Solution.py

"""

You are given a 0-indexed integer array nums and an integer k.
You are initially standing at index 0. In one move, you can jump at most k steps forward without going outside the boundaries of the array. That is, you can jump from index i to any index in the range [i + 1, min(n - 1, i + k)] inclusive.
You want to reach the last index of the array (index n - 1). Your score is the sum of all nums[j] for each index j you visited in the array.
Return the maximum score you can get.
 
Example 1:

Input: nums = [1,-1,-2,4,-7,3], k = 2
Output: 7
Explanation: You can choose your jumps forming the subsequence [1,-1,4,3] (underlined above). The sum is 7.

Example 2:

Input: nums = [10,-5,-2,4,0,3], k = 3
Output: 17
Explanation: You can choose your jumps forming the subsequence [10,4,3] (underlined above). The sum is 17.

Example 3:

Input: nums = [1,-5,-20,4,-1,3,-6,-3], k = 2
Output: 0

 
Constraints:

1 <= nums.length, k <= 105
-104 <= nums[i] <= 104


"""


class Solution:
    def maxResult(self, nums: List[int], k: int) -> int:
        dq = collections.deque()
        ss = [None for _ in nums]
        for i, n in enumerate(nums):
            if i == 0:
                ss[i] = n
                dq.append(i)
                continue
            if i - dq[0] > k:
                dq.popleft()
            c = ss[dq[0]] + n
            if i - dq[0] >= k:
                dq.popleft()
            while dq and ss[dq[0]] <= c:
                dq.popleft()
            while dq and ss[dq[-1]] <= c:
                dq.pop()
            dq.append(i)
            ss[i] = c
        return ss[-1]