Algorithms: COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms: COMP3121/9101 School of Computer Science and Engineering University of New South Wales 3. RECURRENCES – part A COMP3121/3821/9101/9801 1 / 22 Asymptotic notation “Big Oh” notation: f(n) = O(g(n)) is an abbreviation for: “There exist positive constants c and n0 such that 0 ≤ f(n) ≤ […]
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Algorithms COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms COMP3121/9101 Aleks Ignjatović School of Computer Science and Engineering University of New South Wales 5. THE FAST FOURIER TRANSFORM (not examinable material) COMP3121/9101 1 / 33 Our strategy to multiply polynomials fast: Given two polynomials of degree at most n, PA(x) = Anx n + .
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More on Linear Programming Aleks Ignjatovic .edu.au THE UNIVERSITY OF NEW SOUTH WALES School of Computer Science and Engineering The University of New South Wales Sydney 2052, Australia We now move to one of the most important cases of convex programming, called Linear Programming, (LP), in which the objective is a linear function and the
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Algorithms: COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms: COMP3121/9101 School of Computer Science and Engineering University of New South Wales 10. LINEAR PROGRAMMING COMP3121/9101 1 / 18 Linear Programming problems – Example 1 Problem: You are given a list of food sources f1, f2, . . . , fn; for each source fi you
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Algorithms Tutorial 1 Problems 1. You are given an array S of n integers and another integer x. (a) Describe an O(n log n) algorithm (in the sense of the worst case perfor- mance) that determines whether or not there exist two elements in S whose sum is exactly x. (b) Describe an algorithm that
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Algorithms: COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms: COMP3121/9101 School of Computer Science and Engineering University of New South Wales 10. LINEAR PROGRAMMING COMP3121/9101 1 / 18 Linear Programming problems – Example 1 Problem: You are given a list of food sources f1, f2, . . . , fn; for each source fi you
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Algorithms: COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms: COMP3121/9101 Aleks Ignjatović School of Computer Science and Engineering University of New South Wales 6. THE GREEDY METHOD COMP3121/3821/9101/9801 1 / 47 The Greedy Method Activity selection problem. Instance: A list of activities ai, (1 ≤ i ≤ n) with starting times si and finishing times
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Algorithms Tutorial 4 Problems 1. You are traveling by a canoe down a river and there are n trading posts along the way. Before starting your journey, you are given for each 1 ≤ i < j ≤ n the fee F (i, j) for renting a canoe from post i to post j. These
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Algorithms Tutorial 5 Solutions 1. In the country of Pipelistan there are several oil wells, several oil refineries and many distribution hubs connected by oil pipelines. To visualise Pipelistan’s oil infrastructure, just imagine a directed graph with k source vertices (the oil wells), m sinks (refineries) and n vertices which are distribution hubs linked with
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Algorithms: COMP3121/9101 THE UNIVERSITY OF NEW SOUTH WALES Algorithms: COMP3121/9101 School of Computer Science and Engineering University of New South Wales 8. MAXIMUM FLOW COMP3121/3821/9101/9801 1 / 29 Flow Networks A flow network G = (V,E) is a directed graph in which each edge e = (u, v) ∈ E has a positive integer capacity
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