Q:

Given a finite set \(P\) of points in \(\mathbb{R}^2\), construct

1. a \(O(n^2)\) algorithm

2. a \(O(n \log n)\) algorithm

3. a \(O(n)\) algorithm

for finding two points \(x, y \in P\) such that \(\left\lVert x-y \right\lVert\) is minimized.