Balanced binary tree python

Question

# stack_depth is initialised to 0
def find_in_tree(node, find_condition, stack_depth):
    assert (stack_depth < max_stack_depth), 'Deeper than max depth'
    stack_depth += 1
    result = []
    if find_condition(node):
        result += [node]
    for child_node in node.children:
        result.extend(find_in_tree(child_node, find_condition, stack_depth))
    return result

I need help understanding this piece of code. The question i want to answer is

The Python function above searches the contents of a balanced binary tree. If an upper limit of 1,000,000 nodes is assumed what should the max_stack_depth constant be set to?

From what I understand, this is a trick question. If you think about it, stack_depth is incremented every time the find_in_tree() function is called in the recursion. And we are trying to find a particular node in the tree.So the worst case would be when we have to search through all the nodes in the tree before we find it. Hence, max_stack_depth should 1,000,000?

If you look at when stack_depth increments then it looks like we will increment every time we access a node. And in our case we are accessing every single node every time. Because there is no return condition when stops the algorithm when the correct node is found.

Can someone please try to explain me their thought process.

Answer 1

Instead of multiplying the number of nodes on each layer, you have to add them. For example, the number of nodes in the first four layers is 1+2+4+8=15, not 1*2*4*8=64.

                #                      1
      #                   #          + 2
  #       #           #       #      + 4
#   #   #   #       #   #   #   #    + 8 = 15

In general, the number of nodes in the first n layers is 2**(n+1)-1. You can use logarithms to get the correct power and get the floor of that number. If you want fewer that that number, you would also have to subtract one from the power.

>>> math.floor(math.log(1000000, 2))
19
>>> sum(2**i for i in range(1, 20))
1048574

Concerning your edit: Yes, stack_depth is incremented with each node, but you are incrementing a local variable. The increment will carry to the child nodes (passed as a parameter) but not to the siblings, i.e. all the nodes at level n will be called with stack_depth == n-1 (assuming it started as 0 on the first level). Thus, max_stack_depth should be 19 (or 20 if it starts with 1) to visit the ~1,000,000 nodes in the first 19 levels of the tree.