13.2.3. Assumption for Analysis

Try these first

1. 1.

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

   Hint

   Think about how many comparisons you need to make.

2. 2.

   What does 'divide and conquer' mean?

   Hint

   Remember the steps: split, solve, combine.

3. 3.

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

   • O(n)
   • O(n^2)
   • O(n log n)

   Hint

   How many pairs are there for n points?

4. 4.

   True or False: The divide and conquer approach guarantees an optimal solution.

   • True
   • False

   Hint

   What does 'guarantee' mean in terms of algorithm results?

5. 5.

   Given a set of random points, implement the divide and conquer algorithm to find the closest pair and explain each step taken.

   Hint

   Refer back to each step in the process.

6. 6.

   Discuss the trade-offs when implementing the closest pair problem for 1D and 2D datasets. What complexities arise?

   Hint

   Consider spatial dimensions and their implications.