13.7. Complexity Analysis

Try these first

1. 1.

   What is the time complexity of the brute-force method for finding the closest pair of points?

   Hint

   Consider how many pairs you need to check.

2. 2.

   What theorem do we use for distance calculations?

   Hint

   Remember the formula using x and y differences.

3. 3.

   What is the time complexity of the divide and conquer approach for the closest pair of points?

   • O(n)
   • O(n log n)
   • O(n²)

   Hint

   Think about sorting and splitting in the process.

4. 4.

   Is the brute-force method efficient for large datasets?

   • True
   • False

   Hint

   Consider the growth rate of pair comparisons.

5. 5.

   Given 10 random points, explain step-by-step how the closest pair would be determined using the divide and conquer approach while providing specific distance calculations.

   Hint

   Remember to calculate distances as you compare candidates.

6. 6.

   In a dataset of 50 random points, simulate the divide and conquer approach and describe how many pairwise distance checks would be required versus using a naive method.

   Hint

   Use the formula for combinations to count pairs: n(n-1)/2.