Strict Fibonacci Heaps
... Loss reduction To reduce the total loss we have two different transformations. The one-node loss reduction applies when there exists an active node x with loss ≥ 2. Let y be the parent of x. In this case x is linked to the root and made an active root with loss zero, and the rank of y is decreased b ...
... Loss reduction To reduce the total loss we have two different transformations. The one-node loss reduction applies when there exists an active node x with loss ≥ 2. Let y be the parent of x. In this case x is linked to the root and made an active root with loss zero, and the rank of y is decreased b ...
Page 1 On Two-Dimensional Indexability and Optimal Range
... and other space lling curves, k-d-B-trees [21], hBtrees [15], and various R-trees [9, 25] have been proposed. Often these structures are the data structures of choice in applications, because they are relatively simple, require linear space, and in practice perform well most of the time. However, t ...
... and other space lling curves, k-d-B-trees [21], hBtrees [15], and various R-trees [9, 25] have been proposed. Often these structures are the data structures of choice in applications, because they are relatively simple, require linear space, and in practice perform well most of the time. However, t ...
Heaps Simplified Bernhard Haeupler , Siddhartha Sen , and Robert E. Tarjan
... Given a set of items with real-valued keys, one can determine the item of minimum key by running a single-elimination tournament on the items. To run such a tournament, repeatedly match pairs of items until only one item remains. To match two items, compare their keys, declare the item of smaller ke ...
... Given a set of items with real-valued keys, one can determine the item of minimum key by running a single-elimination tournament on the items. To run such a tournament, repeatedly match pairs of items until only one item remains. To match two items, compare their keys, declare the item of smaller ke ...
Document
... If heap-order is not violated, just decrease the key of x. Otherwise, cut tree rooted at x and meld into root list. To keep trees flat: as soon as a node has its second child cut, cut it off and meld into root list (and unmark it). ...
... If heap-order is not violated, just decrease the key of x. Otherwise, cut tree rooted at x and meld into root list. To keep trees flat: as soon as a node has its second child cut, cut it off and meld into root list (and unmark it). ...
Basic Data Structures
... – The first difference is the space cost – Algorithms need to think of space costs too! – Main factor is that n is changing dynamically and differently for each of the strategies! – Amortised complexity takes this into account – Counts the average time per operation over a series of operations N D G ...
... – The first difference is the space cost – Algorithms need to think of space costs too! – Main factor is that n is changing dynamically and differently for each of the strategies! – Amortised complexity takes this into account – Counts the average time per operation over a series of operations N D G ...
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Non-blocking binary search trees
... not interfere with one another if they are on different parts of the tree. In contrast, the lock-based algorithms described in Section 2 require locking all nodes along a path from the root to a leaf (although not all simultaneously). To achieve a non-blocking implementation, we use a strategy simila ...
... not interfere with one another if they are on different parts of the tree. In contrast, the lock-based algorithms described in Section 2 require locking all nodes along a path from the root to a leaf (although not all simultaneously). To achieve a non-blocking implementation, we use a strategy simila ...
Stacks and Linked Lists
... • Assume that we start with an empty stack represented by an array of size 1 • We call amortized time of a push operation the average time taken by a push over the series of operations, i.e., T(n)/n ...
... • Assume that we start with an empty stack represented by an array of size 1 • We call amortized time of a push operation the average time taken by a push over the series of operations, i.e., T(n)/n ...
Stacks and Linked Lists - TAMU Computer Science Faculty Pages
... • Assume that we start with an empty stack represented by an array of size 1 • We call amortized time of a push operation the average time taken by a push over the series of operations, i.e., T(n)/n ...
... • Assume that we start with an empty stack represented by an array of size 1 • We call amortized time of a push operation the average time taken by a push over the series of operations, i.e., T(n)/n ...
The S-Linked List–A Variant Of The Linked List Data Structure
... complexity and highly flexible in itself, enabling easy traversal and update, but it often demands more memory space compared to other list data strucure – this is as a result of the space required for the extra pointers, doubling the amount needed for a singly linked list. In this paper, we introdu ...
... complexity and highly flexible in itself, enabling easy traversal and update, but it often demands more memory space compared to other list data strucure – this is as a result of the space required for the extra pointers, doubling the amount needed for a singly linked list. In this paper, we introdu ...
Review: Kd-tree Traversal Algorithms for Ray Tracing
... scene. The naive algorithm for ray tracing with O(N) complexity computes the intersections with all geometric primitives. This can be used efficiently only for a small number of primitives (N up to 100). For larger scenes we need to restrict the number of computed intersections along the ray path. T ...
... scene. The naive algorithm for ray tracing with O(N) complexity computes the intersections with all geometric primitives. This can be used efficiently only for a small number of primitives (N up to 100). For larger scenes we need to restrict the number of computed intersections along the ray path. T ...
External Memory Techniques for Isosurface Extraction in Scientific
... has a list of cells that are cubes or tetrahedra or of some other geometric type. Each cell is defined by its vertices, where each vertex is a 3D sample point x given in the list of tuples (x, F (x)). Given an isovalue (a scalar value) q, to extract the isosurface of q is to compute and display the ...
