'Amortized time' presentation slideshows

Splay trees (Sleator, Tarjan 1983)

Splay trees (Sleator, Tarjan 1983). Main idea. Try to arrange so frequently used items are near the root. We shall assume that there is an item in every node including internal nodes. We can change this assumption so that items are at the leaves. First attempt.

903 views • 72 slides

Review

Review. ArrayStack ( ArrayList ), [ ArrayDeque , and DualArrayDeque ] implement the List interface using one or two arrays. get(i) , set(i,x) take constant time. add(size(),x) , remove(size()-1) [ add(0,x) , remove(0) ] take constant amortized time. Can waste a lot of space

786 views • 64 slides

Elementary Data Structures

Elementary Data Structures. Stacks, Queues, & Lists Amortized analysis Trees. An abstract data type (ADT) is an abstraction of a data structure An ADT specifies: Data stored Operations on the data Error conditions associated with operations.

539 views • 50 slides

CSE 4101/5101

CSE 4101/5101. Prof. Andy Mirzaian. Disjoint Set Union. References:. [CLRS] chapter 21 Lecture Note 6. Disjoint Set Union.

612 views • 48 slides

Disjoint Sets

Disjoint Sets. Andreas Klappenecker [Based on slides by Prof. Welch]. Dynamic Sets. In mathematics, a set is understood as a collection of clearly distinguishable entities (called elements). Once defined, the set does not change.

829 views • 44 slides

Disjoint Sets

Disjoint Sets. Andreas Klappenecker [Based on slides by Prof. Welch]. Dynamic Sets. In mathematics, a set is understood as a collection of clearly distinguishable entities (called elements). Once defined, the set does not change.

599 views • 44 slides

CMSC 341

CMSC 341. Binomial Queues and Fibonacci Heaps. Basic Heap Operations. Amortized Time. Binomial Queues and Fibonacci Heaps have better performance in an amortized sense Cost per operation vs. cost for sequence of operations RB trees are O(lgN) per operation

638 views • 42 slides

CPSC 411 Design and Analysis of Algorithms

CPSC 411 Design and Analysis of Algorithms. Set 6: Amortized Analysis Prof. Jennifer Welch Fall 2008. Analyzing Calls to a Data Structure. Some algorithms involve repeated calls to one or more data structures Example: Heapsort repeatedly insert keys into a priority queue (heap)

703 views • 28 slides

CSCE 411 Design and Analysis of Algorithms

CSCE 411 Design and Analysis of Algorithms. Set 6: Amortized Analysis Slides by Prof. Jennifer Welch Spring 2014. Analyzing Calls to a Data Structure. Some algorithms involve repeated calls to one or more data structures Example: Heapsort

284 views • 28 slides

CSE 326: Data Structures Lecture #13 Extendible Hashing and Splay Trees

CSE 326: Data Structures Lecture #13 Extendible Hashing and Splay Trees. Alon Halevy Spring Quarter 2001. Extendible Hashing. Hashing technique for huge data sets optimizes to reduce disk accesses each hash bucket fits on one disk block better than B-Trees if order is not important

404 views • 23 slides

Incremental topological ordering with Bernhard Haeupler, Sid Sen

Incremental topological ordering with Bernhard Haeupler, Sid Sen. Two problems on digraphs: Cycle detection Topological ordering: a total order O such that v ? w ? O ( v ) < O ( w ). Incremental topological ordering.

388 views • 23 slides

165 views • 16 slides

Union-Find Partition Structures

Union-Find Partition Structures. makeSet (x): Create a singleton set containing the element x and return the position storing x in this set union (A,B ): Return the set A U B, destroying the old A and B find (p): Return the set containing the element at position p.

249 views • 14 slides

Vectors and Array Lists

Vectors and Array Lists. The Vector ADT extends the notion of array by storing a sequence of arbitrary objects An element can be accessed, inserted or removed by specifying its rank (number of elements preceding it)

117 views • 11 slides

Growing Arrays

Growing Arrays. Problem with fixed-size Arrays. In the implementation of stack or queue with an array, we had to set the array size to some initial capacity If the number of pushes (for a stack) or enqueues (for a queue) passes this capacity, we had to throw an exception

62 views • 6 slides