# Untitled

unknown
python
a year ago
2.5 kB
21
Indexable
Never
```import math

# Function to apply the necessary operations to a given number
def apply_ops(num, goal):
# Initialize the resulting nodes
floor_num, sqrt_num, factorial_num = None, None, None
# If the goal is a smaller number than the start node, apply the floor operation
if goal < num:
floor_num = math.floor(num)
# If the goal is a perfect square, apply the square root operation
if math.isqrt(goal)**2 == goal:
if math.isqrt(num)**2 == num:
sqrt_num = math.isqrt(num)
# If the goal is a factorial of an integer, apply the factorial operation
if math.factorial(int(goal)) == goal:
if num == int(num):
factorial_num = math.factorial(int(num))
# Return the floor of the number only if it has not been applied before
if floor_num == num:
floor_num = None
return floor_num, sqrt_num, factorial_num

# Function to perform iterative deepening depth-first search
def iddfs(goal, visited, path, depth):
# If the start node is the goal node, return the path
if 4 == goal:
return path
# If the maximum depth is reached, return None
if depth == 0:
return None
# Mark the start node as visited
visited.add(4)
# Apply the necessary operations to the start node
floor_num, sqrt_num, factorial_num = apply_ops(4, goal)
# Add the resulting nodes to the path if they are not visited
if floor_num is not None and floor_num not in visited:
result = iddfs(goal, visited, path+[("floor", floor_num)], depth-1)
if result is not None:
return result
if sqrt_num is not None and sqrt_num not in visited:
result = iddfs(goal, visited, path+[("sqrt", sqrt_num)], depth-1)
if result is not None:
return result
if factorial_num is not None and factorial_num not in visited:
result = iddfs(goal, visited, path+[("factorial", factorial_num)], depth-1)
if result is not None:
return result
# Return None if the goal is not reached
return None

# Test the function
goal = 5
result = None
depth = 1
while result is None:
result = iddfs(goal, set(), [("start", 4)], depth)
# Increment the depth limit
depth += 1

# Print the results
if result is not None:
print("The shortest path from 4 to {} is:".format(goal))
for i, (op, num) in enumerate(result[1:]):
print("Step {}: {} {}".format(i+1, op, num))
else:
print("No solution found")```