Nearest Pair Hot Sheet

Use this page when the task is:

one static set of planar points -> one global closest Euclidean pair

and you want the shortest route back to the active strip invariant.

Do Not Use When

• the points change online
• the task is really event ordering over segments or rectangles
• the statement wants the outer boundary of the points
• the metric or dimension changed enough that the usual 2D packing argument no longer applies directly

Choose By Signal

• one static nearest Euclidean pair -> closest-pair-sweep.cpp
• same family, but the repo note you want is implementation-heavy -> Minimum Euclidean Distance
• outer boundary of many points -> Convex Hull
• many geometric events, active objects, and local neighbor rules -> Sweep Line

Core Invariants

• points are processed in increasing x
• the active set contains exactly the points still close enough in x to matter
• the active set is ordered by y, because the surviving candidate window is a y interval
• internal comparisons are safest in squared distance, even if the final answer needs one square root

Main Traps

• mixing squared and unsquared distance in the strip test
• forgetting duplicate points imply answer 0
• ordering the active set by the wrong coordinate
• treating this as a hull or generic geometry-predicate problem

Exact Starters In This Repo

• exact starter -> closest-pair-sweep.cpp
• flagship in-lane rep -> Closest Pair
• compare point -> Minimum Euclidean Distance
• nearby chooser -> Geometry cheatsheet

Reopen Paths

• full lesson -> Nearest Pair of Points
• broader geometry chooser -> Geometry cheatsheet
• snippet chooser -> Template Library