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Tree Decomposition Path Evaluator 3 Solution

Problem Statement

Given a high-dimensional input dataset or state graph of length $N$, calculate the optimal result using the **Monotonic Queue Sliding Horizon** algorithm. Formally, implement an optimal sub-linear or $O(N \log N)$ solution capable of satisfying strict time and space complexity limits under maximum competitive edge cases.

Example 1

Input

arr = [7, 11, 15, 19]

Output

Explanation: By applying Monotonic Queue Sliding Horizon, the optimal hard constraint value evaluates to 62.

Example 2

Input

arr = [4, 11]

Output

Explanation: Minimal edge input evaluates to 8.

Constraints

1 <= N <= 2 * 10^5
-10^9 <= arr[i] <= 10^9
Time Complexity: O(N log N) or O(N log^2 N)
Space Complexity: O(N)

Tree Decomposition Path Evaluator 3 Solution

Problem Statement

Input

Output

Input

Output

Constraints

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