2.1.4. Handling Holes

Try these first

1. 1.

   What is the number of paths to point (1,0) from (0,0)?

   Hint

   Think of how you can only move from (0,0) to (1,0) directly.

2. 2.

   If a hole is placed at point (2,2), how many paths can go through it?

   Hint

   Consider what happens when a point is obstructed.

3. 3.

   What is the base case for paths(0,0)?

   • 0
   • 1
   • 2

   Hint

   Consider what it means to be at the origin without moving.

4. 4.

   Can paths go through holes?

   • True
   • False

   Hint

   Think about what a hole represents in terms of pathfinding.

5. 5.

   Design a 5x5 grid with two holes and calculate the number of unique paths from (0,0) to (4,4). Provide a step-by-step explanation.

   Hint

   Map out the valid paths while taking into consideration each hole's impact.

6. 6.

   Explain how the choice between using memoization versus dynamic programming can affect the performance of computing paths on a grid with multiple obstacles.

   Hint

   Reflect on memory usage versus time efficiency.