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What is the difference between a tree and a graph?

A tree is a type of graph that is connected and acyclic, while a graph can have cycles and does not have to be connected.

Trees and graphs are both fundamental data structures in computer science, but they have distinct characteristics and properties that set them apart. A tree is a specialized type of graph that is connected and acyclic, meaning that there is exactly one path between any two nodes and no cycles (closed loops) exist. Trees are hierarchical structures consisting of nodes, with one node designated as the root, and all other nodes are connected to it through parent-child relationships. Each node can have multiple children, but only one parent, making it a directed acyclic structure. Trees are widely used in various applications, such as representing hierarchical data (like file systems or organizational charts), implementing binary search trees, and constructing decision trees in machine learning. On the other hand, a graph is a more general data structure that consists of a set of nodes (or vertices) connected by edges. Graphs can be directed or undirected, weighted or unweighted, and they can contain cycles, meaning that there can be multiple paths between nodes. Graphs are versatile structures that can represent complex relationships, such as social networks, transportation systems, and web page link structures. While all trees are graphs, not all graphs are trees. Understanding the differences between trees and graphs is crucial for selecting the appropriate data structure based on the specific requirements of the problem being solved.

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