jump-game-vi

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1696. Jump Game VI (Medium)

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

Related Topics

[Queue] [Array] [Dynamic Programming] [Sliding Window] [Monotonic Queue] [Heap (Priority Queue)]

Hints

Hint 1

Let dp[i] be "the maximum score to reach the end starting at index i". The answer for dp[i] is nums[i] + max{dp[i+j]} for 1 <= j <= k. That gives an O(n*k) solution.

Hint 2

Instead of checking every j for every i, keep track of the largest dp[i] values in a heap and calculate dp[i] from right to left. When the largest value in the heap is out of bounds of the current index, remove it and keep checking.