2140. Solving Questions With Brainpower

Description

You are given a 0-indexed 2D integer array questions where questions[i] = [points_i, brainpower_i].

The array describes the questions of an exam, where you have to process the questions in order (i.e., starting from question 0) and make a decision whether to solve or skip each question. Solving question i will earn you points_i points but you will be unable to solve each of the next brainpower_i questions. If you skip question i, you get to make the decision on the next question.

For example, given questions = [[3, 2], [4, 3], [4, 4], [2, 5]]:
- If question 0 is solved, you will earn 3 points but you will be unable to solve questions 1 and 2.
- If instead, question 0 is skipped and question 1 is solved, you will earn 4 points but you will be unable to solve questions 2 and 3.

Return the maximum points you can earn for the exam.

Example 1:

Input: questions = [[3,2],[4,3],[4,4],[2,5]]
Output: 5
Explanation: The maximum points can be earned by solving questions 0 and 3.
- Solve question 0: Earn 3 points, will be unable to solve the next 2 questions
- Unable to solve questions 1 and 2
- Solve question 3: Earn 2 points
Total points earned: 3 + 2 = 5. There is no other way to earn 5 or more points.

Example 2:

Input: questions = [[1,1],[2,2],[3,3],[4,4],[5,5]]
Output: 7
Explanation: The maximum points can be earned by solving questions 1 and 4.
- Skip question 0
- Solve question 1: Earn 2 points, will be unable to solve the next 2 questions
- Unable to solve questions 2 and 3
- Solve question 4: Earn 5 points
Total points earned: 2 + 5 = 7. There is no other way to earn 7 or more points.

Constraints:

1 <= questions.length <= 10⁵
questions[i].length == 2
1 <= points_i, brainpower_i <= 10⁵

Solution

solving-questions-with-brainpower.py

class Solution:
    def mostPoints(self, questions: List[List[int]]) -> int:
        n = len(questions)

        @cache
        def go(index):
            if index >= n: return 0

            points, skip = questions[index]

            res = go(index + 1)
            res = max(res, points + go(index + skip + 1))

            return res

        return go(0)