Taking Maximum Energy From the Mystic Dungeon

Taking Maximum Energy From the Mystic Dungeon

What is this problem about?

The Taking Maximum Energy From the Mystic Dungeon interview question involves an array representing energy levels at different levels of a dungeon. You are also given an integer k. You can start at any dungeon level i. From level i, you must jump to level i + k, then i + 2k, and so on, until you jump out of the dungeon (beyond the array boundary). The energy you collect is the sum of energy at all levels you visit. Your goal is to find the maximum possible energy you can collect.

Why is this asked in interviews?

Companies like Amazon and JPMorgan ask this question to test a candidate's ability to optimize a summation problem using prefix sums or dynamic programming. It evaluates whether you can identify independent subproblems (each path starting at different i) and how you handle negative energy values. It's a test of efficient array traversal and logical grouping.

Algorithmic pattern used

The primary pattern is the Prefix Sum or Dynamic Programming interview pattern, specifically applied with a "step" of k. Instead of starting from the beginning and calculating all paths (which would involve redundant calculations), start from the end of the array. For each level i from n-1 down to 0:

• If i + k >= n, your total energy at i is just energy[i].
• If i + k < n, your total energy at i is energy[i] + total_energy[i+k]. This way, you calculate the result for each possible starting point in a single pass O(n).

Example explanation

Energy: [5, 2, -10, 9, 5], k = 3.

• i = 4: Energy = 5. (Jump out)
• i = 3: Energy = 9. (Jump out)
• i = 2: Energy = -10. (Jump out)
• i = 1: Start at index 1 (2), next is 1+3=4 (5). Total = 2 + 5 = 7.
• i = 0: Start at index 0 (5), next is 0+3=3 (9). Total = 5 + 9 = 14. Max energy is 14 (starting at level 0).

Common mistakes candidates make

A common error is forgetting that energy levels can be negative. Some candidates assume that starting earlier is always better, but a large negative value at an early level might make a later starting point more optimal. Another mistake is using a nested loop to calculate the sum for each starting point, which results in O(n²/k) complexity—this might time out for large arrays and small k.

Interview preparation tip

When preparing for the Taking Maximum Energy From the Mystic Dungeon coding problem, practice "backward" iteration techniques. Problems where your current decision depends on future outcomes are often best solved from end to start. Understanding the Prefix Sum interview pattern in various contexts (like stepping by k) is a great way to boost your problem-solving efficiency.