What's the difference between the data structure Tree and Graph?
Câu trả lời
The data structures of trees and graphs are fundamental in computer science, used to represent relationships and hierarchies among elements. Here are the key differences between them:
1. Definition and Basic Structure
Tree: A tree is a hierarchical data structure consisting of nodes connected by edges. It has a single root node and every other node has exactly one parent, creating a clear hierarchical lineage. Trees do not contain cycles, meaning there is only one path between any two nodes[1][4][5].
Graph: A graph is a more general data structure compared to a tree. It consists of vertices (or nodes) and edges that connect pairs of vertices. Unlike trees, graphs can have cycles, multiple paths between nodes, and do not necessarily have a hierarchical structure[1][4][5].
2. Properties
Root Node: Trees have a designated root node where the structure begins. Graphs do not have a root node; any node can potentially be accessed first depending on the application[1][4][5].
Edges and Nodes: In a tree, if there are $$ n $$ nodes, there will always be $$ n-1 $$ edges. Each node (except the root) has exactly one incoming edge (from its parent). Graphs, however, can have any number of edges, and nodes can have multiple incoming and outgoing edges[1][4][5].
Direction: Trees are inherently directed from the root downwards (though they can be represented as undirected for some specific needs). Graphs can be either directed or undirected[1][4][5].
3. Cycles and Connectivity
Cycles: Trees are acyclic by definition, which means they do not have any cycles. Graphs can include cycles, allowing for more complex connectivity[1][4][5].
Connectivity: Trees are always connected, meaning there is a path from the root to any other node. Graphs can be either connected or disconnected, with some nodes potentially having no path between them[1][4][5].
