Your task is to count the number of nodes at a given depth in a tree.
For example, in the following tree, the node 1 is at the depth 0, the nodes 4, 5 and 2 are at the depth 1, and the nodes 3, 7 and 6 are at the depth 2.
In a file depths.py, implement the function count_nodes that takes a reference to the root of the tree and the desired depth as parameters and returns the node count.
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_nodes(node, depth):
# TODO
if __name__ == "__main__":
tree1 = Node(1, [Node(4, [Node(3), Node(7)]),
Node(5),
Node(2, [Node(6)])])
print(count_nodes(tree1, 0)) # 1
print(count_nodes(tree1, 1)) # 3
print(count_nodes(tree1, 2)) # 3
print(count_nodes(tree1, 3)) # 0
tree2 = Node(1, [Node(2, [Node(3, [Node(4)])])])
print(count_nodes(tree2, 0)) # 1
print(count_nodes(tree2, 1)) # 1
print(count_nodes(tree2, 2)) # 1
print(count_nodes(tree2, 3)) # 1
print(count_nodes(tree2, 4)) # 0
tree3 = Node(1, [Node(2), Node(3), Node(4)])
print(count_nodes(tree3, 0)) # 1
print(count_nodes(tree3, 1)) # 3
print(count_nodes(tree3, 2)) # 0