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Part 1 By Alex Allain The binary tree is a fundamental data structure used in computer science. The binary tree is a useful data structure for rapidly storing sorted data and rapidly retrieving stored data.

A binary tree is composed of parent nodes, or leaves, each of which stores data and also links to up to two other child nodes leaves which can be visualized spatially as below the first node with one placed to the left and with one placed to the right.

It is the relationship between the leaves linked to and the linking leaf, also known as the parent node, which makes the binary tree such an efficient data structure. It is the leaf on the left which has a lesser key value i.

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As a result, the leaves on the farthest left of the tree have the lowest values, whereas the leaves on the right of the tree have the greatest values. More importantly, as each leaf connects to two other leaves, it is the beginning of a new, smaller, binary tree.

Due to this nature, it is possible to easily access and insert data in a binary tree using search and insert functions recursively called on successive leaves. It begins with a root node, which contains the original key value.

The root node has two child nodes; each child node might have its own child nodes. Ideally, the tree would be structured so that it is a perfectly balanced tree, with each node having the same number of child nodes to its left and to its right. A perfectly balanced tree allows for the fastest average insertion of data or retrieval of data. The worst case scenario is a tree in which each node only has one child node, so it becomes as if it were a linked list in terms of speed.

The typical representation of a binary tree looks like the following: Notice that if one removed the root node and the right child nodes, that the node storing the value 6 would be the equivalent a new, smaller, binary tree. The structure of a binary tree makes the insertion bank earn on binary options review search functions simple to implement using recursion.

In best online trading site for day traders, the two insertion and search functions are also both very similar.

To insert data into a binary tree involves a function searching for an unused node in the proper position in the tree in which to insert the key value.

The insert function is generally a recursive function that deletion in binary search tree source code moving down the levels of a binary tree until there is an unused leaf in a position which follows the rules of placing nodes. The rules are that a lower value should be to the left of the node, and a greater or equal value should be to the right.

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Following the rules, an insert function should check each node to see if it is empty, if so, it would insert the data to be stored along with the key value in most implementations, an empty node will simply be a NULL pointer from a parent node, so the function would also have to create the node. If the node is filled already, the insert function should check to see if the key value to be inserted is less than the key value of the current node, and if so, the insert function should be recursively called on the left child node, or if the key value to be inserted is greater than or equal to the key value of the current node the insert function should be recursively called on the right child node.

The search function works along a similar fashion. It should check to see if the key value of the current node is the value to be searched. If not, it should check to see if the value to be searched for is less than the deletion in binary search tree source code of the node, in which case notional value of a put option should be recursively called on the left child node, or if it is greater than the value of the node, it should be recursively called on the right child node.

Of course, it is also necessary to check to ensure that the left or right child node actually exists before calling the function on the node. Because binary trees have log base 2 n layers, the average search time for a binary tree is log base 2 n.

Let's take a look at the necessary code for a simple implementation of a binary tree. First, it is necessary to have a struct, or class, defined as a node.

In fact, the node itself is very similar to the node in a linked list.

A basic knowledge of the code for a linked list will be very helpful in understanding the techniques of binary trees. Essentially, pointers are necessary to allow the arbitrary creation of new nodes in the tree.

It is most logical to create a binary tree class to encapsulate the workings of the tree into a single area, and also making it reusable.

The class will contain functions to insert data into the tree and to search for data. Due to the use of pointers, it will be necessary to include a function to delete the tree in order to conserve memory after the program has finished. The insert and search functions which will be called recursively are the ones which contain two parameters, allowing them to travel down the tree.

The code for the class would look similar to the following: In the example tree above, the order of deletion of nodes would be 5 8 6 11 18 14 Note that it is necessary to delete all the child nodes to avoid wasting memory.

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The insert function searches, moving down the tree of children nodes, following the prescribed rules, left for a lower value to be inserted and right for a greater value, until it finds an empty node which it creates using the 'new' keyword and initializes with the key value while setting the new node's child node pointers to NULL. After creating the new node, the insert function will no longer call itself. It returns a pointer to the node to the previous instance of the function which called it, handing the pointer back up to the search function accessible outside the class.

If the root node already exists, insert is called with the root node as the initial node of the function, and the recursive insert function takes over. Still not getting it? Variable argument lists to functions Next: