Children

Your task is to build a list that contains the child counts of all the nodes in a tree from the smallest to the largest.

For example, in the tree below, the desired list is $[0, 0, 0, 0, 1, 2, 3]$. The tree has four nodes that have no children. The node $2$ has one child, the node $4$ has two children, and the node $1$ has three children.

In a file children.py, implement the function count_children that takes a reference to the root of a tree as parameter and returns the list of child counts.

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_children(node):
    # TODO

if __name__ == "__main__":
    tree1 = Node(1, [Node(4, [Node(3), Node(7)]),
                     Node(5),
                     Node(2, [Node(6)])])
    print(count_children(tree1)) # [0, 0, 0, 0, 1, 2, 3]

    tree2 = Node(1, [Node(2, [Node(3, [Node(4)])])])
    print(count_children(tree2)) # [0, 1, 1, 1]

    tree3 = Node(1, [Node(2), Node(3), Node(4)])
    print(count_children(tree3)) # [0, 0, 0, 3]