Question

I’m working on a problem for class I’m stuck on. It involves adding a methods to the Binary Search Tree found here: http://algs4.cs.princeton.edu/32bst/BST.java.html

I need to develop an iterative ceiling method that finds the ceiling for a given key. It cannot be recursive.

Here is my code so far. I understand the basics of the algorithm I am supposed to implement, but I’m finding actually doing so hard to wrap my head around.

Thanks in advance for any help you might be able to offer.

public Key ceiling_i(Key key)
{
    Node t = root;
    for(int i = 0; i < size(); i++){
        int cmp = key.compareTo(t.key);
        if(cmp == 0) return t.key;
        else if(cmp < 0) t = t.left;
        else if(cmp > 0) t = t.right;

    }
    return null;
}

Edit: The main problem I am having is how to deal with the iterations after the first one. According to my book, “If a given key is greater than the key at the root of a BST,
then the ceiling of key (the largest key in the BST greater
than or equal to key) must be in the right subtree. If key is
less than the key at the root, then the ceiling of key could
be in the left subtree; if not (or if key is equal to the key
at the root), then the key at the root is the ceiling of key.” I am not sure how to deal with that in the loop.

Answer 1

Your code is a good start. But your for loop does not make sense to me.

public Key ceiling_i(Key key)
{
    Node t = root;
    Node t largestVisited = null;
    while(t != null) {
        int cmp = key.compareTo(t.key);
        if(cmp == 0) return t.key;
        else if(cmp < 0) { largestVisited = Min(t, largestVisited); t = t.left; }
        else if(cmp > 0) { t = t.right; largestVisited = Min(t, largestVisited); }

    }
    return largestVisited;
}

Node Min(Node a, Node b) { return the node with the smaller key; }

Tip: You could have derived this code by first writing the recursive solution and noticing that it is tail recursive. Tail recursive functions can trivially made non-recursive by just reusing the already existing local variables. No need to open another stack-frame if you won’t ever use the old one again.