Top tree
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Top trees are a self-adjusting data structure that can be used by multiple tree algorithms simultaneously. They allow for simple divide-and-conquer algorithms. A top tree is defined for an underlying tree and up to two external boundary vertices. It is a binary tree where nodes are clusters of the underlying tree, leaves are edges of that tree, and neighboring clusters that intersect at a single vertex are parent and child clusters.
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Binary trees are a data structure where nodes are connected in a parent-child relationship. Each node can have up to two children. Binary search trees have the additional property that the value of each node's left child is less than its own value, and the value of its right child is greater. This structure allows efficient search, insertion, and deletion operations. Basic tree operations include traversing the tree in different orders (pre-order, in-order, post-order) and searching for a node by its value. New nodes are inserted by finding the correct position based on value comparison to existing nodes.
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Bfs dfs mst
Depth-first search (DFS) and breadth-first search (BFS) are algorithms for traversing or searching trees and graphs. DFS uses a stack and recursively explores as far as possible along each branch before backtracking, while BFS uses a queue and explores neighboring nodes first before moving to the next level. A minimum spanning tree (MST) is a subgraph that connects all vertices with minimum total edge weight. Common algorithms to find an MST are Kruskal's algorithm, which adds edges in order of weight, and Prim's algorithm, which grows the tree from an initial vertex.
Introduction to data structures (ss)
In this you will learn about
1. Definitions
2. Introduction to Data Structures
3. Classification of Data structures
a. Primitive Data structures
i. int
ii. Float
iii. char
iv. Double
b. Non- Primitive Data structures
i. Linear Data structures
1. Arrays
2. Linked Lists
3. Stack
4. Queue
ii. Non Linear Data structures
1. Trees
2. Graphs
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Top tree
- 1. TOP TREE BY PARID VAROSHI
- 2. • Top trees are a dynamic self-adjusting data structure that can be used by any tree algorithm. Actually, an arbitrary number of different tree algorithms can use a single structure. The usage still requires a detail knowledge of the structure which is quite complex. Moreover about them.The TFL is a special programming language which combines declarative and procedural approaches that results in simpler and faster algorithm designing. The query language TQL provides an easy top trees administration. The implementation of top trees, the programming language TFL and the query language TQL together form a complex solution for using top trees.
- 3. ANOTHER DEFINITION • A top tree is a data structure based on a binary tree for unrooted dynamic trees that is used mainly for various path- related operations. It allows simple divide-and-conquer algorithms. It has since been augmented to maintain dynamically various properties of a tree such as diameter, center and median. A top tree 784 is defined for an underlying tree 784 and a set 784 of at most two vertices called as External Boundary Vertices i
- 4. • :A top tree R over (T, ∂T) is a binary tree such that: • 1. The nodes of R are the clusters of (T, ∂T). • 2. The leaves of R are the edges of T. • 3. Two clusters are called neighbors if they intersect in a single vertex. Their union is a parent cluster.
- 5. HOTKEYS: • Boundary Vertex A vertex in a connected subtree is a Boundary Vertex if it is connected to a vertex outside the subtree by an edge. • External Boundary Vertices Up to a pair of vertices in the top tree can be called as External Boundary Vertices, they can be thought of as Boundary Vertices of the cluster which represents the entire top tree. • Cluster A cluster is a connected subtree with at most two Boundary Vertices. The set of Boundary Vertices of a given cluster is denoted as With each cluster the user may associate some meta information n hand give methods to maintain it under the various internal operations.
- 6. • Path Cluster If contains at least one edge then is called a Path Cluster. • Cluster Path The path between the Boundary Vertices of is called the cluster path of and it is denoted by • Path Edge Cluster Edge Clusters with two Boundary Nodes. • Edge Cluster A Cluster containing a single edge is called an Edge Cluster.
- 7. FIG. 1. THE CASES OF JOINING TWO NEIGHBOURING CLUSTERS INTO THE PARENT CLUSTER THE • ARE THE BOUNDARY VERTICES OF THE PARENT CLUSTER. THE ◦ ARE THE BOUNDARY VERTICES OF CHILDREN CLUSTERS THAT DID NOT BECOME THE BOUNDARY VERTICES OF THE PARENT. THE DASHED LINE PRESENTS THE CLUSTER PATH OF THE PARENT CLUSTER. MOREOVER, THERE EXIST SYMMETRIC VARIANTS FOR (B) AND (C).
- 8. REFERENCES: • http://ceur-ws.org/Vol-471/paper7.pdf • https://en.wikipedia.org/wiki/Top_tree • PARID VAROSHI • EPOKA UNIVERSITY TIRANA,ALBANIA • DATA STRUCTURES