Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259676512
Author: Kenneth H Rosen
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 3.1, Problem 62E
To determine
To prove:
a greedy algorithm that schedules talks in a lecture hall, as described in Example 7, by selecting at each step the talk that overlaps the fewest other talks, does not always produce an optimal schedule.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A box contains 5 red ,3 yellow and 12 blue biro pens .2 biro pens are picked at random without replacement.find the probability that one of the biros picked was blue
Simply:(p/(x-a))-(p/(x+a))
Make M the subject: P=2R(M/√M-R)
Chapter 3 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 3.1 - List all the steps used by Algorithm 1 to find the...Ch. 3.1 - Determine which characteristics of an algorithm...Ch. 3.1 - Devise an algorithm that finds the sum of all the...Ch. 3.1 - Describe an algorithm that takes as input a list...Ch. 3.1 - Describe an algorithm that takes as input a list...Ch. 3.1 - Describe an algorithm that takes as input a list...Ch. 3.1 - Describe an algorithm that takes as input a list...Ch. 3.1 - Describe an algorithm that takes as input a list...Ch. 3.1 - Apalindromeis a string that reads the same forward...Ch. 3.1 - Devise an algorithm to computexn, wherexis a real...
Ch. 3.1 - Describe an algorithm that interchanges the values...Ch. 3.1 - cribe an algorithm that uses only assignment...Ch. 3.1 - List all the steps used to search for 9 in the...Ch. 3.1 - List all the steps used to search for 7 in the...Ch. 3.1 - cribe an algorithm that inserts an integerxin the...Ch. 3.1 - Describe an algorithm for finding the smallest...Ch. 3.1 - Describe an algorithm that locates the first...Ch. 3.1 - Describe an algorithm that locates the last...Ch. 3.1 - Describe an algorithm that produces the maximum,...Ch. 3.1 - Describe an algorithm for finding both the largest...Ch. 3.1 - Describe an algorithm that puts the first three...Ch. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Describe an algorithm that determines whether a...Ch. 3.1 - Describe an algorithm that will count the number...Ch. 3.1 - nge Algorithm 3 so that the binary search...Ch. 3.1 - Theternary search algorithmlocates an element in a...Ch. 3.1 - Specify the steps of an algorithm that locates an...Ch. 3.1 - Devise an algorithm that finds a mode in a list of...Ch. 3.1 - Devise an algorithm that finds all modes. (Recall...Ch. 3.1 - Two strings areanagramsif each can be formed from...Ch. 3.1 - ennreal numbersx1,x2,...,xn , find the two that...Ch. 3.1 - Devise an algorithm that finds the first term of a...Ch. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Use the bubble sort to sort 6, 2, 3, 1, 5, 4,...Ch. 3.1 - Use the bubble sort to sort 3, 1, 5, 7, 4, showing...Ch. 3.1 - Use the bubble sort to sortd,f,k,m,a,b, showing...Ch. 3.1 - Adapt the bubble sort algorithm so that it stops...Ch. 3.1 - Use the insertion sort to sort the list in...Ch. 3.1 - Use the insertion sort to sort the list in...Ch. 3.1 - Use the insertion sort to sort the list in...Ch. 3.1 - Sort these lists using the selection sort....Ch. 3.1 - Write the selection sort algorithm in pseudocode.Ch. 3.1 - Describe an algorithm based on the linear search...Ch. 3.1 - Describe an algorithm based on the binary search...Ch. 3.1 - How many comparisons does the insertion sort use...Ch. 3.1 - How many comparisons does the insertion sort use...Ch. 3.1 - Show all the steps used by the binary insertion...Ch. 3.1 - Compare the number of comparisons used by the...Ch. 3.1 - Prob. 51ECh. 3.1 - Devise a variation of the insertion sort that uses...Ch. 3.1 - Prob. 53ECh. 3.1 - List all the steps the naive string matcher uses...Ch. 3.1 - List all the steps the naive string matcher uses...Ch. 3.1 - Use the cashier’s algorithm to make change using...Ch. 3.1 - Use the cashier’s algorithm to make change using...Ch. 3.1 - Use the cashier’s algorithm to make change using...Ch. 3.1 - Prob. 59ECh. 3.1 - Show that if there were a coin worth 12 cents, the...Ch. