2.2. Using Dynamic Programming on the Grid

Try these first

1. 1.

   Define what dynamic programming is.

   Hint

   Think about strategies to optimize complex problems.

2. 2.

   What will be the value of paths(0,0)?

   Hint

   Consider how many movements are needed to stay put.

3. 3.

   What are the two valid moves on the grid?

   • Up and Down
   • Left and Right
   • Right and Up

   Hint

   Think about how you navigate through a checkerboard.

4. 4.

   True or False: Dynamic programming is equivalent to brute force methods.

   • True
   • False

   Hint

   Recall the essence of optimization in programming.

5. 5.

   Given a 4x4 grid with holes at positions (1,1) and (2,2), calculate the number of ways to get from (0,0) to (3,3).

   Hint

   Start by laying out the grid and systematically fill in values on the way.

6. 6.

   Design an algorithm that identifies the optimal path through a grid containing multiple holes while visiting all non-holes.

   Hint

   Think about how you'd navigate challenges while ensuring all lanes are covered.