3147. Taking Maximum Energy From the Mystic Dungeon

Time: O(n)

Space: O(1)

Approach

Scan from end; for each chain anchor collect every k-th element's energy backward.

Key Techniques

Array problems involve manipulating elements stored in a contiguous block of memory. Key techniques include two-pointer traversal, prefix sums, sliding windows, and in-place partitioning. In C#, arrays are zero-indexed and fixed in size — use List<T> when you need dynamic resizing.

Dynamic Programming

Dynamic programming solves problems by breaking them into overlapping sub-problems and storing results to avoid redundant work. The key steps are: define state, write a recurrence relation, set base cases, and choose top-down (memoization) or bottom-up (tabulation). DP often yields O(n²) → O(n) time improvements over brute force.

3147.cs

// Approach: Scan from end; for each chain anchor collect every k-th element's energy backward.
// Time: O(n) Space: O(1)

public class Solution
{
    public int MaximumEnergy(int[] energy, int k)
    {
        int[] dp = (int[])energy.Clone();
        for (int i = energy.Length - 1 - k; i >= 0; --i)
            dp[i] += dp[i + k];
        return dp.Max();
    }
}

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