Question

Given an array of n points in a 2D plane, write a pseudocode to find out the closest pair of points in the array using the divide-and-conquer approach.

Answer 1

To find the closest pair of points using divide-and-conquer, one needs to sort the points, divide them into halves, recursively find the closest pair in each half, and then find the closest cross-pair, returning the overall closest pair.

Step-by-step explanation:

The problem statement given involves applying a divide-and-conquer approach to find the closest pair of points among a set of points on a 2D plane. This is a classic computational geometry problem that falls under the subject of Computers and Technology and is generally introduced at the college level as part of a data structures or algorithms course.

To tackle this problem, we can use the following pseudocode:

1. Sort all points according to x-coordinates.
2. Divide the set of points into two equal halves by drawing a vertical line.
3. Recursively find the closest pair of points in both halves.
4. Find the closest pair of points that sits on the opposite sides of the dividing line.
5. Return the closest pair found in steps 3 and 4.

It's important to note that step 4 requires us to only consider points that are within the smallest distance found in step 3, reducing the number of comparisons significantly.