Hello again! This lesson's topic is Binary Search Trees (BST) in JavaScript. A BST is a data structure that stores key-value pairs in an ordered manner, making data manipulation organized and efficient. JavaScript doesn't include a built-in binary search tree data structure. However, we can utilize the @datastructures-js/binary-search-tree library to manage our data in a sorted and efficient manner. Today's goal is to work with BSTs using JavaScript.

A Binary Search Tree (BST) is a node-based data structure where each node has at most two children referred to as the left child and the right child. The key in each node must be greater than (or equal to) any key stored in the left subtree, and less than (or equal to) any key stored in the right subtree. This property makes the binary search tree an efficient data structure for operations such as insertion, deletion, and searching.

Example of a Binary Search Tree

Consider the following BST:

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1     50
2   /    \
3 30     70
4 / \    / \
520 40  60 80

In this tree:

• The root node is 50.
• The left subtree of 50 contains nodes 30, 20, and 40.
• The right subtree of 50 contains nodes 70, 60, and 80.
• The key in the root node (50) is greater than all keys in its left subtree (20, 30, 40) and less than all keys in its right subtree (60, 70, 80).
• And this property is satisfied for all nodes, not just the root.

This property allows for efficient searching, as you can disregard half of the remaining tree at each step, leading to an average time complexity of O(log n) for search operations.

Now, let's move forward and see how to implement and work with BSTs in JavaScript using the @datastructures-js/binary-search-tree library.

Using the BinarySearchTree, we can implement several useful methods for managing and traversing the BST:

• lowerBound(searchKey): This method finds the node with the biggest key less or equal a given searchKey.
• upperBound(searchKey): This method finds the node with the smallest key bigger or equal a given searchKey.
• remove(searchKey): Removes the specified key and its associated value.
• find(searchKey): Returns the node for the key if it exists.
• min(): Returns the node with the smallest key.
• max(): Returns the node with the largest key.

We will use the BinarySearchTree class from the @datastructures-js/binary-search-tree library to handle sorted elements. Here's how to get started:

JavaScript
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1const { BinarySearchTree } = require('@datastructures-js/binary-search-tree');
2
3// Initialize a binary search tree with a custom comparison function for strings
4const bst = new BinarySearchTree();
5
6// Inserting single elements (strings)
7const items = ['banana', 'apple', 'pear', 'orange'];
8items.forEach(item => bst.insert(item));
9
10// Using the BST methods to find lower and upper bounds
11const lowerBound = bst.lowerBound('apricote');
12console.log('Lower bound for apricote:', lowerBound ? lowerBound._value : 'Not found');
13// Output: Lower bound for apple: apple
14
15const upperBound = bst.upperBound('apricote');
16console.log('Upper bound for apricote:', upperBound ? upperBound._value : 'Not found');
17// Output: Upper bound for apple: banana
18
19// Remove 'apple' and print the removed item
20const item = bst.find('apple');
21bst.remove('apple');
22console.log('Deleted item:', item ? item._value : 'Not found');
23// Output: Deleted item: apple
24
25// Attempt to fetch a nonexistent key
26const value = bst.find('apple');
27console.log('Value:', value ? value._value : 'Not found');
28// Output: Value: Not found
29
30// Peek at the minimum and maximum items
31const minItem = bst.min();
32console.log('Min item:', minItem ? minItem._value : 'Tree is empty');
33// Output: Min item: banana
34
35const maxItem = bst.max();
36console.log('Max item:', maxItem ? maxItem._value : 'Tree is empty');
37// Output: Max item: pear

Consider the following JavaScript code, which incorporates key-value pairs represented as arrays. To manage these pairs, we will initialize the BinarySearchTree with a custom comparison function:

JavaScript
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1const { BinarySearchTree } = require('@datastructures-js/binary-search-tree');
2
3const entries = [['banana', 3], ['apple', 4], ['pear', 1], ['orange', 2]];
4const compareArrays = (a, b) => a[0].localeCompare(b[0]);
5const bst = new BinarySearchTree(compareArrays);
6entries.forEach(entry => bst.insert(entry));
7
8const value = bst.find(['apple']);
9console.log('Value:', value ? value._value[1] : 'Not found');
10// Output: 4
11
12const lowerBound = bst.lowerBound(['apple'], false);
13console.log('Exclusive lower bound for apple:', lowerBound ? lowerBound._value : 'Not found');
14// Output: Exclusive lower bound for apple: Not found
15
16const upperBound = bst.upperBound(['apple'], false);
17console.log('Exclusive upper bound for apple:', upperBound ? upperBound._value : 'Not found');
18// Output: Exclusive upper bound for apple: [ 'banana', 3 ]
19
20const minItem = bst.min();
21console.log('Min item:', minItem ? minItem._value : 'Tree is empty');
22// Output: Min item: [ 'apple', 4 ]
23
24const maxItem = bst.max();
25console.log('Max item:', maxItem ? maxItem._value : 'Tree is empty');
26// Output: Max item: [ 'pear', 1 ]

Here, we pass a custom comparison function compareArrays to the BinarySearchTree constructor. This function takes two arguments, a and b, which are arrays representing key-value pairs. The function compares the first elements of these arrays (the keys) using localeCompare to ensure the tree is sorted based on the keys in lexicographical order.

In the lowerBound and upperBound methods, the second parameter is a boolean that dictates whether the search is inclusive or exclusive:

• By default, if the second parameter is not provided or set to true, the search is inclusive, meaning it will return the node with the search key if it exists.
• If the second parameter is false, the search is exclusive, meaning it will find the next closest node and exclude the node with the exact search key. This is useful for scenarios where you need to find the bounds around a given key.

Congratulations! You have successfully delved into Binary Search Trees in JavaScript. This exploration included understanding how to utilize the @datastructures-js/binary-search-tree library to manage sorted data functionality in JavaScript, creating instances with single elements and key-value pairs, and navigating the valuable methods associated with this data structure. Keep practicing to fortify your understanding and expand your skill set!