13.4.3. Recursive Call for Q and R

Try these first

1. 1.

   What is the time complexity of the naive solution to the closest pair problem?

   Hint

   Consider how many pairs you have to check in the brute-force method.

2. 2.

   Explain why sorting is beneficial in the closest pair algorithm.

   Hint

   Think about how adjacent points relate to the closest pairing.

3. 3.

   What algorithmic technique does the closest pair problem use?

   • Greedy Algorithm
   • Divide and Conquer
   • Brute Force

   Hint

   Think about how we break down the problem into smaller pieces.

4. 4.

   True or False: The closest pair algorithm can only be applied if all points have unique coordinates.

   • True
   • False

   Hint

   Consider how duplicates may or may not affect overall results.

5. 5.

   You're given six points: A(1, 1), B(1, 3), C(4, 2), D(5, 1), E(2, 4), F(3, 5). Apply the closest pair algorithm to find the closest pair. Show your working.

   Hint

   Run through the algorithm step-by-step, sorting first and checking adjacent pairs.

6. 6.

   Imagine applying a nearest neighbor technique for a group of 10 random points. Propose a method that ensures the algorithm stays efficient and does not revert to O(n²) even with duplicates.

   Hint

   Think about leveraging both sorting and efficient data structures.