A tree data structure consists of nodes that are connected by edges. In the context of a tree, an edge is a link between two nodes. It represents the relationship between a parent node and its child node.
The concept of edges is essential in understanding the hierarchical nature of trees. Each node, except for the root node, has exactly one incoming edge from its parent and zero or more outgoing edges to its children nodes.
Types of Edges:
There are different types of edges that can exist in a tree:
- Root Edge: The edge that connects the root node to its child nodes is called the root edge.
- Parent Edge: The edge that connects a parent node to its child node is called the parent edge.
- Child Edge: The edge that connects a child node to its parent node is called the child edge.
- Sibling Edge: The edges that connect siblings (nodes with the same parent) are called sibling edges.
In a tree, there is only one path between any two nodes. This property ensures that there are no cycles or loops in the structure. If an edge were to create a cycle by connecting an ancestor with one of its descendants, it would violate this property and result in a graph rather than a tree.
The number of edges in a tree:
The number of edges in a tree depends on the number of nodes it contains. In a binary tree, where each node can have at most two children, the total number of edges will always be one less than twice the number of nodes. This relationship can be expressed as:
number_of_edges = 2 * number_of_nodes – 1
Traversal of Tree using Edges:
Edges are essential for traversing a tree and accessing its nodes. There are different ways to traverse a tree, including:
- Pre-order Traversal: In pre-order traversal, we visit the current node first, then traverse the left subtree, and finally traverse the right subtree.
- In-order Traversal: In in-order traversal, we first traverse the left subtree, then visit the current node, and finally traverse the right subtree.
- Post-order Traversal: In post-order traversal, we first traverse the left subtree, then traverse the right subtree, and finally visit the current node.
The concept of edges in a tree data structure is crucial for understanding how nodes are connected in a hierarchical manner. The different types of edges define the relationship between parent and child nodes. By utilizing these edges correctly, you can efficiently navigate and manipulate tree structures.