Strictly speaking, binary tree pre-order traversal is the same as binary tree depth first search. Binary tree in-order and post-order traversals are not the same as binary tree depth first search. Am I right?
All three tree traversals are produced by a depth first search. Whether the current node is added to the output before, after, or between its children doesn't make a difference - the algorithms walk the nodes of the tree in exactly the same order.
Related
The below is an excerpt from geeksforgeeks
If the given Binary Tree is Binary Search Tree, we can store it by
either storing preorder or postorder traversal. In case of Binary
Search Trees, only preorder or postorder traversal is sufficient to
store structure information.
Questions
Is it not possible to use in-order traversal for serialization and deserialization of Binary Trees?. if so why?
what is the distinction between Binary Tree and BST serialization?. the above statement is not clear about this distinction
In-order traversal of a BST produces the sorted list of data, regardless of how the tree looked like.
On the contrary, given a list produced by pre-order traversal, the BST can be reconstructed:
The first element is a root.
Split the rest by the value of the root. The S of BST guarantees that the split point exists, and the first/second slices encompass the left/right subtrees respectively.
Recursively apply the procedure to first and second slice.
This procedure relies heavily on the S property of BST. An arbitrary Binary Tree doesn't have the split point.
For a Binary SEARCH Tree, a preorder or a postorder traversal is sufficient to reconstruct its original binary search tree unambigiously.
But I cannot find a proof or a explanation for why it is so.
For inorder traversal, it is trivial to come up with a counter-example to show that there may be many different BSTs correspond to a given inorder traversal.
Is there any proof or reference that a preorder or a postorder traversal is sufficient to reconstruct its original BST unambiguously?
This is for a BST, not for a general binary tree.
By the definition of pre-order traversal, it is guaranteed that root will be the first element.
Now, given the root, there is a unique set of elements that will come in the left half of the root - i.e. all elements having value less that root->val.
Likewise for the right subtree.
Now, we have to apply the above logic recursively for the left subtree and the right subtree.
Since, post-order traversal is just the reverse of pre-order traversal on the reverse tree, the same logic applies to post-order traversal too.
I just finished an exam on this, where I used an inorder traversal to check correct node order in one of my splay trees. Is this valid?
Yes, in-order traversal accesses a splay tree's elements in increasing order.
By the definition of a splay tree in the original article:
The splay tree, (is) a self-adjusting form of binary search tree
So, a splay tree is just a regular binary search tree by structure, which is all that is required for in-order traversal to access elements in increasing order. Apart from that, operations along the search path of a splay tree modify the structure, but they do so in a way which doesn't violate the binary search tree invariants.
I have Binary Search tree and have to perform three types of tree traversal:
Are this results correct?
Pre-order (root,left,right): 30,15,59,43,40,92
In-order (left,root,right): 15,30,59,40,43,92
Post-order (left,right,root): 15,59,40,43,92,30
UPDATE:
In-order: 15,30,40,43,59,92 (projection?)
Post-order: 15,40,43,92,59,30.
Is it right?
Given this updated tree, your preorder traversal is correct.
Your inorder traversal, though, is incorrect. As a hint, doing an inorder traversal of a binary tree always lists the values off in sorted order.
Finally, your postorder traversal is incorrect. The value 59 won't be produced until after all of the nodes in its two subtrees are produced, so it should come second-to-last. Using this fact, try seeing if you can come up with the correct answer.
Hope this helps!
What is the name of the binary tree (or the family of the binary
trees), that is balanced, and has the minimum number of nodes
possible for its height?
balanced binary tree
(data structure)
Definition: A binary tree where no leaf is more than a certain amount farther from the root than any other. After inserting or deleting a node, the tree may rebalanced with "rotations."
Generalization (I am a kind of ...)
binary tree.
Specialization (... is a kind of me.)
AVL tree, red-black tree, B-tree, balanced binary search tree.
Aggregate child (... is a part of or used in me.)
left rotation, right rotation.
See also BB(α) tree, height-balanced tree.
-- http://www.itl.nist.gov/div897/sqg/dads/HTML/balancedbitr.html
It is called Fibonacci tree
AVL is a balanced tree with log(n) height (this is the lowest height possible for binary tree).
Another implementation of a similar data structure is Red Black Tree.
Both trees implement all operations in O(log(n)).
AVL Tree is something that you have been looking for.
From Wikipedia:
In computer science, an AVL tree is a self-balancing binary search tree, and it is the first such data structure to be invented. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; therefore, it is also said to be height-balanced. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations.