7.
Explanation
Trees can be represented in memory using various data structures. The choice of representation depends on the specific requirements and the type of tree. Here are some common ways to represent trees in memory:
1. Node-Based Representation:
◦ In a node-based representation, each element in the tree is represented by a node object. Each node contains data and references (or pointers) to its child nodes.
◦ Common attributes of a node object include data, a pointer to the left child, a pointer to the right child, and possibly a pointer to the parent node (in the case of a binary tree).
◦ This is the most straightforward way to represent trees and is commonly used in various tree structures, including binary trees, binary search trees, and general trees.
2. Array-Based Representation (Heap and Binary Heaps):
◦ In some specialized cases, trees can be represented using arrays. This is commonly used for binary heaps, where the tree structure has a specific order.
◦ The elements of the tree are stored in an array where each index represents a specific node, and the relationships between nodes are determined by the array indices.
◦ For a binary heap, the parent of a node at index i can be found at index (i-1)//2, and its children can be found at indices 2*i+1 and 2*i+2.
3. Adjacency List Representation (General Trees):
◦ In the case of general trees where nodes can have varying numbers of children, an adjacency list representation is often used.
◦ Each node contains data and a list of references or pointers to its child nodes.
◦ This representation is flexible and efficient for trees with arbitrary structures.
4. Parent-Pointer Tree Representation (N-ary Trees):
◦ For N-ary trees, where nodes can have multiple children, a parent-pointer tree representation is common.
◦ In this representation, each node contains data and a reference to its parent node, as well as references to its children.
5. Threaded Binary Tree:
◦ A threaded binary tree is a binary tree with special links that allow for in-order traversal without using a stack for recursion. In threaded binary trees, each node contains data, and some of its pointers are modified to create threads (pointers that point to in-order predecessor or successor nodes).
6. Balanced Search Tree Structures (AVL, Red-Black Trees, etc.):
◦ Self-balancing search tree structures like AVL trees and Red-Black trees are often implemented using node-based representations with additional attributes for balancing information.
The choice of representation depends on the specific type of tree and the operations you want to perform efficiently. Node-based representations are the most general and flexible, while array-based representations are typically used for specialized tree structures like binary heaps.