<｜begin▁of▁sentence｜>### Instruction:
Imagine that I am working with a patient recovering from a lower extremity injury, and we're creating a tailored rehabilitation routine that includes navigating through a specific environment to improve spatial awareness and mobility. We have designed a grid-like mock-up of a town square that the patient will traverse, scaled down to a 3x3 model for simplicity's sake. The objective is for the patient to move from the 'park' located at the bottom-left corner to the 'library' at the top-right corner.

The challenge here is that the difficulty of moving across the grid increases as you proceed eastward—the 'cost' associated with each step multiplies by a factor of 2 with every step to the right, symbolizing increased endurance and strength requirements at those points on our grid (specifically linked to the x-coordinate of the squares on the grid).

We will be utilizing a technical method known as the A* algorithm to ascertain the most efficient path for the patient to take. This approach will not only consider the physical layout of the town square but also incorporate a "heuristic" based on a straight-line (Euclidean) distance to keep the path as direct as possible.

In this tailored exercise, could we map out what this optimal rehabilitation path would look like within our grid, respecting the increasing 'cost' as we move eastward across the squares? It is crucial that this navigation exercise remains both challenging and achievable to promote recovery optimally.
### Response:
import networkx as nx

# Create a graph
G = nx.grid_graph(dim=[3,3])  # nodes are two-tuples (x,y)

# Set edge weights
nx.set_edge_attributes(G, {e: e[1][0]*2 for e in G.edges()}, "weight")

# Define a heuristic function
def euclidean_dist(a, b):
    (x1, y1) = a
    (x2, y2) = b
    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

# Use A* algorithm to find the shortest path
path = nx.astar_path(G, (0, 0), (2, 2), heuristic=euclidean_dist, weight='weight')

print("Shortest path using A* algorithm:", path)
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