Question

which algorithm first sorts them in non-decreasing order, and and then considers them in order checking the distance between adjacent points to find the minimum,

Answer 1

The algorithm that first sorts the points in non-decreasing order and then checks the distance between adjacent points to find the minimum is called the nearest neighbor algorithm or the greedy algorithm.

Step-by-step explanation:

The algorithm that first sorts the points in non-decreasing order and then checks the distance between adjacent points to find the minimum is called the nearest neighbor algorithm or the greedy algorithm.

Here's an example to illustrate how this algorithm works:

1. Consider a set of points: (2,1), (4,3), (7,5), and (6,2).
2. Sort the points in non-decreasing order based on their x-coordinates: (2,1), (4,3), (6,2), and (7,5).
3. Starting from the first point, calculate the distances between adjacent points: (2,1) to (4,3) has a distance of sqrt((4-2)^2 + (3-1)^2) = 2.828, (4,3) to (6,2) has a distance of sqrt((6-4)^2 + (2-3)^2) = 2.236, and (6,2) to (7,5) has a distance of sqrt((7-6)^2 + (5-2)^2) = 3.162.
4. The minimum distance is 2.236, which corresponds to the pair of points (4,3) and (6,2).