Introduction

In this blog post, we will explore how to solve the LeetCode problem "2140" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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: 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 <= pointsi, brainpoweri <= 105

Explanation

Here's a solution to the problem, along with explanations:

• High-Level Approach:

  • Dynamic Programming: Use dynamic programming to store the maximum points achievable up to each question.
  • Iterate Backwards: Iterate through the questions in reverse order. For each question, determine whether solving it or skipping it yields more points.
  • Memoization: Store the computed maximum points for each question to avoid redundant calculations.

• Complexity:

  • Runtime Complexity: O(n), where n is the number of questions.
  • Storage Complexity: O(n)

Code

    def max_points(questions):
    n = len(questions)
    dp = [0] * (n + 1)  # dp[i] stores max points from question i to the end

    for i in range(n - 1, -1, -1):
        points, brainpower = questions[i]
        next_question = i + brainpower + 1
        solve = points + (dp[next_question] if next_question <= n - 1 else 0)
        skip = dp[i + 1]
        dp[i] = max(solve, skip)

    return dp[0]