CustomCC0-1.0#cp0081500
Minimum Total Weight to Balance Array
Summary
- •Phase 4 / greedy, math, optimization
- •Reasoning-first competitive programming drill
Problem Description
You are given an array of n integers. In one operation, you may add or subtract a weight w (1 ≤ ) to any element. What is the minimal total weight needed to make all elements equal?
How to read this problem in plain language:
- This is a Phase 4 reasoning drill focused on greedy, math, optimization.
- Typical lenses to test first: greedy, array, math.
- Constraints reminder: 1 ≤ 1 ≤ 1 ≤
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 ≤ 1 ≤ 1 ≤
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.
greedyarraymath