13.7.1. Initial Sorting Phase

Try these first

1. 1.

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

   Hint

   Think about how many pairs need to be checked.

2. 2.

   Why do we sort the points before finding the closest pair?

   Hint

   Consider the steps of the divide and conquer method.

3. 3.

   What is the efficiency of the closest pair algorithm using divide and conquer?

   • O(n²)
   • O(n log n)
   • O(log n)

   Hint

   Think about how the algorithm is structured.

4. 4.

   Is it true that the closest pair might not be within the same half when using divide and conquer?

   • True
   • False

   Hint

   Consider the way boundary pairs are checked.

5. 5.

   Given the points (3, 4), (2, 3), (5, 1), (1, 5), and (6, 8), find the closest pair.

   Hint

   Use the distance formula and consider sorting to help with comparisons.

6. 6.

   Why does the distance branching reduce the number of comparisons for points in the boundary? Provide a mathematical explanation.

   Hint

   Think about the geometric arrangement of points and their distances.