2.2.3. Handling Holes in Computation

Try these first

1. 1.

   What is the formula for calculating the number of paths to a point (i, j) on the grid?

   Hint

   Think about where you can come from to reach (i, j).

2. 2.

   If there's a hole at (2, 2), what is the value of Paths(2, 2)?

   Hint

   What does a hole represent in terms of path counts?

3. 3.

   What value do we assign to paths when there's a hole in the grid?

   • 1
   • 0
   • infinity

   Hint

   Recall the definition of a hole in the context of paths.

4. 4.

   True or False: Dynamic programming only calculates necessary paths as needed.

   • True
   • False

   Hint

   Consider how each method approaches problem-solving.

5. 5.

   You have a grid of size 6x6 with holes at (2, 2), (3, 3), and (1, 5). Calculate the number of unique paths from (0, 0) to (5, 5). What strategies will you employ?

   Hint

   Focus on filling values in a structured manner and adjust according to hole placements.

6. 6.

   Compare the efficiency of dynamic programming versus memoization in a scenario where 70% of the grid is filled with holes. Discuss any trade-offs.

   Hint

   Analyze how the structure of the grid and placement of holes contribute to each method’s computational efficiency.