CustomCC0-1.0#P005-4511400
Nearest Power Multiple
Summary
- •Phase 4 / number_theory/powers_of_two
- •Reasoning-first competitive programming drill
Problem Description
Given an integer N and an array of length N, for each index i, determine the minimal such that A[i] * k is a power of 2. If not possible (for A[i]=0), output -1.
How to read this problem in plain language:
- This is a Phase 4 reasoning drill focused on numbe/power_two.
- Typical lenses to test first: number theory, bit manipulation.
- Constraints reminder: 1 ≤ 0 ≤ A[i] ≤ 10^9
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 ≤ 0 ≤ A[i] ≤ 10^9
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.
number theorybit manipulation