'Worst case time' diaporamas de présentation

Elementary Data Structures: Part 1: Arrays , Lists

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COMPSCI 102

COMPSCI 102. Introduction to Discrete Mathematics. This is The Big Oh!. Lecture 21 (November 12, 2007). How to add 2 n-bit numbers. * *. * *. * *. * *. * *. * *. * *. * *. * *. * *. * *. +. How to add 2 n-bit numbers. * *. * *. * *. * *. * *. * *. * *. * *. * *. * * *.

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The Heap Data Structure

The Heap Data Structure. Overview. Usage of a heap Priority queue HeapSort Definitions: height, depth, full binary tree, complete binary tree Definition of a heap Methods of a heap. Priority Queue. A priority queue is a collection of zero or more items,

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Abstract Data Types Queue + Dequeue Amortized analysis

Abstract Data Types Queue + Dequeue Amortized analysis. 5 4 17 21. Q. 5 4 17 21. Can one Implement A Queue with stacks?. You are given the STACK ABSTRACT data structure (1, 2 .. as many as you want) Can you use it to implement a queue. S 2. S 1. Implementation of Queue with stacks.

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A look at Sorting

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CSCE 411 Design and Analysis of Algorithms

CSCE 411 Design and Analysis of Algorithms. Set 7: Disjoint Sets Slides by Prof. Jennifer Welch Spring 2014. Disjoint Sets Abstract Data Type. State: collection of disjoint dynamic sets number of sets and composition can change, but must always be disjoint

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CSE 326: Data Structures Part 9 Really, Really Hard Problems

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CSE332: Data Abstractions Lecture 25: Amortized Analysis

CSE332: Data Abstractions Lecture 25: Amortized Analysis. Sandra B. Fan Winter 2011. Announcements. Homework 8 due NOW Pick up Homeworks 1-7 after lecture from TAs Project 3 due last night 11pm Unless you are using late days Final exam is Tues, March 15, 2:30-4:20pm HERE

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Divide and Conquer

Divide and Conquer. Andreas Klappenecker [based on slides by Prof. Welch]. Divide and Conquer Paradigm. An important general technique for designing algorithms: divide problem into subproblems recursively solve subproblems combine solutions to subproblems to get solution to original problem

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Timing Analysis

Timing Analysis. Reference: Tremblay and Cheston : Section 5.1. Quality of a project/method is determined by many factors: Simplicity Readability Verifiability Correctness: yields the correct results according to its specification Validity Solves the original problem Robustness

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Updates

Updates. HW#1 has been delayed until next MONDAY . There were two errors in the assignment.

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Finger search trees

Finger search trees. Goal. Keep sorted lists subject to the following operations: find(x,L) insert(x,L) delete(x,L) catenate(L1,L2) : Assumes that all items in L2 are greater than all items in L1.

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Order statistics a dynamic version

Order statistics a dynamic version. rank and select. The dictionary ADT. Insert ( x,D ) Delete ( x,D ) Find ( x,D ): Returns a pointer to x if x ? D, and a pointer to the successor or predecessor of x if x is not in D. Suppose we want to add to the dictionary ADT.

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Lecture 9

Lecture 9. Lower Bounds for Sorting, Searching and Selection. Plan. Finish Heaps Lower Bounds Selection (Find Min): adversary arguments Sorting: information theory lower bound for comparison based algorithms Searching: ITLB. Finish Heaps. Building a heap from an array, in O(n) time.

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CSE332: Data Abstractions Lecture 25: Amortized Analysis

CSE332: Data Abstractions Lecture 25: Amortized Analysis. Dan Grossman Spring 2012. Amortized . Recall our plain-old stack implemented as an array that doubles its size if it runs out of room How can we claim push is O ( 1 ) time if resizing is O ( n ) time?

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MPSC Procedures An update

MPSC Procedures An update. Alick Macpherson Rutgers University/ETH Zurich. MPSC Procedures: Observations. Purpose: Procedures are required for systems that can by their malfunctioning cause significant damage to LHC equipment Procedures are required for 3 types of system:

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CSE332: Data Abstractions Lecture 21: Amortized Analysis

CSE332: Data Abstractions Lecture 21: Amortized Analysis. Dan Grossman Spring 2010. Amortized . Recall our plain-old stack implemented as an array that doubles its size if it runs out of room How can we claim push is O ( 1 ) time if resizing is O ( n ) time?

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Design and Analysis of Algorithms Quicksort

Design and Analysis of Algorithms Quicksort. Haidong Xue Summer 2012, at GSU. Review of insertion sort and merge sort. Insertion sort Algorithm Worst case number of comparisons = O(?) Merge sort Algorithm Worst case number of comparisons = O(?). Sorting Algorithms. Quicksort Algorithm.

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ADVANCED COMPUTATIONAL MODELS AND ALGORITHMS

ADVANCED COMPUTATIONAL MODELS AND ALGORITHMS. Instructor: Dr. Gautam Das March 10, 2009 Class notes by Alexandra Stefan. Topics covered . Linear Programming (LP) Problem instance: Set of n real variables Set of restrictions in the form of linear inequalities

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Self-Organizing Linked List

Self-Organizing Linked List. Motivation. Searching for an element in a linked list takes O(N) worst case time If we are lucky, and the element is at the beginning, then search is fast Our goal is to try to keep elements that are likely to be searched in the near future close to the head

214 views • 8 slides