Can a Binary Search Tree Contain Negative Numbers?

A binary search tree (BST) can indeed contain negative numbers. This versatile data structure maintains a specific order among its elements: for any given node, all values in the left subtree are less than the node's value, and all values in the right subtree are greater. This property holds true for any type of value, including negative numbers, positive numbers, and even zero. Therefore, you can freely insert negative numbers into a BST alongside positive numbers, and it will still maintain its properties.

Flexibility in Value Types

A BST can contain any value within a predefined ordered set. The integers are an example of an ordered set, such as -5, -1, 0, and -6543. The ordered set doesn't have to be limited to numbers; for instance, the 26 letters of the English alphabet can also form an ordered set: L {A, B, C, ..., X, Y, Z}. This demonstrates the flexibility of a BST in handling various types of data.

Node Data Types

The data contained within a BST node can be of any kind, such as integers, floats, strings, characters, or even custom data types. This adaptability depends on the specific use-case. For this question, a BST node can certainly contain a negative number as part of its data.

Data Comparison and Ordering

A BST is fundamentally a data structure for comparing values, allowing it to contain anything that can be compared. This means that the values, whether they are positive, negative, or even non-numeric, must be comparable among themselves. For example, you can insert strings into a BST and order them alphabetically. This concept is not limited to positive whole numbers; it can accommodate a wide range of values, as long as they can be ordered.

Practical Considerations

A BST can contain any elements belonging to the same totally ordered set. This means that you can line up elements from least to greatest, with some elements possibly being equal. For instance, strings can be ordered alphabetically, and negative numbers can be inserted and ordered. However, there are certain elements that cannot be ordered in a meaningful way within a BST. Examples of such elements include shapes or colors, as it is an awkward question to determine, for example, if green is greater than blue. A meaningful comparison must be possible within the set.