2.1.3. Initial Conditions

Try these first

1. 1.

   How many paths are there to the point (0,0)?

   Hint

   Consider your starting point.

2. 2.

   What happens to the path count if there’s a hole at (2,3)?

   Hint

   Think about the implications of obstacles.

3. 3.

   What is the path count from (0,0) to (0,0)?

   • 0
   • 1
   • More than 1

   Hint

   Think about movement options.

4. 4.

   Paths to a point with a hole are counted as?

   • True
   • False

   Hint

   Remember the role of obstacles.

5. 5.

   In a 6x6 grid with holes at (2,2) and (3,3), compute the number of paths to (5,5) through dynamic programming and illustrate your table.

   Hint

   Start with your base cases and fill each cell considering blockage from holes.

6. 6.

   Construct a comprehensive table showing both memoized and dynamically programmed solutions for a 5x5 grid with four holes randomly distributed.

   Hint

   Use both methods to fill the same grid and compare the resulting path counts, especially noting differences in efficiency.