# Write a function to decide whether two binary trees are similar

As with all binary trees, one may conduct a pre-order traversal or a post-order traversalbut neither are likely to be useful for binary search trees. Tango trees are trees optimized for fast searches.

## Given two bsts, check whether the elements of them are the same or not

Tango trees are trees optimized for fast searches. In practice, the added overhead in time and space for a tree-based sort particularly for node allocation make it inferior to other asymptotically optimal sorts such as heapsort for static list sorting. First the leftmost node in the right subtree, the in-order successor E, is identified. In either case, this node will have only one or no child at all. This process continues, until the new node is compared with a leaf node, and then it is added as this node's right or left child, depending on its key: if the key is less than the leaf's key, then it is inserted as the leaf's left child, otherwise as the leaf's right child. This way, insertion and deletion both take logarithmic time, just as they do in a binary heap , but unlike a binary heap and most other priority queue implementations, a single tree can support all of find-min, find-max, delete-min and delete-max at the same time, making binary search trees suitable as double-ended priority queues. As pointed out in section Traversal , an in-order traversal of a binary search tree returns the nodes sorted. In all cases, when D happens to be the root, make the replacement node root again. In a treap tree heap , each node also holds a randomly chosen priority and the parent node has higher priority than its children. Because in the worst case this algorithm must search from the root of the tree to the leaf farthest from the root, the search operation takes time proportional to the tree's height see tree terminology. A binary tree sort equipped with such a comparison function becomes stable. There are several schemes for overcoming this flaw with simple binary trees; the most common is the self-balancing binary search tree. There are many possibilities to do this. If its key is less than the root's, it is then compared with the key of the root's left child.

Then I will sort the two dummy trees recursively and sort them based on level. The major advantage of binary search trees over other data structures is that the related sorting algorithms and search algorithms such as in-order traversal can be very efficient; they are also easy to code.

Another way to explain insertion is that in order to insert a new node in the tree, its key is first compared with that of the root.

The BST property—every node on the right subtree has to be larger than the current node and every node on the left subtree has to be smaller than the current node—is the key to figuring out whether a tree is a BST or not.

Deleting a node with two children: call the node to be deleted D. Such a tree might be compared with Huffman treeswhich similarly seek to place frequently used items near the root in order to produce a dense information encoding; however, Huffman trees store data elements only in leaves, and these elements need not be ordered.

This process is repeated until the key is found or the remaining subtree is null. Insertion[ edit ] Insertion begins as a search would begin; if the key is not equal to that of the root, we search the left or right subtrees as before.

Definition[ edit ] A binary search tree is a rooted binary treewhose internal nodes each store a key and optionally, an associated value and each have two distinguished sub-trees, commonly denoted left and right.

Deletion[ edit ] When removing a node from a binary search tree it is mandatory to maintain the in-order sequence of the nodes. Similar to heapsortwe insert all the values we wish to sort into a new ordered data structure—in this case a binary search tree—and then traverse it in order.

An in-order traversal of a binary search tree will always result in a sorted list of node items numbers, strings or other comparable items.

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