PPT-2 . 8. Binary Space Partitioning Trees

2 8 Binary Space Partitioning Trees Exploration of BSP trees BSP Trees Overview of binary spacepartitioning trees BSP Tree Hierarchies A binary spacepartitioning BSP tree recursively partitions space into pairs of subspaces with respect to dividing planes of arbitrary position and orientation The two partitions are referred to as the positive and negative. CIS 606. Spring 2010. Search trees. Data structures that support many dynamic-set operations.. Can . be used as both a dictionary and as a priority queue.. Basic . operations take time proportional to the height of the tree.. Liwen. Sun, Michael J. Franklin, Sanjay Krishnan, Reynold S. . Xin†. UC . Berkeley and †. Databricks. Inc. .. VLDB 2014. March 17, 2015. Heymo. Kou. Introduction. Overview. Workload Analysis. The Partitioning Problem. CS 46101 Section 600. CS 56101 Section 002. . Dr. Angela Guercio. Spring 2010. Search trees. Data structures that support many dynamic-set operations.. Can . be used as both a dictionary and as a priority queue.. Topics to be discussed….. Trees Data Structures. Trees. Binary Search Trees. Tree traversal. Types of Binary Trees. Threaded binary trees. Applications . Trees Data Structures. Tree. Nodes. Each node can have 0 or more . N. children. Definition. Perfect . N. -. ary. trees. Complete . N. -. ary. trees. Implementation using templates. Outline. N. -ary Trees. One generalization of binary trees are a class of trees termed . Search Trees. Marek Chrobak, Neal Young . UC Riverside. Ian Munro U Waterloo. Mordecai Golin. HKUST. Early version of paper at arxiv.org. Optimal search trees with 2-way comparisons. Decimal. . vs. Binary. = 1001. = 101. = 10. 1 = on =. 0 = off = . On and off. Creating a decimal number 
from a binary number. STAGE 1. The decimal number is ________. Creating decimal 
from binary. What is binary?. You and I write numbers like this: twelve is 12, sixty eight is 68, and one hundred is 100. Binary is a . number system . that computers use. That is, binary is the way that computers express numbers.. A . tree. is a connected undirected graph with no simple circuits.. Since a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops.. Therefore, any tree must be a . simple graph. (§10.1). A binary search tree is a binary tree storing keys (or key-element pairs) at its internal nodes and satisfying the following property:. Let . u. , . v. , and . w. be three nodes such that . To learn how to. use a tree to represent a . hierarchical organization . of information. use recursion to process trees. implement . binary trees, binary search trees. , and . heaps. using linked data structures and . Definitions and examples. Number of nodes: . 2. h. 1. – 1. Logarithmic height. Number of leaf nodes: . 2. h. Applications. Definition. Standard definition:. A perfect binary tree of height . h. Announcements. Submit P1 Conflict quiz on CMS by end of day Wednesday. We won’t be sending confirmations; no news is good news. Extra time people will eventually get an email from Lacy. Please be patient.. 2 . 8. Binary Space Partitioning Trees Exploration of BSP trees BSP Trees Overview of binary space-partitioning trees BSP Tree Hierarchies A binary space-partitioning (BSP) tree recursively partitions space into pairs of subspaces with respect to dividing planes of arbitrary position and orientation. The two partitions are referred to as the positive and negative