binary-search

Included with Lifetime

$97 forever

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.

General

What this skill does


## 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.

Files: 1

Size: 1.4 KB

Complexity: 10/100

Category: General

Source: https://github.com/knoopx/pi/tree/main/agent/skills/knowledge/binary-search

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