binary-search

name	binary-search
description	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.
topic	Binary Search
token_cost	90
related	["sorting-choice","two-pointers","hash-vs-tree"]
keywords	["binary","search","sorted","monotonic","bisect","minimum","maximum","feasible","predicate","lower","upper","bound","log","efficient","mid","pivot","rotated"]

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.