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Devise a greedy algorithm that determines the...Ch. 3.1 - Suppose we have three menm1,m2, andm3and three...Ch. 3.1 - Write the deferred acceptance algorithm in...Ch. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prove that the Boyer-Moore majority vote algorithm...Ch. 3.1 - Show that the problem of determining whether a...Ch. 3.1 - Prob. 71ECh. 3.1 - Show that the problem of deciding whether a...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Prob. 11ECh. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - Exercises 1—14, to establish a big-Orelationship,...Ch. 3.2 - ermine whetherx3isO(g(x))for each of these...Ch. 3.2 - Explain what it means for a function to be 0(1)Ch. 3.2 - w that iff(x)isO(x)thenf(x)isO(x2).Ch. 3.2 - Suppose thatf(x),g(x), andh(x)are functions such...Ch. 3.2 - kbe a positive integer. Show...Ch. 3.2 - Prob. 19ECh. 3.2 - To simplify:(3a5)3 27a15 Given information:(3a5)3....Ch. 3.2 - ange the functionsn, 1000 logn,nlogn,2n!,2n,3n,...Ch. 3.2 - Arrange the...Ch. 3.2 - Suppose that you have two different algorithms for...Ch. 3.2 - Suppose that you have two different algorithms for...Ch. 3.2 - Give as good a big-Oestimate as possible for each...Ch. 3.2 - e a big-Oestimate for each of these functions. For...Ch. 3.2 - Give a big-Oestimate for each of these functions....Ch. 3.2 - each function in Exercise 1, determine whether...Ch. 3.2 - Prob. 29ECh. 3.2 - Show that each of these pairs of functions are of...Ch. 3.2 - Prob. 31ECh. 3.2 - w thatf(x)andg(x)are functions from the set of...Ch. 3.2 - Prob. 33ECh. 3.2 - Show that3x2+x+1is(3x2)by directly finding the...Ch. 3.2 - Prob. 35ECh. 3.2 - lain what it means for a function to be(1).Ch. 3.2 - Prob. 37ECh. 3.2 - Give a big-Oestimate of the product of the...Ch. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - pose thatf(x)isO(g(x)). Does it follow...Ch. 3.2 - Prob. 43ECh. 3.2 - pose thatf(x),g(x), andh(x)are functions such...Ch. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - ress the relationshipf(x)is(g(x))using a picture....Ch. 3.2 - Prob. 49ECh. 3.2 - w that iff(x)=anxn+an1xn1++a1x+a0,...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - w thatx5y3+x4y4+x3y5is(x3y3).Ch. 3.2 - w thatxyisO(xy).Ch. 3.2 - w thatxyis(xy).Ch. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - (Requires calculus) Prove or disprove that (2n)!...Ch. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Show thatnlognisO(logn!).Ch. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - (Requires calculus) For each of these pairs of...Ch. 3.3 - Give a big-Oestimate for the number of operations...Ch. 3.3 - Give a big-Oestimate for the number additions used...Ch. 3.3 - Give a big-Oestimate for the number of operations,...Ch. 3.3 - Give a big-Oestimate for the number of operations,...Ch. 3.3 - Prob. 5ECh. 3.3 - Use pseudocode to describe the algorithm that puts...Ch. 3.3 - Suppose that an element is known to be among the...Ch. 3.3 - Prob. 8ECh. 3.3 - Give a big-Oestimate for the number of comparisons...Ch. 3.3 - Show that this algorithm determines the number of...Ch. 3.3 - pose we havensubsetsS1,S2, ...,Snof