Question

I’m trying to implement the OS-Rank() function for my binary tree that I’ve built. OS-Rank tags a node with a count of smaller nodes from the tree, and stores it in node.size. This allows OS-Select to easily select the i’th smallest node in O(nlgn) time.

Here is the pseudo code:

OS-RANK(x)
    r = x.left.size + 1
    y = x
    while y != T.root
        if y == y.parent.right
            r = r + y.parent.left.size + 1
        y = y.parent
    return r

Here’s my code:

def osrank(self, root):
    r = 0
    if self.left != None:
        r = self.left.size + 1
    else:
        r += 1
    y = self
    while y != root:
        if y == y.parent.right:
            if y.parent.left != None:
                r = r + y.parent.left.size + 1
            else:
                r += 1
        y = y.parent
    self.size = r

Not too different, except that I had to handle cases where nodes were null.

However, when I print out my in order traversal after inserting {5,2,7,1,6}, I get this:

L L 1(1) U 2(1) U 5(1) R L 6(3) U 7(3) U U

(L/U/R describes traversals, and the number in brackets is node.size, or the rank).
I think I’m expecting something like this:

L L 1(1) U 2(2) U 5(5) R L 6(1) U 7(2) U U

Any advice?

Answer 1

Embarrassingly, I’ve misunderstood the purpose of OS-Rank(). I thought it set the size value of each node, but it appears that’s actually done on insert. OS-Rank() returns the rank of a node by using that size value.

No more 2am coding, I promise!