Is Maximum Array Hopping Score I easy or hard?

Maximum Array Hopping Score I is rated Medium difficulty. The base dynamic programming idea is straightforward, but optimizing the transition using a monotonic stack requires deeper insight. Recognizing this pattern is the main challenge in interviews.

Maximum Array Hopping Score I Python/Java solution

Python and Java implementations typically build a dp array and iterate from right to left. A stack stores candidate indices for optimal jumps, and dp[i] is computed using the best candidate on the stack. The same logic translates directly to C++, Go, and TypeScript with O(n) time complexity.

How to solve Maximum Array Hopping Score I in O(n)?

Compute dp[i] from right to left where dp[i] represents the best score starting at index i. Maintain a monotonic stack of candidate jump positions that give better score contributions. Remove dominated indices and use the top candidate to compute dp[i]. Because each index is processed once, the algorithm runs in linear time.

What is the best approach for Maximum Array Hopping Score I?

The most efficient approach uses dynamic programming combined with a monotonic stack. Define dp[i] as the maximum score starting from index i and compute it from right to left. The stack keeps candidate indices that produce better jump scores, reducing the transition search. This optimization reduces the runtime from O(n²) to O(n).

Is Maximum Array Hopping Score I asked at Google/Amazon/Meta?

Problems combining dynamic programming with monotonic stacks are common in interviews at companies like Google, Amazon, and Meta. Variations of array hopping, jump optimization, and DP transition pruning frequently appear in technical screens. Understanding how to reduce O(n²) DP transitions to O(n) is a valuable interview skill.

What data structure is used in Maximum Array Hopping Score I?

The optimized solution uses a monotonic stack along with a dynamic programming array. The stack maintains candidate indices whose values produce better jump scores for earlier positions. This structure allows efficient pruning of dominated transitions during the DP computation.

What is the time complexity of Maximum Array Hopping Score I?

The optimized solution runs in O(n) time using dynamic programming with a monotonic stack, since each index is pushed and popped at most once. A straightforward memoized DFS or DP that checks every possible next index requires O(n²) time. Space complexity is O(n) for the DP array and stack.

Description Hints 2 Solution Video 14:14

3205. Maximum Array Hopping Score I

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Given an array nums, you have to get the maximum score starting from index 0 and hopping until you reach the last element of the array.

In each hop, you can jump from index i to an index j > i, and you get a score of (j - i) * nums[j].

Return the maximum score you can get.

Example 1:

Input: nums = [1,5,8]

Output: 16

Explanation:

There are two possible ways to reach the last element:

0 -> 1 -> 2 with a score of (1 - 0) * 5 + (2 - 1) * 8 = 13.
0 -> 2 with a score of (2 - 0) * 8 = 16.

Example 2:

Input: nums = [4,5,2,8,9,1,3]

Output: 42

Explanation:

We can do the hopping 0 -> 4 -> 6 with a score of (4 - 0) * 9 + (6 - 4) * 3 = 42.

Constraints:

2 <= nums.length <= 10³
1 <= nums[i] <= 10⁵

Asked at 1 company

Zluri

Topics

Hints open one at a time

Hint 1

Define dp[i] as the maximum score if we start from index i.

Hint 2

We can calculate dp[i] as the maximum score from hopping to all indices j > i.

14:14

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[1,5,8]

Input

[4,5,2,8,9,1,3]

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