the set {1, 2,...Ch. 3.3 - Consider the following algorithm, which takes as...Ch. 3.3 - The conventional algorithm for evaluating a...Ch. 3.3 - re is a more efficient algorithm (in terms of the...Ch. 3.3 - t is the largestnfor which one can solve within...Ch. 3.3 - What is the largestnfor which one can solve within...Ch. 3.3 - What is the largestnfor which one can solve within...Ch. 3.3 - How much time does an algorithm take to solve a...Ch. 3.3 - Prob. 19ECh. 3.3 - What is the effect in the time required to solve a...Ch. 3.3 - Prob. 21ECh. 3.3 - Determine the least number of comparisons, or...Ch. 3.3 - Analyze the average-case performance of the linear...Ch. 3.3 - An algorithm is calledoptimalfor the solution of a...Ch. 3.3 - Describe the worst-case time complexity, measured...Ch. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Analyze the worst-case time complexity of the...Ch. 3.3 - Analyze the worst-case time complexity of the...Ch. 3.3 - Analyze the worst-case time complexity of the...Ch. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Determine a big-O estimate for the worst-case...Ch. 3.3 - Determine the number of character comparisons used...Ch. 3.3 - Determine a big-Oestimate of the number of...Ch. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Show that the greedy algorithm for making change...Ch. 3.3 - rcises 41 and 42 deal with the problem of...Ch. 3.3 - rcises 41 and 42 deal with the problem of...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3 - Define the termalgorithm. What are the different...Ch. 3 - Describe, using English, an algorithm for finding...Ch. 3 - Prob. 3RQCh. 3 - Prob. 4RQCh. 3 - Prob. 5RQCh. 3 - Define what the worst-case time complexity,...Ch. 3 - Prob. 7RQCh. 3 - Describe the bubble sort algorithm. Use the bubble...Ch. 3 - Describe the insertion sort algorithm. Use the...Ch. 3 - Explain the concept of a greedy algorithm. Provide...Ch. 3 - Prob. 11RQCh. 3 - Describe an algorithm for locating the last...Ch. 3 - Prob. 2SECh. 3 - Give an algorithm to determine whether a bit...Ch. 3 - Suppose that a list contains integers that are in...Ch. 3 - Prob. 5SECh. 3 - Prob. 6SECh. 3 - Prob. 7SECh. 3 - Prob. 8SECh. 3 - Prob. 9SECh. 3 - Prob. 10SECh. 3 - Show the steps used by the shaker sort to sort the...Ch. 3 - Express the shaker sort in pseudocode.Ch. 3 - Prob. 13SECh. 3 - Prob. 14SECh. 3 - Prob. 15SECh. 3 - w that8x3+12x+100logxisO(x3).Ch. 3 - Prob. 17SECh. 3 - Prob. 18SECh. 3 - Prob. 19SECh. 3 - w thatnnis notO(n!).Ch. 3 - Prob. 21SECh. 3 - Prob. 22SECh. 3 - Prob. 23SECh. 3 - Prob. 24SECh. 3 - Arrange the...Ch. 3 - Prob. 26SECh. 3 - Prob. 27SECh. 3 - Show that if the denominations of coins arec0,c1,...Ch. 3 - Prob. 29SECh. 3 - Prob. 30SECh. 3 - Prob. 31SECh. 3 - Show that the deferred acceptance algorithm given...Ch. 3 - Prob. 33SECh. 3 - Show that when woman do the proposing in the...Ch. 3 - Prob. 35SECh. 3 - Prob. 36SECh. 3 - Prob. 37SECh. 3 - Prob. 38SECh. 3 - Prob. 39SECh. 3 - Prob. 40SECh. 3 - Prob. 41SECh. 3 - Exercises 4246 we will study the problem of load...Ch. 3 - Prob. 43SECh. 3 - Prob. 44SECh. 3 - Prob. 45SECh. 3 - Prove that the algorithm from Exercise 44 is a...Ch. 3 - Prob. 1CPCh. 3 - Prob. 2CPCh. 3 - Prob. 3CPCh. 3 - Prob. 4CPCh. 3 - Prob. 5CPCh. 3 - Prob. 6CPCh. 3 - Prob. 7CPCh. 3 - Given an integern, use the cashier’s algorithm to...Ch. 3 - Prob. 9CPCh. 3 - Prob. 10CPCh. 3 - Prob. 11CPCh. 3 - Prob. 1CAECh. 3 - Prob. 2CAECh. 3 - Using a generator of random orderings of the...Ch. 3 - Prob. 4CAECh. 3 - Write a program that animates the progress of all...Ch. 3 - Examine the history of the wordalgorithmand...Ch. 3 - Prob. 2WPCh. 3 - Explain how sorting algorithms can be classified...Ch. 3 - Prob. 4WPCh. 3 - Prob. 5WPCh. 3 - Prob. 6WPCh. 3 - Describe the historic trends in how quickly...Ch. 3 - Develop a detailed list of algorithmic paradigms...Ch. 3 - Explain what the Turing Award is and describe the...Ch. 3 - Prob. 10WPCh. 3 - Prob. 11WPCh. 3 - Describe six different NP-complete problems.Ch. 3 - Prob. 13WP