... has a list of cells that are cubes or tetrahedra or of some other geometric type. Each cell is defined by its vertices, where each vertex is a 3D sample point x given in the list of tuples (x, F (x)). Given an isovalue (a scalar value) q, to extract the isosurface of q is to compute and display the ...
struct node - CSE@IIT Delhi
... Example: An array The array index is used for accessing and manipulation of array elements Problems with arrays The array size has to be specified at the beginning (at least during dynamic allocation) realloc ...
... Example: An array The array index is used for accessing and manipulation of array elements Problems with arrays The array size has to be specified at the beginning (at least during dynamic allocation) realloc ...
Augmenting Data Structures, Dynamic Order Statistics, Interval Trees
... Suppose that the search goes left, and assume that {i L : i overlaps i } = . • Then, the code dictates that low[i] m[left[x]] = high[ j] for some j L. • Since j L, it does not overlap i, and hence high[i] < low[ j]. • But, the binary-search-tree property implies that for all i R, we ...
... Suppose that the search goes left, and assume that {i L : i overlaps i } = . • Then, the code dictates that low[i] m[left[x]] = high[ j] for some j L. • Since j L, it does not overlap i, and hence high[i] < low[ j]. • But, the binary-search-tree property implies that for all i R, we ...
Data structures
... 68. If more than one subscript is used, an array is known as a__________. A. One- dimensional array B. Single dimensional array C. Multi- dimensional array D. None of the above 69. What is the simplest form of an array? A. One- dimensional array B. Multi- dimensional array C. Single- dimensional arr ...
... 68. If more than one subscript is used, an array is known as a__________. A. One- dimensional array B. Single dimensional array C. Multi- dimensional array D. None of the above 69. What is the simplest form of an array? A. One- dimensional array B. Multi- dimensional array C. Single- dimensional arr ...
read it here
... 64 B. We will first describe fully associative caches. When the CPU tries to access a memory location, the cache is checked first before accessing main memory. If the cache doesn’t contain the requested data, it is loaded into the cache. When the cache becomes full (i.e., when all m cache lines are ...
... 64 B. We will first describe fully associative caches. When the CPU tries to access a memory location, the cache is checked first before accessing main memory. If the cache doesn’t contain the requested data, it is loaded into the cache. When the cache becomes full (i.e., when all m cache lines are ...
Insert after specified number of nodes
... Integers, reals, and booleans have operations associated with them and so do data types such union, intersection, find, size, and complement. Why Linked lists? Let us consider an example of implementation of a STACK or a QUEUE using a linear array then it is necessary to declare the SIZE of the STAC ...
... Integers, reals, and booleans have operations associated with them and so do data types such union, intersection, find, size, and complement. Why Linked lists? Let us consider an example of implementation of a STACK or a QUEUE using a linear array then it is necessary to declare the SIZE of the STAC ...
the lecture notes from the Foundations of Computer Science module
... trying to solve. Sometimes that will be based on a particular representation of the associated data, sometimes it will be presented more abstractly. Typically, it will have to specify how the inputs and outputs of the algorithm are related, though there is no general requirement that the specificati ...
... trying to solve. Sometimes that will be based on a particular representation of the associated data, sometimes it will be presented more abstractly. Typically, it will have to specify how the inputs and outputs of the algorithm are related, though there is no general requirement that the specificati ...
Document
... Show (ipl BT) = sum of the lengths of the paths from the root to all nodes in the tree. Prove by structural induction Base case. 0 is needed to get the proper value for a tree with a single node. Assume (ipl (left BT)) and (ipl (right BT)) compute the sum of the lengths of paths in the left an ...
... Show (ipl BT) = sum of the lengths of the paths from the root to all nodes in the tree. Prove by structural induction Base case. 0 is needed to get the proper value for a tree with a single node. Assume (ipl (left BT)) and (ipl (right BT)) compute the sum of the lengths of paths in the left an ...
Chapters 8
... Red-Black Trees in present a very useful data structure that allows O(log N) searches, insertions and deletions regardless of how data is entered. This is because they self balanced dynamically on insertion and deletion of nodes. Two basic types of trees exist. Those that insert top down and change ...
... Red-Black Trees in present a very useful data structure that allows O(log N) searches, insertions and deletions regardless of how data is entered. This is because they self balanced dynamically on insertion and deletion of nodes. Two basic types of trees exist. Those that insert top down and change ...
1 - My FIT
... This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to their elements. So accessing individual elements in a linked lis ...
... This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to their elements. So accessing individual elements in a linked lis ...
1 - My FIT
... The elements of an array are stored contiguously in memory. This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to thei ...
... The elements of an array are stored contiguously in memory. This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to thei ...
1 - Vanderbilt University
... This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to their elements. So accessing individual elements in a linked lis ...
... This allows immediate access to any array element, because the address of any element can be calculated directly based on its position relative to the beginning of the array. Linked lists do not afford such immediate “direct access” to their elements. So accessing individual elements in a linked lis ...
Data Structure and Algorithms
... or a function, and in the latter case it also supplies the value of the function. We do not declare the type of parameters in procedures and functions, nor the type of the result returned by a function, unless such declarations make the algorithm easier to understand. Scalar parameters are passed by ...
... or a function, and in the latter case it also supplies the value of the function. We do not declare the type of parameters in procedures and functions, nor the type of the result returned by a function, unless such declarations make the algorithm easier to understand. Scalar parameters are passed by ...
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.