(2,3)-Tree - University of Queensland
... Theorem: If a good 3-ary tree has n leaf nodes, the height of the tree is O(log n). Proof: Suppose that the height of the tree is h. Thus, all the leaf nodes are at level h − 1. Since every internal node has at least 2 child nodes, the number of nodes at level h − 2 is at most n/2. Similarly, the nu ...
... Theorem: If a good 3-ary tree has n leaf nodes, the height of the tree is O(log n). Proof: Suppose that the height of the tree is h. Thus, all the leaf nodes are at level h − 1. Since every internal node has at least 2 child nodes, the number of nodes at level h − 2 is at most n/2. Similarly, the nu ...
presentation source
... BST Operations: Delete Why will case 2 always go to case 0 or case 1? A: because when x has 2 children, its successor is the minimum in its right subtree Could we swap x with predecessor instead of ...
... BST Operations: Delete Why will case 2 always go to case 0 or case 1? A: because when x has 2 children, its successor is the minimum in its right subtree Could we swap x with predecessor instead of ...
Numerical Representations as Purely Functional Data
... In this paper a class of purely functional data structures termed numerical representations is explored. The discussion here is motivated by a chapter in (Okasaki, 1998). Contributions of this paper are: • formalization of analogy with number system; • implementation and correctness proof for a segm ...
... In this paper a class of purely functional data structures termed numerical representations is explored. The discussion here is motivated by a chapter in (Okasaki, 1998). Contributions of this paper are: • formalization of analogy with number system; • implementation and correctness proof for a segm ...
Priority queues, binary heaps
... be less than its parent After swapping the element and its parent, still only the new element can be in the wrong place (why?) ...
... be less than its parent After swapping the element and its parent, still only the new element can be in the wrong place (why?) ...
Lecture 9 — 16 Feb, 2012 1 Overview 2 The problem
... to the corresponding node in the prefix tree and look at the minimum and maximum of that node. If minimum(maximum) = x, then the predecessor(successor) has a shorter common sequence. So we search in the shorter prefix hash tables. Otherwise, the predecessor(successor) has a longer common subsequence ...
... to the corresponding node in the prefix tree and look at the minimum and maximum of that node. If minimum(maximum) = x, then the predecessor(successor) has a shorter common sequence. So we search in the shorter prefix hash tables. Otherwise, the predecessor(successor) has a longer common subsequence ...
Tree-based Data Structures for Triangle Mesh Connectivity Encoding
... 3 Overview of Mesh Encoding Algorithms In the last years the increasing popularity of triangle meshes has rapidly accelerated the pace of research in the area of mesh encoding. As a result, many diverse techniques have emerged for the encoding of triangle mesh connectivity, each one with some advant ...
... 3 Overview of Mesh Encoding Algorithms In the last years the increasing popularity of triangle meshes has rapidly accelerated the pace of research in the area of mesh encoding. As a result, many diverse techniques have emerged for the encoding of triangle mesh connectivity, each one with some advant ...
A Locality-Preserving Cache-Oblivious Dynamic Dictionary
... • “Array” refers to the dynamic packed-memory structure storing the data • “Tree” refers to the static cache-oblivious tree that serves as an index • N data items are stored in “array” of size O(N) (sorted, some blank entries) • There are pointers between array position A[i] and leaf Ti for all valu ...
... • “Array” refers to the dynamic packed-memory structure storing the data • “Tree” refers to the static cache-oblivious tree that serves as an index • N data items are stored in “array” of size O(N) (sorted, some blank entries) • There are pointers between array position A[i] and leaf Ti for all valu ...
Finger trees: a simple general
... where ‘/0 ’ and ‘.0 ’ are the previously defined liftings of ‘/’ and ‘.’, and nodes groups a list of elements into Nodes: nodes nodes nodes nodes nodes ...
... where ‘/0 ’ and ‘.0 ’ are the previously defined liftings of ‘/’ and ‘.’, and nodes groups a list of elements into Nodes: nodes nodes nodes nodes nodes ...
Improving the Performance of Data Cube Queries Using Families of
... One way to reduce the cost of paging STs in and out of memory is to transmit only the leaves of the ST. The internal nodes can be generated in memory without additional I/O. A more effective approach is to partition an ST into multiple, smaller subtrees, each representing a certain part of the data. ...
... One way to reduce the cost of paging STs in and out of memory is to transmit only the leaves of the ST. The internal nodes can be generated in memory without additional I/O. A more effective approach is to partition an ST into multiple, smaller subtrees, each representing a certain part of the data. ...
csc215-10-data-structures-part-1
... Iterating Over a List ●Let's build a function that prints out all the items of a list. To do this: • we need to use a current pointer that will keep track of the node we are currently printing. • After printing the value of the node, we set the current pointer to the next node, and print again, unt ...
... Iterating Over a List ●Let's build a function that prints out all the items of a list. To do this: • we need to use a current pointer that will keep track of the node we are currently printing. • After printing the value of the node, we set the current pointer to the next node, and print again, unt ...
Slides for Linked List
... Recall: Array Representation of Sequences Requires an estimate of the maximum size of the list waste space + always need to track/update “size” insert and delete: have prohibitive overheads when the sequences are sorted (or, if we insist on inserting at a given ...
... Recall: Array Representation of Sequences Requires an estimate of the maximum size of the list waste space + always need to track/update “size” insert and delete: have prohibitive overheads when the sequences are sorted (or, if we insist on inserting at a given ...
Quadtree
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. A similar partitioning is also known as a Q-tree. All forms of quadtrees share some common features: They decompose space into adaptable cells Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits The tree directory follows the spatial decomposition of the quadtree.