DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
8th Edition
ISBN: 9781260521337
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 3.3, Problem 40E
- Show that the greedy algorithm for making change forncents using quarters, dimes, nickels, and pennies hasO(n) complexity measured in terms of comparisons needed.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Use the greedy algorithm to make change using quarters, dimes, nickels, and pennies for 5100 rupees
What is the maximum number of unique license plate numbers which can be made by combining
any three capital letters from the 26 letters in English alphabet, followed by any three numbers
from 0-9? Suppose that repeating of letters and numbers is NOT allowed. One example of such a
plate number is ABC123.
Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the corresponding numbers is equal to (2n+1)/3.
Chapter 3 Solutions
DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
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
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is less than 7 AND the second digit is greater than or equal to 2.arrow_forwardUse the greedy algorithm to make change using Quarters, Dimes, and Pennies (but no Nickels) for 43 cents.arrow_forwardNeed help with this problem. It states: Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0. My current solution: I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!! Also how should I set up my characteristic polynomial? (S(k))? I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!arrow_forward
- There are six job which must go through two machine A and B in the order A-B. Processing time (in hours) is given here: Job Machine a 10 11 12 16 20 A Machine 7 15 10 14 13 Determine the optimum sequence and the total elapsed time?arrow_forwardDiscuss the important characteristic that a counting problem has to have in order to classify it as a permutation problem.arrow_forwardCan you find the second subpart to this wuearrow_forward
- show full and complete procedure. this problem is about sequencesarrow_forwardShow that if 5000 boys registered for driving license during the last month(31 days) at driving school, then at least 167 of them were registered on the same day of the montharrow_forwardSuppose a company needs temporary passwords for the trial of a new time management software. Each password will have two letters followed by two digits. The digits 7, 8,9 will not be used. So, there are 26 letters and 7 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format?arrow_forward
- 4. [Ocean Weather] Information about ocean weather can be extracted from radar returns with the aid of a special algorithm. A study is conducted to estimate the difference in wind speed as measured on the ground and via the Seasat satellite. To do so, wind speeds (miles per hour) are measured on the ground and via the Seasat satellite simultaneously at 12 special times. The data is shown in the following table. The table also shows the difference between the wind speed on the ground and that via the Seasat satellite at each time, as well as some summary statistics. Difference Time Ground (x) Satellite (y) d= x – y 1 4.46 4.08 0.38 3.99 3.94 0.05 3 3.73 5.00 -1.27 4 3.29 5.20 -1.91 4.82 3.92 0.90 6 6.71 6.21 0.50 7 4.61 5.95 -1.34 8. 3.87 3.07 0.80 3.17 4.76 -1.59 10 4.42 3.25 1.17 11 3.76 4.89 -1.13 12 3.30 4.80 -1.50 d = -0.41 Sd = 1.14 It is claimed that the wind speed measured on the ground is lower than that measured via the Satellite on average. Set up your hypotheses to test this…arrow_forwardThere are 8 numbers in a sequence that add up to 250 (ex. 1,2,3,4,5,6,7,8). The average of these 8 numbers is = 31.25. My question is, is there a way to calculate the values of all 8 numbers, being that #1 will be the lowest number of the sequence, and #8 being the highest number in the sequence. Is there any other variable required to calculate this?arrow_forwardIf the sum of the co-efficients in the expansion of (a + b)" is 1024, then the greatest co-efficient in the expansion is (a) 252 (b) 352 (c) 452 (d) 552arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended 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...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY