Your task is to build a list that contains the subtree sizes for all the nodes in a tree from the smallest to the largest.
For example, in the tree below, the desired list is [1, 1, 1, 1, 2, 3, 7]. The tree has four leaves with a subtree size of 1. The node 2 has a subtree of size 2, the node 4 has a subtree of size 3, and the node 1 has a subtree of size 7.
In a file subtrees.py, implement the function count_subtrees that takes a reference to the root of a tree as parameter and returns the list of subtree sizes.
class Node:
def __init__(self, value, children=None):
self.value = value
self.children = children if children else []
def __repr__(self):
if self.children == []:
return f"Node({self.value})"
else:
return f"Node({self.value}, {self.children})"
def count_subtrees(node):
# TODO
if __name__ == "__main__":
tree1 = Node(1, [Node(4, [Node(3), Node(7)]),
Node(5),
Node(2, [Node(6)])])
print(count_subtrees(tree1)) # [1, 1, 1, 1, 2, 3, 7]
tree2 = Node(1, [Node(2, [Node(3, [Node(4)])])])
print(count_subtrees(tree2)) # [1, 2, 3, 4]
tree3 = Node(1, [Node(2), Node(3), Node(4)])
print(count_subtrees(tree3)) # [1, 1, 1, 4]