COMP3121/9101/3821/9801 Lecture Notes More on Dynamic Programming (DP) LiC: Aleks Ignjatovic THE UNIVERSITY OF NEW SOUTH WALES School of Computer Science and Engineering The University of New South Wales Sydney 2052, Australia 1 Turtle Tower You are given n turtles, and for each turtle you are given its weight and its strength. The strength of […]
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NEW SOUTH WALES Algorithms: COMP3121/9101 School of Computer Science and Engineering University of New South Wales 9. STRING MATCHING ALGORITHMS COMP3121/3821/9101/9801 1 / 13 String Matching algorithms Assume that you want to find out if a string B = b0b1 . . . bm−1 appears as a (contiguous) substring of a much longer string A
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NEW SOUTH WALES Algorithms: COMP3121/9101 Aleks Ignjatovi ́c 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 fi. No two activities
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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; COMP3121/9101 2 / 18 Linear Programming problems – Example 1 Problem: You are given a list
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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 c(u, v) > 0.
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NEW SOUTH WALES Algorithms: COMP3121/9101 Aleks Ignjatovi ́c 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 fi. No two activities
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Algorithms COMP3121/9101 Aleks Ignjatovi ́c, ignjat@cse.unsw.edu.au office: 504 (CSE building) Course Admin: Anahita Namvar, cs3121@cse.unsw.edu.au School of Computer Science and Engineering University of New South Wales Sydney 1. INTRODUCTION COMP3121/3821/9101/9801 1 / 21 Introduction What is this course about? It is about designing algorithms for solving practical problems. What is an algorithm? An algorithm is
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Algorithms: COMP3121/9101 Aleks Ignjatovi ́c, ignjat@cse.unsw.edu.au office: 504 (CSE building) Course Admin: Anahita Namvar, comp3121.unsw@gmail.com School of Computer Science and Engineering University of New South Wales Sydney 2. DIVIDE-AND-CONQUER COMP3121/3821/9101/9801 1 / 28 A Puzzle An old puzzle: We are given 27 coins of the same denomination; we know that one of them is counterfeit
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Algorithms Tutorial 1 Solutions 1. You are given an array S of n integers and another integer x. (a) Describe an O(nlogn) 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 accomplishes the
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NEW SOUTH WALES Algorithms COMP3121/9101 Aleks Ignjatovi ́c 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)=Anxn +…+A0; PB(x)=Bnxn +…+B0 1 convert them into value representation
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