13.2.2. Distance Formula

Try these first

1. 1.

   Calculate the distance between the points (3, 4) and (7, 1).

   Hint

   Use the Distance Formula.

2. 2.

   If A is (2, 2) and B is (5, 5), can you find the distance between A and B?

   Hint

   What do the coordinates tell you about the distance?

3. 3.

   What is the time complexity of the brute-force method to find the closest pair of points?

   • O(n log n)
   • O(n²)
   • O(n)

   Hint

   Think about how many pairs you would check.

4. 4.

   Statement: The Distance Formula assumes points have the same coordinates to start. True or False?

   • True
   • False

   Hint

   What does the formula require for its application?

5. 5.

   Consider a set of points: (1, 3), (2, 9), (3, 6), (5, 1), and (7, 8). Apply the divide and conquer method to find the closest pair, detailing your steps.

   Hint

   Remember to only focus on points near the boundary; many distances might not apply.

6. 6.

   Given ten random points in a 2D-plane, devise a strategy using the concepts from this section to find the closest pair in the least amount of time.

   Hint

   Efficiency in reducing the search space is crucial.