Python - Inversion in nested dictionary

# Python3 code to demonstrate working of 
# Inversion in nested dictionary
# Using loop + recursion

# utility function to get all paths till end 
def extract_path(test_dict, path_way):
    if not test_dict:
        return [path_way]
    temp = []
    for key in test_dict:
        temp.extend(extract_path(test_dict[key], path_way + [key]))
    return temp

# function to compute inversion
def hlper_fnc(test_dict):
    all_paths = extract_path(test_dict, [])
    res = {}
    for path in all_paths:
        front = res
        for ele in path[::-1]:
            if ele not in front :
                front[ele] = {}
            front = front[ele]
    return res

# initializing dictionary
test_dict = {"a" : {"b" : {"c" : {}}},
             "d" : {"e" : {}},
             "f" : {"g" : {"h" : {}}}}

# printing original dictionary
print("The original dictionary is : " + str(test_dict))

# calling helper function for task 
res = hlper_fnc(test_dict)

# printing result 
print("The inverted dictionary : " + str(res)) 

# Sample input dictionary
test_dict = {"a": {"b": {}}, "d": {"e": {}}, "f": {"g": {}}}

# Invert the nested dictionary using a stack
stack = [(test_dict, None)]
inverted_dict = {}
while stack:
    d, parent_key = stack.pop()
    for k, v in d.items():
        if parent_key is not None:
            inverted_dict.setdefault(k, {}).update({parent_key: {}})
        if isinstance(v, dict):
            stack.append((v, k))

# Output the inverted dictionary
print(inverted_dict)