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Bitwise Or Interval Count

Thinking Mode

Summary

  • •Phase 4 / bitmasks, set_maintenance
  • •Reasoning-first competitive programming drill

Problem Description

Given an array of n integers, count the number of distinct values obtained as the bitwise OR of all subarrays. How to read this problem in plain language: - This is a Phase 4 reasoning drill focused on bitmasks, setm​aintenance. - Typical lenses to test first: bitmasks, set, subarrays. - Constraints reminder: 1 ≤ n≤1e5, 0 ≤ ai<220 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≤1e5, 0 ≤ ai<220

Analysis

Key Insight

The goal is to force explicit intermediate reasoning before revealing more.

bitmaskssetsubarrays
bitmaskssetsubarrays