DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 1E:
List all the steps used by Algorithm 1 to find the maximum of the list 1, 8, 12, 9, 11, 2, 14, 5,...Problem 2E:
Determine which characteristics of an algorithm described in the text (after Algorithm 1) the...Problem 4E:
Describe an algorithm that takes as input a list of n integers and produces as output the largest...Problem 5E:
Describe an algorithm that takes as input a list ofnintegers in nondecreasing order and produces the...Problem 6E:
Describe an algorithm that takes as input a list ofnintegers and finds the number of negative...Problem 7E:
Describe an algorithm that takes as input a list ofnintegers and finds the location of the last even...Problem 8E:
Describe an algorithm that takes as input a list ofndistinct integers and finds the location of the...Problem 9E:
Apalindromeis a string that reads the same forward and backward. Describe an algorithm for...Problem 10E:
Devise an algorithm to computexn, wherexis a real number andnis an integer. [Hint: First give a...Problem 11E:
Describe an algorithm that interchanges the values of the variablesxandy, using only assignments....Problem 12E:
cribe an algorithm that uses only assignment statements that replaces the triple(x,y,z)with(y,z,x)....Problem 13E:
List all the steps used to search for 9 in the sequence 1, 3, 4, 5, 6, 8, 9, 11 using a linear...Problem 14E:
List all the steps used to search for 7 in the sequence given in Exercise 13 for both a linear...Problem 15E:
cribe an algorithm that inserts an integerxin the appropriate position into the lista1,a2,...,an of...Problem 16E:
Describe an algorithm for finding the smallest integer in a finite sequence of natural numbers.Problem 17E:
Describe an algorithm that locates the first occurrence of the largest element in a finite list of...Problem 18E:
Describe an algorithm that locates the last occurrence of the smallest element in a finite list of...Problem 19E:
Describe an algorithm that produces the maximum, median, mean, and minimum of a set of three...Problem 20E:
Describe an algorithm for finding both the largest and the smallest integers in a finite sequence of...Problem 21E:
Describe an algorithm that puts the first three terms of a sequence of integers of arbitrary length...Problem 24E:
Describe an algorithm that determines whether a function from a finite set to another finite set is...Problem 25E:
Describe an algorithm that will count the number of is in a bit string by examining each bit of the...Problem 26E:
nge Algorithm 3 so that the binary search procedure comparesxtoamat each stage of the algorithm,...Problem 27E:
Theternary search algorithmlocates an element in a list of increasing integers by successively...Problem 28E:
Specify the steps of an algorithm that locates an element in a list of increasing integers by...Problem 29E:
Devise an algorithm that finds a mode in a list of nondecreasing integers. (Recall that a list of...Problem 30E:
Devise an algorithm that finds all modes. (Recall that a list of integers is nondecreasing if each...Problem 31E:
Two strings areanagramsif each can be formed from the other string by rearranging its characters....Problem 32E:
ennreal numbersx1,x2,...,xn , find the two that are closest together by a brute force algorithm that...Problem 33E:
Devise an algorithm that finds the first term of a sequence of integers that equals some previous...Problem 39E:
Adapt the bubble sort algorithm so that it stops when no interchanges are required. Express this...Problem 40E:
Use the insertion sort to sort the list in Exercise 36, showing the lists obtained at each step. Use...Problem 41E:
Use the insertion sort to sort the list in Exercise 37, showing the lists obtained at each step. Use...Problem 42E:
Use the insertion sort to sort the list in Exercise 38, showing the lists obtained at each step. Use...Problem 44E:
Write the selection sort algorithm in pseudocode.Problem 45E:
Describe an algorithm based on the linear search for determining the correct position in which to...Problem 46E:
Describe an algorithm based on the binary search for determining the correct position in which to...Problem 48E:
How many comparisons does the insertion sort use to sort the listn,n 1, ..., 2, 1? Thebinary...Problem 49E:
Show all the steps used by the binary insertion sort to sort the list 3, 2, 4. 5, 1, 6.Problem 50E:
Compare the number of comparisons used by the insertion sort and the binary insertion sort to sort...Problem 52E:
Devise a variation of the insertion sort that uses a linear search technique that inserts...Problem 54E:
List all the steps the naive string matcher uses to find all occurrences of the pattern FE in the...Problem 55E:
