13.4. Two Dimensional Case

Try these first

1. 1.

   What is the time complexity of a brute force closest pair algorithm?

   Hint

   Consider how many pairs you have to check.

2. 2.

   Name the formula used to calculate distance in a 2D plane.

   Hint

   It involves squares and square roots.

3. 3.

   What effect does sorting the points have on the closest pair algorithm?

   • A. It decreases time complexity
   • B. It is unnecessary
   • C. It causes the points to overlap

   Hint

   Think about how you would approach finding the closest points without sorting.

4. 4.

   Is the closest pair algorithm based on divide and conquer?

   • True
   • False

   Hint

   Recall the key strategy we discussed.

5. 5.

   Given the coordinates of 10 points in a 2D plane, visualize their positions and demonstrate the divide-and-conquer steps you would take to find the closest pair.

   Hint

   Focus on groups of points and how they might interact on either side of the dividing line.

6. 6.

   Create a real-world scenario where finding the closest pair would be advantageous. Describe how you would implement the algorithm while considering limitations.

   Hint

   Think of a dynamic or changing environment, like a delivery service.