(第1版)数据结构实验指导

3 Projects3.1 Project 1: Performance MeasurementGiven a list of ordered N integers, numbered from 0 to N– 1, checking to see that N is not in this list provides a worst case for many search algorithms.Consider two algorithms: one is called “sequential search”which scans through the list from left to right; and the other is “binary search” which is given on page 24(Figure 2.9) of your textbook. Your tasks are:(1)Implement an iterative version and a recursive version of sequential search;(2)Implement an iterative version of binary search;(3)Analyze the worst case complexities of the above two versions of sequential searchand that of binary search;(4)Measure and compare the worst case performances of the above three functions forN= 100,500,1000,2000,4000,6000,8000,10000.To measure the performance of a function, we may use C‟s standard library time.h as the following:Note: If a function runs so quickly that it takes less than a tick to finish, we may repeat the function calls for K times to obtain a total run time(“Total Time”), and then divide the total time by K to obtain a more accurate duration(“Duration”) for a single fun of the function. The repetition factor must by large enough so that the number of elapsed ticks is at least 10 if we want an accuracy of at least 10%.The test results must be listed in the following table:system for illustration.3.2 Project 2: Implementation of Lists, and PolynomialProblems1. Merge two ordered lists into a new linked list in which the nodes are also in this order. If lengths of original two lists are m and n, the length of new linked list is m + n.For example:Input :5 (length of list 1)4 26 46 56 9511 (length of list 2)15 17 26 30 46 48 56 58 82 90 95Output :4 15 17 26 30 46 48 56 58 82 90 95Demands:(1). You should use single linked list(with a header) to create the functions MakeEmpty , IsEmpty , IsLast , Find , Delete , FindPrevious , Insert , DeleteList , Header , First , Advance , Retrieve (See P40,Figure3.6).(2). Using above functions to solve this problem.(3). The linked implementation of list should be written in separated files (.cpp and .h) in the VC++ workspace.Their names should be linkedlist.h , linkedlist.cpp , merge.cpp .2.The declarations that follow give us the polynomial ADT.Structure Polynomial isObject : 11()n e e n P x a x a x =++ ;a set of ordered pairs of,i i e a <> where i a is the coefficient and i e is the exponent . i e are nonnegative integers.Operations:For all poly,poly1,poly2∈Polynomial ,coef ∈Coefficients , expon ∈ExponentsPolynomial Zero() ::= return the polynomial, P(x)=0Boolean IsZero(poly) ::= if (poly) return FALSE;else return TRUE;Coefficient Coef(poly, expon) ::= if (expon ∈poly) return its coeffientelse return zero.Exponent Lead_Exp(poly) ::= return the largest exponent in poly.Polynomial Attach(poly, coef, expon) ::= if (expon ∈poly) return errorelse return the polynomial poly with the term<coef,expon> inserted.Polynomial Remove(poly, expon) := if (expon ∈poly) return the polynomial poly withthe term whose exponent is expon deletedelse return error.Polynomial SingleMult(poly, coef, expon) := return the polynomial poly*coef*x expon Polynomial Add(poly1,poly2) := return the polynomial poly1 + poly2.Polynomial Mult(poly1,poly2) := return the polynomial poly1 * poly2.end PolynomialDemands :(1). You should choose a suitable representation for Polynomial .(2). You should create the functions Zero , IsZero , Coef , Lead_Exp , Attach , Remove , SingleMult , Add , Mult , and test them.(3). If 205()324A x x x =++ and 432()3231B x x x x =+++, write a function to use above functions to compute ()()()C x A x B x =+ and ()()*()D x A x B x =.(4). Analyze advantages of your representation.(5). The implementation of polynomial ADT should be written in separated files (.cpp and .h) in the VC++ workspace.Their names should be Polynomial.h , Polynomial.cpp , main.cpp .Note:Your program must read from a file “input.txt” and write to a file “output.txt” in thecurrent directory.3.3 Project 3: Implementation and Applications of StacksProblems1. Write a Conversion function to converse any decimal data to binary version.Demands:(1). Implement Stack ADT using linked list representation, which must at least has five basic operations: Create , IsFull, Push , IsEmpty and Pop.(2).Build a new project to implement the Conversion function. The input and output should be according to the following format:Please input the decimal number: 15The corresponding binary version is: 1111Please input the decimal number: -1Bye!2. Write a program to judge whether a bracket sequence (maybe has other letters) is “matching”. The “matching” means that if there has a …(… in a expression and there must has a …)‟ in it .If the input sequence is “matching”, then output …ok‟, otherwise output …ERROR‟.Demands(1). Implement Stack using array representation, which must at least has five basic operations: Create , IsFull, Push , IsEmpty and Pop.