The Maximum Points You Can Obtain from Cards interview question is a popular sliding window problem. You are given an array of card values and an integer k. In one step, you can take one card from either the beginning or the end of the array. You must take exactly k cards. The goal is to maximize the sum of the points of the cards you have taken.
Although you are picking cards from the ends, the problem can be reframed as finding a contiguous subarray of size n - k that has the minimum possible sum. The cards you don't pick are the ones in the middle.
This Maximum Points You Can Obtain from Cards coding problem is a frequent choice for companies like Uber, Microsoft, and Google. It tests "out-of-the-box" thinking. While the problem describes picking from the ends, the most efficient solution involves looking at what remains in the middle. It evaluates your ability to recognize sliding window patterns and prefix sum optimizations, which are fundamental for efficient array manipulation.
The Array, Sliding Window, Prefix Sum interview pattern is ideal here. Instead of simulating the card-picking process, you calculate the total sum of all cards. Then, you find a contiguous subarray of length len(cards) - k with the minimum sum. The difference between the total sum and this minimum subarray sum is your maximum points. This is because taking k cards from the ends leaves n - k cards in the middle.
Cards: [1, 2, 3, 4, 5, 6, 1], k = 3
Total Sum = 22.
We need to leave 7 - 3 = 4 cards in the middle.
Possible 4-card windows:
One frequent mistake in the Maximum Points You Can Obtain from Cards coding problem is trying to use a greedy approach—always picking the larger card from the two ends. This fails because a small card at the end might be blocking a very large card. For example, if cards are [1, 100, 1, 1] and k=2, greedy picks 1 then 1 (total 2), but the optimal is 1 then 100 (total 101) by picking from the other end. Another mistake is over-complicating with recursion/DP when a simple sliding window is sufficient.
Always look for the "complement" of the problem. If you need to maximize something by picking from the ends, check if that's equivalent to minimizing what's left in the middle. This perspective shift is a common theme in sliding window and subarray problems and can lead to much cleaner and faster solutions.
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