Organizations can use different data structures to organize and store data in multiple forms. Data structures include different values, multiple functions, and their relationships to apply to data and function with certain algorithms. A binary search tree is a form of data structure, and you can learn all about it from this article.
A binary search tree includes nodes arranged in a predetermined sequence. The value of the root in a binary search tree is higher than the value of the nodes in the left sub-tree. Meanwhile, the root’s value usually equals or exceeds all the nodes in the right subtree.
A binary search tree in data structures can be expressed as:
left_subtree (keys) < node (key) ≤ right_subtree (keys)
The different components of a binary search tree in the data structure are as follows:
The binary search tree data structure can support different basic operations like:
The operations come with a time complexity of O(h), where h signifies the tree’s height.
A balanced binary search tree includes the same number of nodes on the right and left subtrees of the root. In a balanced binary tree in a data structure, the above operations require O(log n) time (n= number of nodes in the tree). Meanwhile, the time required for operations in a linear binary search tree will be O(n).
On average, a randomly built binary search tree in the data structure has a height of O(log n). Therefore, the basic operations on a randomly built binary tree in data structure will need O(log n) time approximately.
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You can insert a new element in a binary search tree only at the leaf. We should begin searching from the root node to add an element to a binary search tree. When the inserting node has a lesser value than the root, we will look for an empty location in the left subtree.
But when the value of the data element is higher than the node, we will look for an empty space in the right subtree to insert a new element. Maintaining the property of the binary tree during insertion is crucial.
While performing deletion in a binary search tree, we can’t violate its fundamental property. Binary search trees can be deleted under the following circumstances:
A binary tree in data structures can help you search for a specific node or element. The steps to perform a search in a binary tree are as follows:
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The binary search tree in data structures gets implemented in the following steps:
Step 1: Read the user’s search element.
Step 2: Look for the middle element in the sorted list.
Step 3: Use the middle element in the sorted list to compare the search element.
Step 4: When both get matched, it shows “Given element is found!!!” The function also gets terminated.
Step 5: When the elements don’t match, it’s necessary to determine whether the search element is larger or smaller than the middle element.
Step 6: When the search element is smaller than the middle element, it becomes necessary to execute steps 2,3,4 and 5 for the middle element’s left sublist.
Step 7: When the search element is larger than the middle element, it becomes necessary to repeat steps 2, 3, 4, and 5 for the middle element’s right sublist.
Step 8: If that element also fails to match the search element, it shows “Element is not found in the list!!!” After that, the function gets terminated.
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The different real-world applications of a binary search tree are as follows:
A routing table is useful for linking routers to a network. The trie data structure, a variation of the binary tree, is applicable for implementing routing tables.
Binary trees are often used for the purpose of classification. A decision tree is a form of a supervised machine-learning algorithm. The binary tree in a data structure is applied in decision tries for smooth decision-making.
In mathematics, statements evaluating a value with operators and operands are called expressions. The binary tree leaves are the operands, while the internal nodes serve as the operators.
Binary search trees are useful for implementing sorting algorithms that can help order items. The items that need to be sorted are inserted in a binary search tree to begin the sorting procedure. The tree is traversed with the in-order traversal to retrieve the sorted items.
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The different types of binary search trees are as follows:
(Kindly replace this diagram with a new one)
A binary tree in data structures is immensely popular for searching. A binary search tree can be used for indexing, maintaining sorted data streams, and more. Additionally, a binary search tree in data structures is also implemented in different search algorithms.
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