# Binary Search

> Search on monotonic predicates for sorted arrays, answer spaces, and rotated arrays. Use when finding minimum/maximum values, insertion points, or solving 'minimize the maximum' problems.

- Skill: `aibot88/binary-search` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add aibot88/binary-search`
- Raw SKILL.md: https://api.skillmd.com/api/skills/aibot88/binary-search/raw
- Safety review: pending (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: aibot88 (https://skillmd.com/u/aibot88)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/aibot88/binary-search

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## When to use

Binary search works on any monotonic predicate, not just sorted arrays. Pattern: "find minimum X such that condition(X) is true" — binary search on the answer space.

## Rules

- Use bisect.bisect_left/bisect_right for sorted-array insertion points
- For "minimize the maximum" or "maximize the minimum" problems, binary search on the answer and check feasibility
- ALWAYS use lo + (hi - lo) // 2 to avoid overflow
- When searching rotated arrays, check which half is sorted first
- NEVER binary search on unsorted data without a monotonic predicate

## Complexity

Time: O(log n) — whenever you see "sorted" or "monotonic" in a problem, consider binary search.

## Example

"Minimize maximum load" → binary search on answer space. Check if `feasible(mid)` divides into k groups each ≤ mid. Use `lo + (hi - lo) // 2` to avoid overflow.