(2). Build a new project to implement the bracket Matching function. The input and output should be according to the following format:Please input the expression: a*(b+c)The bracket of the expression is matching OK!Please input the expression: a*(b+c))The bracket of the expression is matching ERROR!Please input the expression: (a*(b+c)The bracket of the expression is matching ERROR!NoteThe two implementation of Stack should be written in separated files (.cpp and .h) in the VC++ workspace. Their files should be named differently, such as linkedStack.h, linkedStack.cpp, SqStack.h, SqStack.cpp.3.4 Project 4: Binary Tree Traversals1.ProblemCreate binary tree as follow (Figure-1) in computer, write out the functions of inorder , preorder , postorder and levelorder, and use them to traversal the binary tree. And compute the leaf number and height of the binary tree.Hint: You may choose suitable representation, such as linked representation is often used.Figure-1 a binary tree2.Steps and restrict conditionsStep 1. Write the function of create to create a tree by input data.Step 2. Write recursive version functions of inorder, preorder and postorder to traversal the tree.Step 3. Select a suitable representation to implement stack ADT, which must at least has five basic operations: Create, IsFull, Push, IsEmpty and Pop. The element type in thestack is pointer of node.Step 4. Implement Queue ADT represented by circular queue, which has seven basic operations: CreateQueue, IsEmpty, DisposeQueue, MakeEmpty, EnQueue, Front,DeQueue. The element type in the queue is pointer of node.Step 5. Write an iterative version of inorder, the name is iter_inorder() to inorder traversal tree. Step 6. Write a function for level order traversal of binary tree, the name is level_order.Step 7. Write a function to compute the leaf number of the binary tree, the name is leaf.Step 8. Write a function to compute the height of the binary tree, the name is height.3.5 Project 5: Jumping the Queue: an ACM ProblemThe beginning of a winter break near Spring Festival is always the beginning of a peak period of transportation. If you have ever tried to get a train ticket at that time, you must have witnessed the endless queues in front of every ticket box window. If a guy has seen his friend in a queue, then it is very much likely that this lucky guy might go straight to his friend and ask for a favor. This is called "jumping the queue". It is unfair to the rest of the people in the line, but, it is life. Your task is to write a program that simulates such a queue with people jumping in every now and then, assume that, if one in the queue has several friends asking for favors, he would arrange their requests in a queue of his own.Input Specification:Your program must read test cases from a file “input.txt”. The input file will contain one or more test cases. Each test case begins with the number of groups n (1<= n <=100). Then n group descriptions follow, each one consisting of the number of friends belonging to the group and those people's distinct names. A group is a friend group. People in one group are friend with each other. A name is a string of up to 4 characters chosen from {A, B, ..., Z, a, b, ..., z}. A group may consist of up to 1000 friends. You may assume that there is no one belong to two different groups.Finally, a list of commands follows. There are three different kinds of commands:●ENQUEUE X - Mr. or Ms. X goes into the queue●DEQUEUE - the first person gets the ticket and leave the queue●STOP - end of test caseThe input will be terminated by a value of 0 for n.Output Specification:Output all results to a file “output.txt”. For each test case,first print a line saying "Scenario #k", where k is the number of the test case. Then, for each DEQUEUE command, print the person who just gets a ticket on a single line. Print a blank line between two test cases, but no extra line at the end of output.Sample Input:23 Ann Bob Joe3 Zoe Jim FatENQUEUE AnnENQUEUE ZoeENQUEUE BobENQUEUE JimENQUEUE JoeENQUEUE FatDEQUEUEDEQUEUEDEQUEUEDEQUEUEDEQUEUEDEQUEUESTOP25 Anny Jack Jean Bill Jane6 Eva Mike Ron Sony Geo Zoro ENQUEUE Anny ENQUEUE EvaENQUEUE JackENQUEUE JeanENQUEUE BillENQUEUE JaneDEQUEUEDEQUEUEENQUEUE Mike ENQUEUE RonDEQUEUEDEQUEUEDEQUEUEDEQUEUESTOPSample Output:Scenario #1AnnBobJoeZoeJimFatScenario #2AnnyJackJeanBillJaneEva3.6 Project6: Performances Measurement of Sorting Algorithms1.Problems(1). Sort the list by InsertionSort, ShellSort, Q uickSort, Merge S ort and HeapSort, respectively. And output every pass result of them.Input: (a list)26 5 37 1 61 11 59 15 48 19Output : the every pass result of them.Notes: you should print the original list, every pass result and the last results.