goal start Figure 3: A hexagonal tiling with free cells colored white and impassable cells colored gray.

Consider the problem of path planning on a hexagonal tiling where some of the cells are traversable (white) and some of the cells are untraversable (gray), as shown in Figure 3. An agent must find the shortest path from a start cell to a goal cell, with the length of a path being defined as the number of cells the path goes through.

2. Define an admissible heuristic for this problem. Show that this heuristic is admissible.

3. What is the minimum number of cells A* with your heuristic needs to expand in the grid shown in Figure 3 before finding a path to the goal.

NOTE- Not a coding problem.