Trees in computer memory are represented as a collection of linked nodes, with each node containing a value and references to its child nodes.

A tree is a hierarchical data structure composed of nodes, where each node stores a value and maintains links to its child nodes. The topmost node of the tree is referred to as the root. Each node has a single parent node, along with zero or more child nodes. Nodes that share the same parent are termed siblings, while nodes that do not have any children are known as leaf nodes.

There are various methods to represent trees in computer memory. The most prevalent approach is the node-based representation. In this method, each node is an object or record that includes a value and a list of references to its child nodes. This representation is dynamic, allowing the structure to grow or shrink during runtime.

Alternatively, an array-based representation can be employed, particularly for binary trees, where each node can have at most two children. In this approach, the tree is stored in an array, and the parent-child relationships are determined by the indices of the elements within the array. This representation is static, meaning its size is predetermined at the time of creation.

Both of these methods store nodes in contiguous blocks of memory, which facilitates efficient traversal of the tree. However, the node-based representation offers greater flexibility and can accommodate trees of various shapes and sizes, while the array-based representation is more space-efficient but is limited to complete binary trees.

Beyond these basic representations, there are also advanced structures such as B-trees and tries, which are utilized in databases and text processing, respectively. These sophisticated methods employ specialized algorithms to maintain balance within the tree, ensuring that operations such as insertion, deletion, and search can be executed efficiently.