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This approach employs dynamic programming in combination with a deque to keep track of the best scores possible when jumping to each index within constraints. By using a decreasing deque, we efficiently maintain the maximum score in a window of size k.
Time Complexity: O(n), because each element is inserted and removed from the deque at most once. Space Complexity: O(k), to store the window of indices in the deque.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int MaxResult(int[] nums, int k) {
6 int n = nums.Length;
7 LinkedList<int> deque = new LinkedList<int>();
8 deque.AddLast(0);
9 for (int i = 1; i < n; i++) {
10 if (deque.First.Value < i - k) {
11 deque.RemoveFirst();
12 }
13 nums[i] += nums[deque.First.Value];
14 while (deque.Count > 0 && nums[i] >= nums[deque.Last.Value]) {
15 deque.RemoveLast();
16 }
17 deque.AddLast(i);
18 }
19 return nums[n - 1];
20 }
21}Implemented in C#, this solution utilizes a LinkedList as a deque, where only indices that can provide the maximum possible score for each element are retained. The logic ensures that we calculate the best path to the end of the nums array efficiently.
This approach involves using a dynamic programming solution where we keep track of the best scores using a max-heap (priority queue). By pushing elements onto the heap, we ensure that the maximum score is always accessible, facilitating quick updates for each step in our process.
Time Complexity: O(n log k) due to heap operations. Space Complexity: O(k), maintaining up to k elements in the heap.
1
The solution employs a max-heap by negating values, allowing for priority queue operations to keep track of scores efficiently. The negation allows us to use Python's min-heap to act as a max-heap.