binary-search-tree

I'm prepearing for tech interview, so basically learning algorithms from very beginning :) we are given a BST. I need to find the max length of a desc path in it, which always goes left or right In other words, an example tree's descending path is 2, ie 15-10-6 5 / \ 2 15 / 10 / \ 6 14 I'm very new to algorithmic problems.what are my steps to solving this? My idea was to use DFS and a counter to store the longest path. but I can't figure out how to employ recursion to do the job, whereas recursion seems more natural for this data structure. any suggestions/directions? The wording is a little

Suppose I have a balanced BST (binary search tree). Each tree node contains a special field count , which counts all descendants of that node + the node itself. They call this data structure order statistics binary tree . This data structure supports two operations of O(logN): rank(x) -- number of elements that are less than x findByRank(k) -- find the node with rank == k Now I would like to add a new operation median() to find the median. Can I assume this operation is O(1) if the tree is balanced? If the tree is complete (i.e. all levels completely filled), yes you can. Unless the tree is

I am not sure how to determine if a tree is balanced, perfectly balanced, or neither if I have it as a picture not a code For example if I have this tree How can I check if it's balanced, perfectly balanced, or unbalanced? and can someone give me an example of a perfectly balanced tree? [o] / \ [b] [p] \ / \ [d] [m] [r] Clearly I can tell that the tree is unbalanced if it was something like this: [b] \ [d] \ [r] \ [c] However, if it was something very similar to the one above I don't know how to get it This is a perfectly balanced and balanced tree: [k] / \ [A] [p] / \ [N] [R] Can someone

So this is my first java program, but I've done c++ for a few years. I wrote what I think should work, but in fact it does not. So I had a stipulation of having to write a method for this call: tree.insertNode(value); where value is an int. I wanted to write it recursively, for obvious reasons, so I had to do a work around: public void insertNode(int key) { Node temp = new Node(key); if(root == null) root = temp; else insertNode(temp); } public void insertNode(Node temp) { if(root == null) root = temp; else if(temp.getKey() <= root.getKey()) insertNode(root.getLeft()); else insertNode(root

I'm wondering what the consensus is on the definition of "ancestor" in a computer science context. I only ask because in Introduction to Algorithms , Second Edition, p. 259 there is a description of the algorithm Tree-Successor(x) that seems odd. In finding the successor of node x , [...] if the right subtree of node x is empty and x has a successor y , then y is the lowest ancestor of x whose left child is also an ancestor of x . In a binary search tree with a root having key 2 and children 1 and 3 , the successor of 1 is its parent 2 . In this case, x is the left child of x 's successor, y .