List all the steps the naive string matcher uses to find all occurrences of the pattern ACG in the...Problem 56E:
Use the cashier’s algorithm to make change using quarters, Dimes, nickels, and pennies for 87 cents....Problem 57E:
Use the cashier’s algorithm to make change using quarters, dimes, nickels, and pennies for 51 cents....Problem 58E:
Use the cashier’s algorithm to make change using quarters, dimes, and pennies (but no nickels) for...Problem 60E:
Show that if there were a coin worth 12 cents, the cashier’s algorithm using quarters, 12-cent...Problem 63E:
Devise a greedy algorithm that determines the fewest lecture halls needed to accommodatentalks given...Problem 64E:
Suppose we have three menm1,m2, andm3and three womenw1,w2, andw3. Furthermore, suppose that the...Problem 69E:
Prove that the Boyer-Moore majority vote algorithm outputs the majority element of a sequence, if it...Browse All Chapters of This Textbook
Chapter 1 - The Foundations: Logic And ProofsChapter 1.1 - Propositional LogicChapter 1.2 - Applications Of Propositional LogicChapter 1.3 - Propositional EquivalencesChapter 1.4 - Predicates And QuantifiersChapter 1.5 - Nested QuantifiersChapter 1.6 - Rules Of InferenceChapter 1.7 - Indroduction To ProofsChapter 1.8 - Proof Methods And StrategyChapter 2 - Basic Structures: Sets, Functions, Sequences, Sums, And Matrices
Chapter 2.1 - SetsChapter 2.2 - Set OperationsChapter 2.3 - FunctionsChapter 2.4 - Sequences And SummationsChapter 2.5 - Cardinality Of SetsChapter 2.6 - MatricesChapter 3 - AlgorithmsChapter 3.1 - AlgorithmsChapter 3.2 - The Growth Of FunctionsChapter 3.3 - Complexity Of AlgorithmsChapter 4 - Number Theory And CryptographyChapter 4.1 - Divisibility And Modular ArithmeticChapter 4.2 - Integer Representations And AlgorithmsChapter 4.3 - Primes And Greatest Commom DivisiorsChapter 4.4 - Solving CongruencesChapter 4.5 - Applications Of CongruencesChapter 4.6 - CryptographyChapter 5 - Induction And RecursionChapter 5.1 - Mathematical InductionChapter 5.2 - Strong Induction And Well-orderingChapter 5.3 - Recursive Definitions And Structural InductionChapter 5.4 - Recursive AlgorithmsChapter 5.5 - Program CorrectnessChapter 6 - CountingChapter 6.1 - The Basics Of CountingChapter 6.2 - The Pigeonhole PrincipleChapter 6.3 - Permutations And CombinationsChapter 6.4 - Binomial Coefficients And IdentitiesChapter 6.5 - Generalized Permutations And CombinationsChapter 6.6 - Generating Permutations And CombinationsChapter 7 - Discrete ProbabilityChapter 7.1 - An Introduction To Discrete ProbabilityChapter 7.2 - Probability TheoryChapter 7.3 - Bayes' TheoremChapter 7.4 - Expected Value And VarianceChapter 8 - Advanced Counting TechniquesChapter 8.1 - Applications Of Recurrence RelationsChapter 8.2 - Solving Linear Recurrence RelationsChapter 8.3 - Divide-and-conquer Algorithms And Recurrence RelationsChapter 8.4 - Generating FunctionsChapter 8.5 - Inclusion-exclusionChapter 8.6 - Applications Of Inclusion-exclusionChapter 9 - RelationsChapter 9.1 - Relations And Their PropertiesChapter 9.2 - N-ary Relations And Their ApplicationsChapter 9.3 - Representing RelationsChapter 9.4 - Closures Of RelationsChapter 9.5 - Equivalence RelationsChapter 9.6 - Partial OrderingsChapter 10 - GraphsChapter 10.1 - Graphs And Graph ModelsChapter 10.2 - Graph Terminology And Special Types Of GraphsChapter 10.3 - Representing Graphs And Graph IsomorphismChapter 10.4 - ConnectivityChapter 10.5 - Euler And Hamilton PathsChapter 10.6 - Shortest-path ProblemsChapter 10.7 - Planar GraphsChapter 10.8 - Graph ColoringChapter 11 - TreesChapter 11.1 - Introduction To TreesChapter 11.2 - Applications Of TreesChapter 11.3 - Tree TraversalChapter 11.4 - Spanning TreesChapter 11.5 - Minimum Spanning TreesChapter 12 - Boolean AlgebraChapter 12.1 - Boolean FunctionsChapter 12.2 - Representing Boolean FunctionsChapter 12.3 - Logic GatesChapter 12.4 - Minimization Of CircuitsChapter 13 - Modeling ComputationChapter 13.1 - Languages And GrammarsChapter 13.2 - Finite-state Machines With OutputChapter 13.3 - Finite-state Machines With No OutputChapter 13.4 - Language RecognitionChapter 13.5 - Turing MachinesChapter A - Appendices
Sample Solutions for this Textbook
We offer sample solutions for DISCRETE MATH homework problems. See examples below:
Chapter 1, Problem 1RQA set P is a subset of Q if each element of P is also the element of Q. We have to show that P is a...Chapter 3, Problem 1RQChapter 4, Problem 1RQChapter 5, Problem 1RQChapter 6, Problem 1RQChapter 7, Problem 1RQChapter 8, Problem 1RQIn mathematics, a binary relation on a set A is a set of ordered pairs of elements of A defined as...
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