Binary tree drawing program

Predecessor v O h Time Complexity 8. Inorder Traversal O N Time Complexity Preorder and Postorder Traversal 9. Insert v O h Time Complexity Mini Quiz Remove v - Three Possible Cases Remove v - Case 1 Remove v - Case 2 Remove v - Case 3 Remove v - Case 3 Discussion The Answer Create BST Intermezzo Try Exploration Mode Balanced BST AVL Tree Extra BST Attribute: height v Formal Definition of height v Derivation of the Lower Bound The Combined Bound Step 1: Maintaining height v Efficiently Proof - 1 Proof - 2 Proof - 3 Proof - 4 Step 3: Maintain Invariant Introducing Tree Rotation Non-trivial O 1 Tree Rotation Pseudo-code Four Rebalancing Cases Insert v in AVL Tree Remove v in AVL Tree AVL Tree Summary Extras Online Quiz Online Judge Exercises The Solution.

This special requirement of Table ADT will be made clearer in the next few slides. Yes No Submit Discussion: Why? Hint: Go back to the previous 4 slides ago. We will now introduce BST data structure. See the visualization of an example BST above! If v does not exist, we can report Or in another word, find the k -th smallest element in the BST. Because of the BST properties, we can find the Successor of an integer v assume that we already know where integer v is located from earlier call of Search v as follows: If v has a right subtree, the minimum integer in the right subtree of v must be the successor of v.

Try Successor 23 should be If v does not have a right subtree, we need to traverse the ancestor s of v until we find 'a right turn' to vertex w or alternatively, until we find the first vertex w that is greater than vertex v.

Once we find vertex w , we will see that vertex v is the maximum element in the left subtree of w. Try Successor 7 should be If v is the maximum integer in the BST, v does not have a successor. Try Successor 71 should be none. Discussion: Why? Insert v runs in O h where h is the height of the BST. Quiz: Inserting integers [1,10,2,9,3,8,4,7,5,6] one by one in that order into an initially empty BST will result in a BST of height: 8 9 The height cannot be determined 10 Submit Pro-tip: You can use the 'Exploration mode' to verify the answer.

We can remove an integer in BST by performing similar operation as Search v. If v is not found in the BST, we simply do nothing. The first case is the easiest: Vertex v is currently one of the leaf vertex of the BST. This part is clearly O 1 — on top of the earlier O h search-like effort. This case 3 warrants further discussions: Why replacing a vertex B that has two children with its successor C is always a valid strategy? Can we replace vertex B that has two children with its predecessor A instead?

Why or why not? So, is there a way to make our BSTs 'not that tall'? Formally: v. Quiz: What are the values of height 20 , height 65 , and height 41 on the BST above? Discussion: Do you know how to get skewed left BST instead?

The proof relies on the concept of minimum-size AVL Tree of a certain height h. Look at the example BST again. See that all vertices are height-balanced, an AVL Tree. You have reached the last slide. Return to 'Exploration Mode' to start exploring! Unbalanced Example. Node 2 ;. Node 3 ;. Node 4 ;. Node 5 ;. Node 6 ;. Node 7 ;. Node 8 ;. Node 9 ;. Node 10 ;. Node 11 ;. Node 12 ;. Node 13 ;.

Node 14 ;. Node 15 ;. Node left;. Node right;. Recommended Articles. Check if a binary tree is subtree of another binary tree using preorder traversal : Iterative. Article Contributed By :.

Easy Normal Medium Hard Expert. Writing code in comment? Please use ide. Load Comments. What's New. Printing Binary Trees in Ascii Here we are not going to discuss what binary trees are please refer this, if you are looking for binary search trees , or their operations but printing them in ascii.

TWiStErRob Exactly what i was looking for, thanx a lot! Unfortunately it seems so. This could be it, I haven't tried to run it yet: datastructuresblog. The text appears to have become corrupted, and the code link is broken. If anybody can find the code, please help! A link to pastebin might not be out of line Found it, saved it! I ported this to JS a few years ago github.

Show 2 more comments. Ray Hulha 9, 5 5 gold badges 46 46 silver badges 46 46 bronze badges. I tried to use this with a tree with string values. Didn't really work well, even when increasing the width variable.

Also the fixed amount of lines is unfortunate. That number gives you the printed "horizontal width" of each node at any particular depth. Bula Bula 1, 1 1 gold badge 14 14 silver badges 29 29 bronze badges. Steve Lorimer Steve Lorimer 24k 15 15 gold badges silver badges bronze badges.

I am using your solution, but there is a minor error. The second q. Prehaps you mistyped it when you copied it? Working code here: ideone. Anonymous Anonymous 2, 3 3 gold badges 21 21 silver badges 23 23 bronze badges.