Maximizing Points in the "Solving Questions With Brainpower" Problem

[Antim-IWP]

Discussion: Maximizing Points in the "Solving Questions With Brainpower" Problem

Hi everyone! 👋

I'm currently working on a solution to the problem "Solving Questions With Brainpower" from LeetCode (or any similar problem you're tackling) and need some input on how to approach it efficiently.

Problem Overview:

We are given a 2D integer array questions where each questions[i] is in the form [pointsi, brainpoweri]. The goal is to maximize the total points you can earn by solving or skipping each question, but with the constraint that solving a question prevents you from solving a number of subsequent questions.

Example Input:

questions = [[3, 2], [4, 3], [4, 4], [2, 5]]

Example Output:

5

Problem Constraints:

• 1 <= questions.length <= 10^5
• questions[i].length == 2
• 1 <= pointsi, brainpoweri <= 10^5

Key Observations:

1. Solving a question gives you points but prevents you from solving a number of subsequent questions determined by the brainpoweri.
2. Skipping a question allows you to move to the next one and make a decision without restriction.

My Current Thoughts:

I believe this problem is related to Dynamic Programming (DP). The main challenge is to efficiently track and compute the maximum points as we process each question, while considering the "skipping" mechanic introduced by brainpoweri.

I’m thinking of using a DP array where each entry stores the maximum points achievable from a given question onward, but I’m unsure about the optimal way to handle skipping and the brainpower restriction.

My Approach:

• DP State: Let dp[i] represent the maximum points you can earn starting from question i.
• Transition:
  • If you skip question i, the value of dp[i] will be the same as dp[i+1].
  • If you solve question i, you earn pointsi, but then skip the next brainpoweri questions, and hence the next valid question is i + brainpoweri + 1.

The recurrence relation would look something like this:

dp[i] = max(dp[i+1], points[i] + dp[i + brainpower[i] + 1])

Questions:

• Space Complexity: With the approach above, we're storing the entire dp array which could be large (up to 10^5 elements). Any advice on optimizing space usage here?
• Time Complexity: I believe a bottom-up dynamic programming approach can work in O(n) time since each question is processed once. Is there a faster approach that avoids reprocessing the same subproblems?
• Edge Cases: Are there any edge cases I might be overlooking, like when there is a single question or when the brainpower value is very high?

I would love to hear your thoughts, suggestions, or any alternative approaches you’ve come across for this kind of problem.

Thanks for your help! 🙏

[iamAntimPal]

class Solution:
    def mostPoints(self, questions: List[List[int]]) -> int:
        @cache
        def dfs(i: int) -> int:
            if i >= len(questions):
                return 0
            p, b = questions[i]
            return max(p + dfs(i + b + 1), dfs(i + 1))

        return dfs(0)

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[Antim-IWP]

Thanku