Parent pointer tree

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Parent pointer tree is a simple and intuitive data structure used in computer science for representing a tree. Unlike other tree representations that explicitly store relationships between nodes (such as left child and right child in binary trees), a parent pointer tree represents each node primarily by storing a single reference or pointer to its parent node. The root node of the tree, which has no parent, is represented with a null pointer or a special marker indicating its root status.

Definition

A parent pointer tree consists of nodes where each node contains some data and a pointer to its parent node. The structure is defined recursively as follows:

• The tree has a unique node called the root, which has no parent (its parent pointer is null or a special marker).
• Every other node in the tree has exactly one parent node and zero or more child nodes.
• There is exactly one path from the root node to any other node in the tree, which is traced by following parent pointers in the reverse direction.

Advantages and Disadvantages

Advantages

• Simplicity: The structure is straightforward to implement since each node only needs to keep track of its parent.
• Efficient Path to Root: Finding the path from any node to the root is efficient, as it involves following parent pointers directly to the root.
• Dynamic Tree Modifications: Adding or removing nodes is relatively simple, especially in operations that do not affect the overall tree structure significantly, such as detaching subtrees or changing parent nodes.

Disadvantages

• Traversal Difficulty: Unlike other tree structures that explicitly store child references, traversing a parent pointer tree (e.g., visiting all nodes in a specific order) is less straightforward and often requires additional data structures or algorithms.
• No Direct Sibling Information: Without direct pointers to siblings, finding sibling nodes requires additional steps, typically involving finding the parent node first and then accessing all its children.

Applications

Parent pointer trees are particularly useful in applications where the primary operation involves moving up the tree, such as:

• Implementing union-find algorithms, which are used in disjoint-set operations for tracking element groupings in partitioned sets.
• Representing the hierarchical structure in object-oriented programming languages, where objects have a single parent class or prototype.
• Modeling scenarios in network protocols or file systems where the "backtracking" or "upwards traversal" is a common operation.

Implementation

A basic implementation of a node in a parent pointer tree in C might look like this:

```c typedef struct Node {

   struct Node* parent;
   void* data;

} Node; ```

In this structure, `parent` is a pointer to the parent node, and `data` is a pointer to the node's data. The root node's `parent` pointer would be set to `NULL` to indicate that it has no parent.

See Also

• Tree
• Binary tree
• Union-find data structure
• Disjoint-set data structure