ans = Math.max(ans, s);
    }
    return ans;
  }
}

class Solution {
public:
  int maxScore(vector<int>& cardPoints, int k) {
    int n = cardPoints.size();
    int s = accumulate(cardPoints.end() - k, cardPoints.end(), 0);
    int ans = s;
    for (int i = 0; i < k; ++i) {
      s += cardPoints[i] - cardPoints[n - k + i];
      ans = max(ans, s);
    }
    return ans;
  }
};

func maxScore(cardPoints []int, k int) int {
  n := len(cardPoints)
  s := 0
  for _, x := range cardPoints[n-k:] {
    s += x
  }
  ans := s
  for i := 0; i < k; i++ {
    s += cardPoints[i] - cardPoints[n-k+i]
    ans = max(ans, s)
  }
  return ans
}

function maxScore(cardPoints: number[], k: number): number {
  const n = cardPoints.length;
  let s = cardPoints.slice(-k).reduce((a, b) => a + b);
  let ans = s;
  for (let i = 0; i < k; ++i) {
    s += cardPoints[i] - cardPoints[n - k + i];
    ans = Math.max(ans, s);
  }
  return ans;
}

impl Solution {
  pub fn max_score(card_points: Vec<i32>, k: i32) -> i32 {
    let n = card_points.len();
    let k = k as usize;
    let mut s: i32 = card_points[n - k..].iter().sum();
    let mut ans: i32 = s;
    for i in 0..k {
      s += card_points[i] - card_points[n - k + i];
      ans = ans.max(s);
    }
    ans
  }
}

/**
 * @param {number[]} cardPoints
 * @param {number} k
 * @return {number}
 */
var maxScore = function (cardPoints, k) {
  const n = cardPoints.length;
  let s = cardPoints.slice(-k).reduce((a, b) => a + b);
  let ans = s;
  for (let i = 0; i < k; ++i) {
    s += cardPoints[i] - cardPoints[n - k + i];
    ans = Math.max(ans, s);
  }
  return ans;
};

public class Solution {
  public int MaxScore(int[] cardPoints, int k) {
    int n = cardPoints.Length;
    int s = cardPoints[^k..].Sum();
    int ans = s;
    for (int i = 0; i < k; ++i) {
      s += cardPoints[i] - cardPoints[n - k + i];
      ans = Math.Max(ans, s);
    }
    return ans;
  }
}

class Solution {
  /**
   * @param Integer[] $cardPoints
   * @param Integer $k
   * @return Integer
   */
  function maxScore($cardPoints, $k) {
    $n = count($cardPoints);
    $s = array_sum(array_slice($cardPoints, -$k));
    $ans = $s;
    for ($i = 0; $i < $k; ++$i) {
      $s += $cardPoints[$i] - $cardPoints[$n - $k + $i];
      $ans = max($ans, $s);
    }
    return $ans;
  }
}

object Solution {
  def maxScore(cardPoints: Array[Int], k: Int): Int = {
    val n = cardPoints.length
    var s = cardPoints.takeRight(k).sum
    var ans = s
    for (i <- 0 until k) {
      s += cardPoints(i) - cardPoints(n - k + i)
      ans = ans.max(s)
    }
    ans
  }
}

class Solution {
  func maxScore(_ cardPoints: [Int], _ k: Int) -> Int {
    let n = cardPoints.count
    var s = cardPoints.suffix(k).reduce(0, +)
    var ans = s
    for i in 0..<k {
      s += cardPoints[i] - cardPoints[n - k + i]
      ans = max(ans, s)
    }
    return ans
  }
}

# @param {Integer[]} card_points
# @param {Integer} k
# @return {Integer}
def max_score(card_points, k)
  n = card_points.length
  s = card_points[-k..].sum
  ans = s
  k.times do |i|
  s += card_points[i] - card_points[n - k + i]
  ans = [ans, s].max
  end
  ans
end

class Solution {
  fun maxScore(cardPoints: IntArray, k: Int): Int {
    val n = cardPoints.size
    var s = cardPoints.sliceArray(n - k until n).sum()
    var ans = s
    for (i in 0 until k) {
      s += cardPoints[i] - cardPoints[n - k + i]
      ans = maxOf(ans, s)
    }
    return ans
  }
}