Tree Traversals, TreeSort

Traversals

Traversals Common set of algoritms on trees are traversals A way of visiting all the nodes of a tree “Visit” is defined as performing one operation on a node a b c g d f e h i Traversals Three basic traversals Preorder Postorder Inorder Preorder Traversal

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Trees and Tree Traversals

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Graph Traversals

Graph Traversals. Algorithm : Design & Analysis [14]. In the last class …. Implementing Dynamic Set by Union-Find Straight Union-Find Making Shorter Tree by Weighted Union Compressing Path by Compressing-Find Amortized Analysis of wUnion and cFind. Graph Traversals.

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Graph Traversals

Graph Traversals. Introduction Breadth-First Traversal. The Algorithm. Example. Implementation. Depth-First Traversals. Algorithms. Example. Implementation. Some traversal applications: Connected Components Strongly Connected Components Edge Classification Review Questions.

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Tree properties and traversals

Tree properties and traversals. CS16: Introduction to Data Structures & Algorithms. Tree ADT Binary Tree ADT Breadth-first traversal Depth-first traversal Recursive DFT: pre-order, post-order, in-order Euler Tour traversal Practice problems. Outline.

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Chapter 18 - basic definitions - binary trees - tree traversals

Chapter 18 - basic definitions - binary trees - tree traversals. Intro. to Trees. Trees. A recursively defined data structure Each node has links to two or more subtrees/children-nodes. Each node itself can be the beginning of a new tree.

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BINARY TREES && TREE TRAVERSALS

BINARY TREES && TREE TRAVERSALS. DEFINITION : Binary Tree. root. A binary tree is made of nodes Each node contains a "left" pointer -- left child a "right" pointer – right child a data element.

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Graph Traversals

Is G connected?. Is there a path from vertex a to vertex b ? . Does G have a cycle? . Will removing a single edge disconnect G ?. If G is directed, what are the strongly connected components?. If G is the WWW, follow links to locate information. .

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Graphs Traversals

Graphs Traversals. In many graph problems, we need to traverse the vertices of the graph in some order Analogy: Binary tree traversals Pre-order Traversal In-order Traversal Post-order Traversal. Graph Traversals. 2 graph traversal methods Breadth-First Search (BFS):

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Graph traversals

Graph traversals. Breadth first search Depth first search. Some applications. Is G a tree Is G connected? Does G contain a cycle? Find connected components? Topological sorting. Breadth first search.

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Traversals

Traversals. A systematic method to visit all nodes in a tree Binary tree traversals: Pre-order: root, left, right In-order: left, root, right Post-order: left, right, root General graph traversals (searches) Depth-first search Breadth-first search. Inorder(tree t). if t = nil

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Graph Traversals

Graph Traversals. Graph Traversals. For solving most problems on graphs Need to systematically visit all the vertices and edges of a graph Two major traversals Breadth-First Search (BFS) Depth-First Search(DFS). BFS. Starts at some source vertex s

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Binary Tree Traversals

Binary Tree Traversals. Tree Traversal classification BreadthFirst traversal DepthFirst traversals: Pre-order, In-order, and Post-order Reverse DepthFirst traversals Invoking BinaryTree class Traversal Methods accept method of BinaryTree class BinaryTree Iterator

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Graph Traversals

Graph Traversals. Depth-First Traversals. Algorithms. Example. Implementation. Breadth-First Traversal. The Algorithm. Example. Implementation. Review Questions. Depth-First Traversal Algorithm.

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Iterators and Tree Traversals

Iterators and Tree Traversals. Binary Trees. In a binary tree, each node has at most two subtrees A set of nodes T is a binary tree if either of the following is true T is empty Its root node has two subtrees, TL and TR, such that TL and TR are binary trees. Tree Traversals.

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Tree Traversals & Maps

Tree Traversals & Maps. Nelson Padua-Perez Chau-Wen Tseng Department of Computer Science University of Maryland, College Park. Tree Traversal. Goal Visit every node in binary tree Approaches Depth first Preorder  parent before children Inorder  left child, parent, right child

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Graph Traversals

Graph Traversals. A graph-traversal algorithm Visits all the vertices that it can reach starting at some vertex Visits all vertices of the graph iff the graph is connected (effectively computing Connected Components ) Must not loop forever, if a graph contains a cycle

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Binary Tree Traversals

Binary Tree Traversals. Tree Traversal classification BreadthFirst traversal DepthFirst traversals: Pre-order, In-order, and Post-order Reverse DepthFirst traversals Invoking BinaryTree class Traversal Methods accept method of BinaryTree class BinaryTree Iterator

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Graph Traversals

Graph Traversals. General Traversal Algorithm Depth-First Traversals. Algorithms. Example. Implementation. Breadth-First Traversal. The Algorithm. Example. Implementation. Review Questions. General Traversal Algorithm. This algorithm ensures that all vertices are visited in the graph.

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Graph Traversals

Graph Traversals. Introduction Breadth-First Traversal. The Algorithm. Example. Implementation. Depth-First Traversals. Algorithms. Example. Implementation. Some traversal applications: Connected Components Strongly Connected Components Edge Classification Review Questions.

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Graph Traversals

Graph Traversals. Depth-First Traversals. Algorithms. Example. Implementation. Breadth-First Traversal. The Algorithm. Example. Implementation. Review Questions. Depth-First Traversal Algorithm.

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