#### A Star

P
A
p
"""
The A* algorithm combines features of uniform-cost search and pure heuristic search to
efficiently compute optimal solutions.

The A* algorithm is a best-first search algorithm in which the cost associated with a
node is f(n) = g(n) + h(n), where g(n) is the cost of the path from the initial state to
node n and h(n) is the heuristic estimate or the cost or a path from node n to a goal.

The A* algorithm introduces a heuristic into a regular graph-searching algorithm,
essentially planning ahead at each step so a more optimal decision is made. For this
reason, A* is known as an algorithm with brains.

https://en.wikipedia.org/wiki/A*_search_algorithm
"""

import numpy as np

class Cell:
"""
Class cell represents a cell in the world which have the properties:
position: represented by tuple of x and y coordinates initially set to (0,0).
parent: Contains the parent cell object visited before we arrived at this cell.
g, h, f: Parameters used when calling our heuristic function.
"""

def __init__(self):
self.position = (0, 0)
self.parent = None
self.g = 0
self.h = 0
self.f = 0

"""
Overrides equals method because otherwise cell assign will give
wrong results.
"""

def __eq__(self, cell):
return self.position == cell.position

def showcell(self):
print(self.position)

class Gridworld:
"""
Gridworld class represents the  external world here a grid M*M
matrix.
world_size: create a numpy array with the given world_size default is 5.
"""

def __init__(self, world_size=(5, 5)):
self.w = np.zeros(world_size)
self.world_x_limit = world_size[0]
self.world_y_limit = world_size[1]

def show(self):
print(self.w)

def get_neighbours(self, cell):
"""
Return the neighbours of cell
"""
neughbour_cord = [
(-1, -1),
(-1, 0),
(-1, 1),
(0, -1),
(0, 1),
(1, -1),
(1, 0),
(1, 1),
]
current_x = cell.position[0]
current_y = cell.position[1]
neighbours = []
for n in neughbour_cord:
x = current_x + n[0]
y = current_y + n[1]
if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
c = Cell()
c.position = (x, y)
c.parent = cell
neighbours.append(c)
return neighbours

def astar(world, start, goal):
"""
Implementation of a start algorithm.
world : Object of the world object.
start : Object of the cell as  start position.
stop  : Object of the cell as goal position.

>>> p = Gridworld()
>>> start = Cell()
>>> start.position = (0,0)
>>> goal = Cell()
>>> goal.position = (4,4)
>>> astar(p, start, goal)
[(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]
"""
_open = []
_closed = []
_open.append(start)

while _open:
min_f = np.argmin([n.f for n in _open])
current = _open[min_f]
_closed.append(_open.pop(min_f))
if current == goal:
break
for n in world.get_neighbours(current):
for c in _closed:
if c == n:
continue
n.g = current.g + 1
x1, y1 = n.position
x2, y2 = goal.position
n.h = (y2 - y1) ** 2 + (x2 - x1) ** 2
n.f = n.h + n.g

for c in _open:
if c == n and c.f < n.f:
continue
_open.append(n)
path = []
while current.parent is not None:
path.append(current.position)
current = current.parent
path.append(current.position)
return path[::-1]

if __name__ == "__main__":
world = Gridworld()
# Start position and goal
start = Cell()
start.position = (0, 0)
goal = Cell()
goal.position = (4, 4)
print(f"path from {start.position} to {goal.position}")
s = astar(world, start, goal)
#   Just for visual reasons.
for i in s:
world.w[i] = 1
print(world.w)