Ancestors

Your task is to find out if a node $a$ is an ancestor of a node $b$ in a given tree. This means that one can get from the node $a$ to the node $b$ by going downwards in the tree, i.e., the node $b$ is in the subtree of the node $a$.

For example, in the tree below, the node $1$ is an ancestor of the node $3$ and the node $2$ is an ancestor of the node $6$.

In a file ancestors.py, implement the function ancestor, whose parameters are a reference to the root of a tree and the node identifiers $a$ and $b$. The function returns True or False.

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 ancestor(node, a, b):
    # TODO

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

    tree2 = Node(1, [Node(2, [Node(3, [Node(4)])])])
    print(ancestor(tree2, 1, 4)) # True
    print(ancestor(tree2, 3, 2)) # False

    tree3 = Node(1, [Node(2), Node(3), Node(4)])
    print(ancestor(tree3, 1, 2)) # True
    print(ancestor(tree3, 1, 1)) # True
    print(ancestor(tree3, 2, 1)) # False
    print(ancestor(tree3, 5, 5)) # False