What is the Maximum Points You Can Obtain from Cards pattern?

The Maximum Points You Can Obtain from Cards is a common coding interview pattern in Sliding Window problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use Maximum Points You Can Obtain from Cards?

Use the Maximum Points You Can Obtain from Cards pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is Maximum Points You Can Obtain from Cards asked in FAANG interviews?

Yes, Maximum Points You Can Obtain from Cards is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Sliding Window

Medium

Maximum Points You Can Obtain from Cards

Find the maximum score you can get by taking k cards from either end of the row.

20 min

Solve on LeetCode

Problem Understanding

There are several cards arranged in a row, and each card has an associated number of points. You can take exactly k cards.

Constraint: In each step, you can take one card from either the beginning or the end of the row.

Goal: keyimize the total points of the cards you have taken.

Example:

nums = [1, 2, 3, 4, 5, 6, 1], k = 3
Output: 12
Explanation: Take [1, 2] from left and [1] from right? Sum = 4.
Or take [1] from left and [6, 1] from right? Sum = 8.
Or take [5, 6, 1] from right? Sum = 12. (Max)

Algorithm Strategy

Instead of simulating every decision (Recursion/DP), which is slow, realize that we always select k cards total. If we take i cards from the left means we MUST take k - i cards from the right.

The Sliding Window Approach:

Start: Assume we take all k cards from the beginning (left side). Calculate this current_sum.
Slide: In each step, we give up one card from the left and take one card from the right.
- Subtract card[k - 1 - i] (the rightmost card of our left selection).
- Add card[n - 1 - i] (the corresponding card from the end of the array).
Track: Keep track of the maximum sum found during this sliding process.

Visual Walkthrough

Step 1 / 1

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Custom Input

K Value

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