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.