2140.Solving Questions With Brainpower
===

###### tags: `Medium`,`Array`,`DP`

[2140. Solving Questions With Brainpower](https://leetcode.com/problems/solving-questions-with-brainpower/)

### 題目描述

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*.

### 範例

**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` <= 10^5^
* `questions[i].length` == 2
* 1 <= $points_i$, $brainpower_i$ <= 10^5^

### 解答
#### Javascript

function mostPoints(questions) {
  const n = questions.length - 1;
  const dp = new Array(n).fill(0);
  dp[n] = questions[n][0];
  for (let i = n - 1; i >= 0; i--) {
    const [point, brainpower] = questions[i];
    if (i + brainpower + 1 > n) {
      dp[i] = Math.max(dp[i + 1], point);
    } else {
      dp[i] = Math.max(dp[i + 1], dp[i + brainpower + 1] + point);
    }
  }

  return dp[0];
}

> 第一次錯是沒注意到brainpower應該要從後面往回看才對
> 第二次錯是沒注意到brainpower要+1
> 不過這個跑測試就發現了應該不算錯吧ㄏㄏ
>
> [name=Marsgoat][time=May 12, 2023]

#### Python

class Solution:
    def mostPoints(self, questions: List[List[int]]) -> int:
        n = len(questions)
        dp = [0] * n
        dp[-1] = questions[-1][0]

        for i in range(n - 2, -1, -1):
            dp[i], skip = questions[i]
            if i + skip + 1 < n:
                dp[i] += dp[i + skip + 1]
            dp[i] = max(dp[i], dp[i + 1])
        
        return dp[0]

> [name=Yen-Chi Chen][time=Fri, May 12, 2023]

#### C#

public long MostPoints(int[][] questions) {
    int size = questions.Length;
    long[] points = new long[size];
    points[^1] = questions[^1][0];

    for (int i = size - 2; i >= 0; i--) {
        points[i] = questions[i][0];
        int skipedIndex = i + questions[i][1] + 1;
        if (skipedIndex < size) {
            points[i] += points[skipedIndex];
        }
        points[i] = Math.Max(points[i], points[i + 1]);
    }
    return points[0];
}

> [name=Jim][time=May 13, 2023]
### Reference

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