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NEW SOUTH WALES Algorithms COMP3121/9101 School of Computer Science and Engineering University of New South Wales 4. FAST LARGE INTEGER MULTIPLICATION – part A COMP3121/9101 1 / 35 Basics revisited: how do we multiply two numbers? The primary school algorithm: X X X X 1. Consequently, for such an ε we would have f (n) […]

Algorithms Tutorial Problems 3 Greedy Strategy Solutions 1. There are N robbers who have stolen N items. You would like to distribute the items among the robbers (one item per robber). You know the precise value of each item. Each robber has a particular range of values they would like their item to be worth

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

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

Algorithms Tutorial 4 Solutions 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 fees are

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 / 1 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)≤cg(n) for all n≥n0”. In this case we say

Algorithms Tutorial 2 Solutions Divide and Conquer, polynomial multiplication and the FFT 1. You are given a 2n × 2n board with one of its cells missing (i.e., the board has a hole); the position of the missing cell can be arbitrary. You are also given a supply of “dominoes” each containing 3 such squares;

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