2.1.2. Boundary Conditions

Try these first

1. 1.

   What is the total path count to reach the point (2, 2) in a grid without any holes?

   Hint

   Consider the unique routes without obstruction.

2. 2.

   How many paths are possible to (0,0)?

   Hint

   Think about moving or not moving.

3. 3.

   How many paths lead to the point (3,3) in a grid from (0,0) with no obstructions?

   • 4
   • 6
   • 8

   Hint

   Think about how many ways you can arrange moving right and up.

4. 4.

   True or False: Dynamic programming only solves each problem once.

   • True
   • False

   Hint

   Reflect on how it builds solutions from the ground up.

5. 5.

   Given a 4x4 grid with holes at (2,1) and (3,3), calculate the unique paths from (0,0) to (3,3).

   Hint

   Map out each possible movement and count how many actually reach (3,3).

6. 6.

   Create a dynamic programming solution to count paths in a grid with multiple holes, detailing algorithm steps.

   Hint

   Think about how each hole affects adjacent path calculations.