(2). Measure performances of InsertionSort, ShellSort, Q uickSort, Merge S ort and HeapSort for random data.2.Steps and restrict conditions(1).Implement functions of InsertionSort, ShellSort, QuickSort, MergeSort and HeapSort .(2). Output every pass result of input list L={26 5 37 1 61 11 59 15 48 19} by execute these functions.(3). Analyze the worst case complexities of all above algorithms;(4). Measure performances of the above functions for N= 100,500,1000,2000, 4000, 5000, 10000, 20000.You may use random library function to create the testing data firstly. Second, sort it using above algorithms alternately. Finally, measure their performances.To generate a list random data, we may use C‟s standard library stdlib.h as the following:3.7 Project 7: Traversals and Applications of Graph1.ProblemGiven a directed graph (see Figure2), use the adjacency list method to represent it, and output the sequence of vertex names getting from Depth-First Search and Breadth-First Search. And Given a source v0, Determine a shortest path to each v∈V(G) \ { v0 } and output them.2. Input and Output DemandInput: the number of vertex, the number of edge, all edges (V i,V j) and its weight in a graph. Output:(1).print the graph.(2).print the sequence of vertex names getting from Depth-First Search.(3). print the sequence of vertex names getting from Breadth-First Search.For example (See Figure 1):Input:6 11 // indicate the graph including six vertexes and eleven edges.0 1 50 // indicate an edge from V0 to V1.0 2 100 4 451 2 151 4 102 0 202 3 153 1 203 4 354 3 305 3 3Figure 2Output:0：1 2 41：2 42：0 33：1 44：35：3The sequence of vertex names getting from Depth-First Search (from …V1‟):V1 V2 V0 V4 V3 V5The sequence of vertex names getting from Breadth-First Search (from …V1‟):V1 V2 V4 V0 V3 V5Shortest paths from v0 to each vertex areV0 to V1 45V0 to V2 10V0 to V3 25V0 to V4 45V0 to V5 1000(“1000” means no path.)3.Steps and restrict conditions:Step 1. Implement Depth-First Search Algorithm;Step2. Implement Queue ADT represented by circular queue, which has seven basic operations: CreateQueue, IsEmpty, DisposeQueue, MakeEmpty, EnQueue, Front, DeQueue. The element type is pointer of node;Step 3. Implement Breadth-First Search Algorithm;Step 4. Write a function to determine a shortest path from v i to each v∈V(G) \ { v i }.Note:Your program must read from a file “input.txt” and write to a file “output.txt” in the current directory.4 Minimum Requirements on Writing a Project ReportTitle of ProjectClass Group ID Date of Completion mm-dd-yy1.IntroductionProblem description and (if any) background of the alogithms.2.Algorithm SpecificationDescription(pseudo-code preferred) of all the algorithms involved for solving the problem, including specifications of main data structures.3. Testing ResultsTable of test cases. Each test case usually consists of a brief description of the purpose of this case, the expected result, the actual behavior of your program, the possible case of a bug if your program does not function as expected, and the current status ("passing", or "no passing").4. Analysis and CommentsAnalysis of the time and space complexities of the algorithms. Comments of your work and on your further possible improvements. Suggestions of to teachers.Appendix: Source Code(in C)At least 30% of the lines must be commented. Otherwise the code will NOT be evaluated. Duty Assignments: Scores: Programmer:XXX Programmer:_____ Tester:XXX Tester: _____ Report Writer:XXX Report Writer: _____ Please keep in mind that these are the "minimum" requirements. Other requirements will be specified according to each project assignment.5 Assignments and Hand-inGroup of Three - Duty AssignmentsProgrammer: Write and mantain the source code.(50 pts.) Tester: Fill in the contents of 3 and 4.(30 pts.)Report Writer: Write up one complete project report in a uniform style.(20 pts.)Hand-inEach group is supposed to hand in a zipped file named as G##_Project_#.rar orG##_Project_#.zip, where "##" is the two-digit group number which will be given to you after your group is confirmed. , and "#" is the number of project. The zipped file must contain the following:NoteEach assignment is due at 5:00 pm on a specified date.G##_Project_#.zipG##_Report_#.doccodeSource code files(*.cpp,*.h)Executable file(in case your code cannot compiled by Judge)。