CustomCC0-1.0#cp-tp3-0031650

Weighted Range Reversal

Summary

•Phase 3 / array-reversal
•Reasoning-first competitive programming drill

Problem Description

Given an array of n positive integers, you may perform at most one subarray reversal. After the reversal, what is the maximum possible sum of weighted prefix sums (i.e., sum_{

i=1}^n

a_{i}

)? Output the maximum sum. How to read this problem in plain language: - This is a Phase 3 reasoning drill focused on array-reversal. - Typical lenses to test first: array, prefix-sum, reversal. - Constraints reminder: 1 ≤

n \leq 2 e 5;

1 ≤

a_{i} \leq 1 e 6

Mini examples for mental simulation: 1) Boundary example: Describe why this case is tricky. Explain expected behavior and why naive logic may fail. 2) Adversarial example: Adversarial case where naive greedy/local decision looks correct but fails globally. Lite-mode writing target: - Write 1~2 observations that shrink the search space. - Name one final algorithm and state target complexity explicitly. - Validate with at least 2 edge cases and one hand simulation.

Constraints

•
1 ≤ $n \leq 2 e 5;$ 1 ≤ $a_{i} \leq 1 e 6$

Analysis

Key Insight

Use this hint to refine your reasoning. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.

arrayprefix-sumreversaloptimization