[LeetCode] 2140. Solving Questions With Brainpower
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 earn3
points but you will be unable to solve questions1
and2
. - If instead, question
0
is skipped and question1
is solved, you will earn4
points but you will be unable to solve questions2
and3
.
- If question
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
解决智力问题。
给你一个下标从 0 开始的二维整数数组 questions ,其中 questions[i] = [pointsi, brainpoweri] 。
这个数组表示一场考试里的一系列题目,你需要 按顺序 (也就是从问题 0 开始依次解决),针对每个问题选择 解决 或者 跳过 操作。解决问题 i 将让你 获得 pointsi 的分数,但是你将 无法 解决接下来的 brainpoweri 个问题(即只能跳过接下来的 brainpoweri 个问题)。如果你跳过问题 i ,你可以对下一个问题决定使用哪种操作。
比方说,给你 questions = [[3, 2], [4, 3], [4, 4], [2, 5]] :
如果问题 0 被解决了, 那么你可以获得 3 分,但你不能解决问题 1 和 2 。
如果你跳过问题 0 ,且解决问题 1 ,你将获得 4 分但是不能解决问题 2 和 3 。
请你返回这场考试里你能获得的 最高 分数。来源:力扣(LeetCode)
链接:https://leetcode.cn/problems/solving-questions-with-brainpower
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思路是 DP,我参考了这个帖子。这道题可以从左往右计算,也可以从右往左计算。我这里分享一个从左往右计算的做法,因为比较好思考。这里 dp[i] 的定义是从第 0 个问题到第 I - 1 个问题
对于在 index == i 位置上的问题,questions[i][0] 是得分,questions[i][0] 是需要跳过的问题的个数,所以对于位置 i 来说,
如果不解决这个问题,那么在当前位置的得分 = 上一个位置的得分,即 dp[i] = dp[i - 1]
如果解决这个问题,因为涉及到需要跳过的问题,所以我们直接看他跳到的下一个位置 j 的得分是多少,其中 j = i + 1 + questions[i][0],如果是从位置 i 跳过来的,他的得分 dp[j] = dp[i] + questions[i][0]
时间O(n)
空间O(n)
Java实现
1 class Solution { 2 public long mostPoints(int[][] questions) { 3 var n = questions.length; 4 var f = new long[n + 1]; 5 for (var i = 0; i < n; i++) { 6 f[i + 1] = Math.max(f[i + 1], f[i]); 7 var q = questions[i]; 8 var j = Math.min(i + q[1] + 1, n); 9 f[j] = Math.max(f[j], f[i] + q[0]); 10 } 11 return f[n]; 12 } 13 } 14 // 正序