#### Dijkstra Binary Grid

L
```"""
This script implements the Dijkstra algorithm on a binary grid.
The grid consists of 0s and 1s, where 1 represents
a walkable node and 0 represents an obstacle.
The algorithm finds the shortest path from a start node to a destination node.
Diagonal movement can be allowed or disallowed.
"""

from heapq import heappop, heappush

import numpy as np

def dijkstra(
grid: np.ndarray,
source: tuple[int, int],
destination: tuple[int, int],
allow_diagonal: bool,
) -> tuple[float | int, list[tuple[int, int]]]:
"""
Implements Dijkstra's algorithm on a binary grid.

Args:
grid (np.ndarray): A 2D numpy array representing the grid.
1 represents a walkable node and 0 represents an obstacle.
source (Tuple[int, int]): A tuple representing the start node.
destination (Tuple[int, int]): A tuple representing the
destination node.
allow_diagonal (bool): A boolean determining whether
diagonal movements are allowed.

Returns:
Tuple[Union[float, int], List[Tuple[int, int]]]:
The shortest distance from the start node to the destination node
and the shortest path as a list of nodes.

>>> dijkstra(np.array([[1, 1, 1], [0, 1, 0], [0, 1, 1]]), (0, 0), (2, 2), False)
(4.0, [(0, 0), (0, 1), (1, 1), (2, 1), (2, 2)])

>>> dijkstra(np.array([[1, 1, 1], [0, 1, 0], [0, 1, 1]]), (0, 0), (2, 2), True)
(2.0, [(0, 0), (1, 1), (2, 2)])

>>> dijkstra(np.array([[1, 1, 1], [0, 0, 1], [0, 1, 1]]), (0, 0), (2, 2), False)
(4.0, [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2)])
"""
rows, cols = grid.shape
dx = [-1, 1, 0, 0]
dy = [0, 0, -1, 1]
if allow_diagonal:
dx += [-1, -1, 1, 1]
dy += [-1, 1, -1, 1]

queue, visited = [(0, source)], set()
matrix = np.full((rows, cols), np.inf)
matrix[source] = 0
predecessors = np.empty((rows, cols), dtype=object)
predecessors[source] = None

while queue:
(dist, (x, y)) = heappop(queue)
if (x, y) in visited:
continue

if (x, y) == destination:
path = []
while (x, y) != source:
path.append((x, y))
x, y = predecessors[x, y]
path.append(source)  # add the source manually
path.reverse()
return matrix[destination], path

for i in range(len(dx)):
nx, ny = x + dx[i], y + dy[i]
if 0 <= nx < rows and 0 <= ny < cols:
next_node = grid[nx][ny]
if next_node == 1 and matrix[nx, ny] > dist + 1:
heappush(queue, (dist + 1, (nx, ny)))
matrix[nx, ny] = dist + 1
predecessors[nx, ny] = (x, y)

return np.inf, []

if __name__ == "__main__":
import doctest

doctest.testmod()
```  