動機

記憶化搜尋與dp的分界是?

Problem

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

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 pointsi points but you will be unable to solve each of the next brainpoweri 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: 5Explanation: 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 pointsTotal 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: 7Explanation: 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 pointsTotal 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 <= pointsi, brainpoweri <= 105

TLE: 記憶化搜尋

從後面的選項找一個可能的來用

class Solution:
    @cache
    def dp(self, i):
        if i >= len(self.Q):
            return 0
        return self.Q[i][0] + max([self.dp(j) for j in range(1+i+self.Q[i][1], len(self.Q))], default=0)
    def mostPoints(self, questions: List[List[int]]) -> int:
        self.Q = questions
        return max(self.dp(i) for i in range(len(self.Q)))

sol: DP

定義做到這一題時最多會有多少分數

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