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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)
1public class Solution {
2 public int MaxPoints(int[][] questions) {
3 int n = questions.Length;
4 int[] dp = new int[n + 1];
5 for (int i = n - 1; i >= 0; i--) {
6 int solve = questions[i][0] + (i + 1 + questions[i][1] < n ? dp[i + 1 + questions[i][1]] : 0);
7 int skip = dp[i + 1];
8 dp[i] = Math.Max(solve, skip);
9 }
10 return dp[0];
11 }
12}Similar to the Java implementation, the C# solution employs dynamic programming. It iterates the questions in reverse order, updating a DP array to record the best score achievable from the current question onward. The max operation determines whether solving the current question or skipping it yields better points, with results returned from the start position.
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.