Background
... root node is O(1) and each operation touches at most two root nodes, and so the part of the work done on root nodes by the m operations is O(m). • The majority of the work is done on nodes when they are non-root nodes which is path compression • To reduce the worst-case complexity of the union-find ...
... root node is O(1) and each operation touches at most two root nodes, and so the part of the work done on root nodes by the m operations is O(m). • The majority of the work is done on nodes when they are non-root nodes which is path compression • To reduce the worst-case complexity of the union-find ...
PowerPoint - BYU Computer Science Students Homepage Index
... Each non-leaf node (except the root) must have (n/2, n) pointers ...
... Each non-leaf node (except the root) must have (n/2, n) pointers ...
Review: Pastry routing tables - Stanford Secure Computer Systems
... • Leaf sets: Node closest to target could be dead - Need to find next closest - That’s why leaf sets not just one neighbor (O(log N )) - Easy to update leaf sets by contacting other nearby nodes ...
... • Leaf sets: Node closest to target could be dead - Need to find next closest - That’s why leaf sets not just one neighbor (O(log N )) - Easy to update leaf sets by contacting other nearby nodes ...
Lecture 16 Student Notes
... are at node y in the weight balanced BST representing node x in the trie. Consider all trie children c1 , c2 , ..., cm of node x present in y’s subtree. Let D be the total number of descendant leaves of c1 , c2 , ..., cm . If the number of descendant leaves of any child ci is at most D/3 then follow ...
... are at node y in the weight balanced BST representing node x in the trie. Consider all trie children c1 , c2 , ..., cm of node x present in y’s subtree. Let D be the total number of descendant leaves of c1 , c2 , ..., cm . If the number of descendant leaves of any child ci is at most D/3 then follow ...
Advanced Data Structure
... Case II : Removing a node with a single child Replace the removed node with its child Case III : Removing a node with 2 children Replace the removed node with the minimum element in the right subtree (or maximum element in the left subtree) This may create a hole again Apply Case I or II Som ...
... Case II : Removing a node with a single child Replace the removed node with its child Case III : Removing a node with 2 children Replace the removed node with the minimum element in the right subtree (or maximum element in the left subtree) This may create a hole again Apply Case I or II Som ...
DATA STRUCTURE- THE BASIC STRUCTURE FOR PROGRAMMING
... is a triple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. A binary tree is a rooted tree that is also an ordered tree (aka plane tree) in which every node has at most two children. A rooted tree naturally imparts a notion of levels (distance from the root), thu ...
... is a triple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. A binary tree is a rooted tree that is also an ordered tree (aka plane tree) in which every node has at most two children. A rooted tree naturally imparts a notion of levels (distance from the root), thu ...
Trees
... – To traverse a tree means to visit all the nodes in some specified order. – Level of a particular node refers to how many generations the node is from the root. It is the same thing as the depth. – One data item in a node is usually designated the key value. This value is used to search for the ite ...
... – To traverse a tree means to visit all the nodes in some specified order. – Level of a particular node refers to how many generations the node is from the root. It is the same thing as the depth. – One data item in a node is usually designated the key value. This value is used to search for the ite ...
Algorithms and Data Structures
... If both y and z have only t –1 keys, merge k with the contents of z into y, so that x loses both k and the pointers to z, and y now contains 2t – 1 keys. Free z and recursively delete k from y. P ...
... If both y and z have only t –1 keys, merge k with the contents of z into y, so that x loses both k and the pointers to z, and y now contains 2t – 1 keys. Free z and recursively delete k from y. P ...
power point
... If both y and z have only t –1 keys, merge k with the contents of z into y, so that x loses both k and the pointers to z, and y now contains 2t – 1 keys. Free z and recursively delete k from y. P ...
... If both y and z have only t –1 keys, merge k with the contents of z into y, so that x loses both k and the pointers to z, and y now contains 2t – 1 keys. Free z and recursively delete k from y. P ...
Building Trees
... Since node numbers may be repeated, each node includes a count Let the left and right subtrees be named smaller and greater, alluding to info ordering Thus we have sufficient information to define the node data structure in C++ ...
... Since node numbers may be repeated, each node includes a count Let the left and right subtrees be named smaller and greater, alluding to info ordering Thus we have sufficient information to define the node data structure in C++ ...
Question Bank-2 - nanosoft.net.in
... The leaves of an expression tree are operands such as constants or variable names and the other nodes contain operators. 16.Define Strictly binary tree? If every nonleaf node in a binary tree has nonempty left and right subtrees ,the tree is termed as a strictly binary tree. 17.Define complete binar ...
... The leaves of an expression tree are operands such as constants or variable names and the other nodes contain operators. 16.Define Strictly binary tree? If every nonleaf node in a binary tree has nonempty left and right subtrees ,the tree is termed as a strictly binary tree. 17.Define complete binar ...
6) R-tree: Typically the preferred method for indexing spatial data
... identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids and grids based on diamond-shaped cells. 2. Z-order, Morton order, or Mor ...
... identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids and grids based on diamond-shaped cells. 2. Z-order, Morton order, or Mor ...
CS II: Data Structures Discussion worksheet: Week 9
... 2. Write out a recursive method that searches for a number in a binary search tree. Lastly, if the number is found, return the node, else return null. private class Node { ...
... 2. Write out a recursive method that searches for a number in a binary search tree. Lastly, if the number is found, return the node, else return null. private class Node { ...
