13.4.1. Dividing Points

Try these first

1. 1.

   What is the time complexity of the naive approach to finding the closest pair of points?

   Hint

   Think about how many pairs can be formed with n points.

2. 2.

   What formula do we use to calculate the distance between two points?

   Hint

   Recall the Pythagorean theorem.

3. 3.

   What time complexity does the divide and conquer algorithm achieve for the closest pair of points?

   • O(n)
   • O(n²)
   • O(n log n)

   Hint

   Consider how the recursive nature affects performance.

4. 4.

   True or False: The brute force algorithm is preferable to the divide and conquer method for large datasets.

   • True
   • False

   Hint

   Think about the performance of each method with more points.

5. 5.

   Given a set of 12 points, detail the step-by-step execution of the divide and conquer algorithm to find the closest pair.

   Hint

   Document each stage carefully to identify critical steps.

6. 6.

   Why is it not necessary to check all points across the dividing line when finding the closest pairs?

   Hint

   Focus on describing the zones for potential candidates.