'Pivot element' presentation slideshows

Chapter 4

Chapter 4. The Simplex Method. Outline. 4.1 Slack Variables and the Simplex Tableau 4.2 The Simplex Method I: Maximum Problems 4.3 The Simplex Method II: Minimum Problems 4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems 4.5 Duality.

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SE301: Numerical Methods Topic 3: Solution of Systems of Linear Equations Lectures 12-17:

SE301: Numerical Methods Topic 3: Solution of Systems of Linear Equations Lectures 12-17:. KFUPM Read Chapter 9 of the textbook. Lecture 12 Vector, Matrices, and Linear Equations. VECTORS. MATRICES. MATRICES. Determinant of a MATRICES. Adding and Multiplying Matrices.

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SE301: Numerical Methods Topic 3: Solution of Systems of Linear Equations Lectures 12-17:

SE301: Numerical Methods Topic 3: Solution of Systems of Linear Equations Lectures 12-17:. KFUPM Read Chapter 9 of the textbook. Lecture 12 Vector, Matrices, and Linear Equations. VECTORS. MATRICES. MATRICES. Determinant of a MATRICES. Adding and Multiplying Matrices.

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Mergesort and Quicksort

Mergesort and Quicksort. Chapter 8 Kruse and Ryba. Sorting algorithms. Insertion, selection and bubble sort have quadratic worst-case performance The faster comparison based algorithm ? O(nlogn) Mergesort and Quicksort. Merge Sort.

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Analysis of Quicksort

Analysis of Quicksort. Quicksort Algorithm. Given an array of n elements (e.g., integers): If array only contains one element, return Else pick one element to use as pivot. Partition elements into two sub-arrays: Elements less than or equal to pivot Elements greater than pivot

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Divide And Conquer

Divide And Conquer. Distinguish between small and large instances. Small instances solved differently from large ones. Small And Large Instance. Small instance. Sort a list that has n <= 10 elements. Find the minimum of n <= 2 elements. Large instance.

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CMSC 202

CMSC 202. Computer Science II for Majors. Topics. Sorting Techniques Merge Sort Quick Sort. Merge Sort. Problem Statement: Sort a sequence in an efficient manner. Strategy: Divide input into smaller sequences. Sort smaller sequences. Merge resulting sorted sequences together.

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Data Structure

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Data Structure

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When is A=B?

When is A=B?. Donald Kossmann Systems Group, ETH Zurich http:// systems.ethz.ch. Acknowledgments. Insanity: doing the same thing over and over again and expecting different results . (A. Einstein).

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Quicksort Algorithm

Quicksort Algorithm. Given an array of n elements (e.g., integers): If array only contains one element, return Else pick one element to use as pivot. Partition elements into two sub-arrays: Elements less than or equal to pivot Elements greater than pivot Quicksort two sub-arrays

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Sorting Algorithms: Merge and Quick

Sorting Algorithms: Merge and Quick. Lecture Objectives. Learn how to implement the simple advanced sorting algorithms (merge and quick) Learn how to implement the merge and quick sort algorithms To learn how to estimate and compare the performance of divide and conquer sorting algorithms

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Searching

Searching. Even if you do learn to speak correct English, whom are you going to speak it to? Clarence Darrow . Searching. locating one record (object) from a collection search key unique vs duplicate outcomes found/not found simple vs exhaustive search internal vs external

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Sorting

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Learning Objectives for Section 6.2

Learning Objectives for Section 6.2 . Simplex Method: Maximization with Problem Constraints of the Form ?. The student will be able to set up the initial system: the Simplex Tableau The student will be able to use the pivot operation on the Simplex Tableau.

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Linear Systems

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Elementary Sorting

Elementary Sorting. 30 January 2003. Simple Sort. // List is an array of size == n for (i = 1; i < n; i++) for (j = i+1; j <= n; j++) if (List[i] > List[j]) swap(List[i], List[j]); Simple Sort. Simple Sort. The algorithm starts with the first element of the list.

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Solutions to Midterm 1

Solutions to Midterm 1. Question 1. Recurrence Relation T(n) = 4T(n/2) + n 2, n ? 2 ; T(1) = 1 Height of the recursion tree: Assume n = 2 k height: k = log n . If 2 k-1 < n ? 2 k , k - 1< log n ? k. Therefore, height is ?log 2 n?. Question 1 (contd). Recurrence Relation

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Fundamentals of Algorithms MCS - 2 Lecture # 16

Fundamentals of Algorithms MCS - 2 Lecture # 16. Quick Sort. Quick Sort. Fastest known sorting algorithm in practice. It is being selected in most sorting libraries. The quicksort algorithm sorts an unordered list based on the divide and conquer strategy.

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