The primary aim of utilizing the A* search algorithm is to determine the most optimal route from an initial node to a target node in a graph with assigned weights. This process factors in the cost of the path taken so far and an approximation of the cost of the remaining path leading to the target node.

## Objective

The A* search algorithm is a pathfinding algorithm that is commonly used in artificial intelligence and robotics. It is a best-first search algorithm that uses a heuristic function to estimate the cost of the remaining path to the goal. The algorithm works by maintaining two lists: an open list of nodes that are to be expanded and a closed list of nodes that have already been expanded.

The algorithm starts by adding the starting node to the open list. Then, it repeatedly selects the node with the lowest f value (the sum of the cost of the path already taken and the estimated cost of the remaining path) from the open list, expands it by generating its child nodes, and adds them to the open list if they have not already been visited. The algorithm continues until the goal node is found or the open list is empty.

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```import heapq
class Node:
def __init__(self, state, parent=None, g=0, h=0):
self.state = state
self.parent = parent
self.g = g
self.h = h
self.f = g + h
def __lt__(self, other):
return self.f < other.f
def a_star_search(initial_state, goal_state, heuristic_func):
# Initialize the start node with a zero g value and the given heuristic value
start_node = Node(initial_state, None, 0, heuristic_func(initial_state, goal_state))
# Create a priority queue to store the nodes to be expanded
open_list = []
heapq.heappush(open_list, start_node)
# Create a set to keep track of already visited states
closed_set = set()
while open_list:
# Pop the node with the lowest f value from the priority queue
current_node = heapq.heappop(open_list)
# Check if the current node is the goal state
if current_node.state == goal_state:
# If so, return the solution path
solution_path = []
while current_node:
solution_path.append(current_node.state)
current_node = current_node.parent
solution_path.reverse()
print("Solution path:", solution_path)
print("Solution cost:", solution_path[-1].g)
return
# Generate the child nodes and add them to the priority queue
for next_state in get_next_states(current_node.state):
next_g = current_node.g + get_cost(current_node.state, next_state)
next_h = heuristic_func(next_state, goal_state)
next_node = Node(next_state, current_node, next_g, next_h)
# Check if the next state has already been visited
if next_state in closed_set:
continue
# Otherwise, add the next node to the priority queue
heapq.heappush(open_list, next_node)
# Add the current state to the set of visited states
closed_set.add(current_node.state)
# If no solution is found, return None
print("No solution found.")
return
def get_next_states(state):
# Function to generate the next possible states
# Implement this function according to your problem
pass
def get_cost(state1, state2):
# Function to compute the cost of moving from state1 to state2
# Implement this function according to your problem
pass
def heuristic_func(state, goal_state):
# Function to compute the heuristic value for a given state
# Implement this function according to your problem
pass