1696. Jump Game VI

Medium

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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 = deque([0])
        for i in range(1, len(nums)):
            # Remove old indexes
            while dq and dq[0] < (i-k):
                dq.popleft()
            # Notice that Line 10 causes dq to be in decreasing order,
            # So [0] element in dq will be max
            nums[i] += nums[dq[0]]
            # Make dq in decreasing order
            while dq and nums[dq[-1]] <= nums[i]:
                dq.pop()
            dq.append(i)
        return nums[-1]