File
... c. Process the root node 10. Define in -order traversal? In-order traversal entails the following steps; a. Process the left subtree b. Process the root node c. Process the right subtree 11. What is a balance factor in AVL trees? Balance factor of a node is defined to be the difference between the h ...
... c. Process the root node 10. Define in -order traversal? In-order traversal entails the following steps; a. Process the left subtree b. Process the root node c. Process the right subtree 11. What is a balance factor in AVL trees? Balance factor of a node is defined to be the difference between the h ...
20 - University of Arizona
... The left child of the root (referenced by A) has a value (5) that is less than the value of the root (8). Likewise, the value of the right child of the root has a value (10) that is greater than the root’s value (8). Also, all the values in the subtree referenced by A (4, 5, 7), are less than the v ...
... The left child of the root (referenced by A) has a value (5) that is less than the value of the root (8). Likewise, the value of the right child of the root has a value (10) that is greater than the root’s value (8). Also, all the values in the subtree referenced by A (4, 5, 7), are less than the v ...
Advanced Data Structure
... For each node, do shift down O(NlgN)??? For a binary tree with N nodes • There are at most ceil(N/2h+1) nodes with height h ...
... For each node, do shift down O(NlgN)??? For a binary tree with N nodes • There are at most ceil(N/2h+1) nodes with height h ...
No Slide Title
... A binary search tree is a 1) binary tree, 2) with the additional condition that if a node contains a value k, then every node in its left sub-tree contains a value less than k, and every node in its right sub-tree contains a value greater than or equal to k. An important consequence of the above pro ...
... A binary search tree is a 1) binary tree, 2) with the additional condition that if a node contains a value k, then every node in its left sub-tree contains a value less than k, and every node in its right sub-tree contains a value greater than or equal to k. An important consequence of the above pro ...
PPT - WSU EECS - Washington State University
... Overloaded functions are distinguished by their signatures. ...
... Overloaded functions are distinguished by their signatures. ...
Lecture7AGPrint - School of Computer Science
... Since the depth is not expected to be larger than log(N), and each step down the tree requires constant time, we get O(log N). More later.. ...
... Since the depth is not expected to be larger than log(N), and each step down the tree requires constant time, we get O(log N). More later.. ...
1. The memory address of the first element of an array is called A
... 11. The difference between linear array and a record is A. An array is suitable for homogeneous data but the data items in a record may have different data type B. In a record, there may not be a natural ordering in opposed to linear array. C. A record form a hierarchical structure but a linear arra ...
... 11. The difference between linear array and a record is A. An array is suitable for homogeneous data but the data items in a record may have different data type B. In a record, there may not be a natural ordering in opposed to linear array. C. A record form a hierarchical structure but a linear arra ...
presentation
... which together represent a sequence • each node is composed of a data and a reference (in other words, a link) to the next node in the sequence • this structure allows for efficient insertion or removal of elements from any position in the sequence ...
... which together represent a sequence • each node is composed of a data and a reference (in other words, a link) to the next node in the sequence • this structure allows for efficient insertion or removal of elements from any position in the sequence ...
A Data Structure for Manipulating Priority Queues (by Jean Vuillemin
... -the number of children of a node is equal to the number of l's following the last 0 in its binary numbering; leaves thus correspond to even numbers; -in Bp there is exactly one node, the root, having p children; for 0 _-_k < p there are 2p-k-1 nodes having k children. There are many ways of drawing ...
... -the number of children of a node is equal to the number of l's following the last 0 in its binary numbering; leaves thus correspond to even numbers; -in Bp there is exactly one node, the root, having p children; for 0 _-_k < p there are 2p-k-1 nodes having k children. There are many ways of drawing ...
Powerpoint
... There is no reason why a Knuth binary tree should balance. Average performance for random input should not be greatly below balanced performance, but if the tree is made from sorted input, it will degrade to a linked list with access time of O(N) where there are N nodes. Access time for a node withi ...
... There is no reason why a Knuth binary tree should balance. Average performance for random input should not be greatly below balanced performance, but if the tree is made from sorted input, it will degrade to a linked list with access time of O(N) where there are N nodes. Access time for a node withi ...
Network Simplex Method I
... Theorem: If a minimum cost flow problem has an optimal solution, then it has an optimal solution represented by a basis structure (T,L,U). Proof: Let x be an optimal solution for which the set F(x) of free arcs is minimal. If F(x) contains an undirected cycle C, then let W be a directed cycle in G(x ...
... Theorem: If a minimum cost flow problem has an optimal solution, then it has an optimal solution represented by a basis structure (T,L,U). Proof: Let x be an optimal solution for which the set F(x) of free arcs is minimal. If F(x) contains an undirected cycle C, then let W be a directed cycle in G(x ...
Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a (non-empty) binary tree is a triple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. Some authors allow the binary tree to be the empty set as well.From a graph theory perspective, binary (and K-ary) trees as defined here are actually arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which actually appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. A binary tree is a special case of an ordered K-ary tree, where k is 2.In computing, binary trees are seldom used solely for their structure. Much more typical is to define a labeling function on the nodes, which associates some value to each node. Binary trees labelled this way are used to implement binary search trees and binary heaps, and are used for efficient searching and sorting. The designation of non-root nodes as left or right child even when there is only one child present matters in some of these applications, in particular it is significant in binary search trees. In mathematics, what is termed binary tree can vary significantly from author to author. Some use the definition commonly used in computer science, but others define it as every non-leaf having exactly two children and don't necessarily order (as left/right) the children either.