Use Hall's Theorem to answer the followingSuppose that m people are selected as prize winners in a lottery, where each winner can selecttwo prizes from a collection of different prizes. Show if there are 2m prizes that every winnerwants, then every winner is able to select two prizes that they want.

Answered: Suppose that m people are selected as…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
In a hypothetical study of population dynamics, scientists have been tracking the number of rabbits and foxes on an island. The number of rabbits and foxes are determined once a year using high resolution infrared cameras and advanced computer vision methods.Each year, the number of rabbits and foxes are found to change by the following equations: $$ {\Delta}R = round( kr*R - krf*R*F ) $$ $$ {\Delta}F = round( -kf*F + kfr*R*F ) $$ where $ {\Delta}r $ and $ {\Delta} f $ are the changes in number of rabbits and foxes by the end of that year; and R and F are the population sizes at the end of the previous year. kr, krf, kf, kfr are coefficients that depend on the species of rabbits and foxes.With these dynamics, the scientists realize that one or both species can become extinct on the island. At the end of each year, if there are fewer than 2 animals of a kind, the scientists transfer rabbits and/or foxes to make sure there are at least 2 of each kind.Write a function…
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Suppose that m people are selected as prize winners in a lottery, where each winner can s two prizes from a collection of different prizes. Show if there are 2m prizes that every winne