Knowledge Booster
Similar questions
- Exercice 2: Soit & l'ensemble des nombres réels. Partie A Soit g la fonction définie et dérivable sur R telle que, pour tout réel x. g(x) = - 2x ^ 3 + x ^ 2 - 1 1. a) Étudier les variations de la fonction g b) Déterminer les limites de la fonction gen -oo et en +00. 2. Démontrer que l'équation g(x) = 0 admet une unique solution dans R, notée a, et que a appartient à | - 1 ;0|. 3. En déduire le signe de g sur R. Partie B Soit ƒ la fonction définie et dérivable sur R telle que, pour tout réel s. f(x) = (1 + x + x ^ 2 + x ^ 3) * e ^ (- 2x + 1) On note f la fonction dérivée de la fonction ƒ sur R. 1. Démontrer que lim x -> ∞ f(x) = - ∞ 2. a) Démontrer que, pour tout x > 1 1 < x < x ^ 2 < x ^ 3 b) En déduire que, pour x > 1 0 < f(x) < 4x ^ 3 * e ^ (- 2x + 1) c) On admet que, pour tout entier naturel n. lim x -> ∞ x ^ n * e ^ (- x) = 0 Vérifier que, pour tout réel x, 4x ^ 3 * e ^ (- 2x + 1) = e/2 * (2x) ^ 3 * e ^ (-2x) puis montrer que: lim x -> ∞ 4x ^ 3 * e…arrow_forwardshow me pass-to-passarrow_forwardshow me pleasearrow_forward
- Show me pass-to-passarrow_forwardPlease explain the pass-to-passarrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Automobile Department Subject :Engineering Analysis Time: 2 hour Date:27-11-2022 کورس اول تحليلات تعمیر ) 1st month exam / 1st semester (2022-2023)/11/27 Note: Answer all questions,all questions have same degree. Q1/: Find the following for three only. 1- 4s C-1 (+2-3)2 (219) 3.0 (6+1)) (+3+5) (82+28-3),2- ,3- 2-1 4- Q2/:Determine the Laplace transform of the function t sint. Q3/: Find the Laplace transform of 1, 0≤t<2, -2t+1, 2≤t<3, f(t) = 3t, t-1, 3≤t 5, t≥ 5 Q4: Find the Fourier series corresponding to the function 0 -5arrow_forwardQ1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Automobile Department Subject :Engineering Analysis Time: 2 hour Date:27-11-2022 کورس اول تحليلات تعمیر ) 1st month exam / 1st semester (2022-2023)/11/27 Note: Answer all questions,all questions have same degree. Q1/: Find the following for three only. 1- 4s C-1 (+2-3)2 (219) 3.0 (6+1)) (+3+5) (82+28-3),2- ,3- 2-1 4- Q2/:Determine the Laplace transform of the function t sint. Q3/: Find the Laplace transform of 1, 0≤t<2, -2t+1, 2≤t<3, f(t) = 3t, t-1, 3≤t 5, t≥ 5 Q4: Find the Fourier series corresponding to the function 0 -5arrow_forwardSHU Pra S × (29 (29 Ful SH Fre SH Stu 1b | Stu M De rea Ma tea Tea | b An | filo Tea | filo Filo SH + OXFORD C talentcentral.eu.shl.com/player/testdriver/launch?s=61B06D43-1AC3-4353-8210-9DF5644C9747&from Launch=true ☆ V My Profile → Exit SHL Help▾ 09:21 Community Service Schedule Team A: 4 people Team B: 6 people Team C: 8 people 9 10 11 12 1 2 3 4 5 6 Question You are organizing a community service event today. At least 6 people must be working the event between 10 a.m.5 p.m. (the event is closed for an hour lunch break beginning at 12:00 p.m.). Schedule Team D to ensure adequate coverage throughout the day. Team D: 4 people 9 10 11 12 1 2 3 4 5 LQ Next 6 © 2025 SHL and/or its affiliates. All rights reserved.arrow_forwardQ1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSONThinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education