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This approach leverages dynamic programming to solve the problem. You create a DP array where each element dp[i] represents the maximum points that can be earned starting from question i to the last question. You decide whether to solve or skip a question based on the potential points you can earn. The solution is filled backward, starting from the last question.
Time Complexity: O(n)
Space Complexity: O(n)
1function maxPoints(questions) {
2 const n = questions.length;
3 const dp = new Array(n + 1).fill(0);
4 for (let i = n - 1; i >= 0; i--) {
5 const solve = questions[i][0] + (i + 1 + questions[i][1] < n ? dp[i + 1 + questions[i][1]] : 0);
6 const skip = dp[i + 1];
7 dp[i] = Math.max(solve, skip);
8 }
9 return dp[0];
10}This JavaScript solution applies a dynamic programming strategy. It uses an array to capture maximum points starting from each question, iterating backward to decide whether to solve or skip the question for optimal points accrual. The function returns the maximum points starting from the first question using this methodology.
This approach uses recursion with memoization to avoid recomputing results for overlapping subproblems. It recursively decides the maximum points by considering both solving and skipping options for each question, and stores results in a memoization array for reuse. This provides an efficient way to solve the problem since it avoids redundant calculations.
Time Complexity: O(n)
Space Complexity: O(n)
1
public class Solution {
private int Dfs(int[][] questions, int i, Dictionary<int, int> memo) {
if (i >= questions.Length) return 0;
if (memo.ContainsKey(i)) return memo[i];
int solve = questions[i][0] + Dfs(questions, i + 1 + questions[i][1], memo);
int skip = Dfs(questions, i + 1, memo);
memo[i] = System.Math.Max(solve, skip);
return memo[i];
}
public int MaxPoints(int[][] questions) {
var memo = new Dictionary<int, int>();
return Dfs(questions, 0, memo);
}
}Here, the C# implementation uses a recursive technique with memoization. It applies a dictionary for storing prior outcomes to circumvent replicating tasks. Recursive calls analyze solving and skipping choices, following which the memoization step guarantees reflection of the most rewarding computation. It subsequently outputs the maximum viable points for starting point zero.