2.3.3. Conclusion on Dynamic Programming

Try these first

1. 1.

   Define dynamic programming in your own words.

   Hint

   Think about how you can simplify larger problems.

2. 2.

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

   Hint

   Consider the definition of paths at the starting point.

3. 3.

   What does dynamic programming primarily aim to solve?

   • Minimizing space
   • Optimizing recursive calls
   • Iteratively computing results

   Hint

   Consider how dynamic programming processes information.

4. 4.

   True or False: Memoization will calculate all grid points even if they are blocked by obstacles.

   • True
   • False

   Hint

   Think about the nature of memoization.

5. 5.

   Given a 5x5 grid with holes at (1,2), (2,1), and (3,3), calculate the number of distinct paths from (0,0) to (4,4). Discuss your process.

   Hint

   Break down the problem row by row or column by column.

6. 6.

   Analyze the implications of having a dense line of holes in a grid. How would that affect path computations utilizing dynamic programming?

   Hint

   Consider how paths can be blocked entirely by closely placed holes.