# DATA STRUCTURE BY SARTAJ SAHNI EBOOK

by By Sahni, Sartaj · data Rachel_Carson,_Al_Gore, _Lois_and_Louis_darling_S(zlibraryexau2g3p_onion).pdf Data Structures and Algorithm Analysis in C. Data Structures, Algorithms, and Applications in C++ Sartaj Sahni is a Distinguished Professor and Chair of Computer and Information Sciences and. Dr. Sahni provides several applications for each data structure and algorithm design method disussed, taking examples from topics such as Sartaj Sahni.

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This is an introductory text on data structures and algorithms which emphasises algorithm analysis and the development of efficient code. Important background. Universities Press. COMPUTER SCIENCE. Data Structures,. Algorithms and. Applications IN. • C++. 8 B. Second Edition. SARTAJ SAHNI copyrighted. bestthing.info: Data Structures, Algorithms, And Applications In C++ ( ): Sartaj Sahni: Books.

Different situations call for different decisions, but we suggest you eliminate the idea of working on both at the same time. If you do decide to scrap your work and begin again, you can take comfort in the fact that it will probably be easier the second time. In fact you may save as much debugging time later on by doing a new version now.

## Search Here

This is a phenomenon which has been observed in practice. The graph in figure 1. For each compiler there is the time they estimated it would take them and the time it actually took.

For each subsequent compiler their estimates became closer to the truth, but in every case they underestimated. Unwarrented optimism is a familiar disease in computing.

But prior experience is definitely helpful and the time to build the third compiler was less than one fifth that for the first one. Verification consists of three distinct aspects: program proving, testing and debugging. Each of these is an art in itself. Before executing your program you should attempt to prove it is correct.

Proofs about programs are really no different from any other kinds of proofs, only the subject matter is different. If a correct proof can be obtained, then one is assured that for all possible combinations of inputs, the program and its specification agree. Testing is the art of creating sample data upon which to run your program. If the program fails to respond correctly then debugging is needed to determine what went wrong and how to correct it. One proof tells us more than any finite amount of testing, but proofs can be hard to obtain.

Many times during the proving process errors are discovered in the code. The proof can't be completed until these are changed. This is another use of program proving, namely as a methodology for discovering errors. Finally there may be tools available at your computing center to aid in the testing process.

One such tool instruments your source code and then tells you for every data set: i the number of times a statement was executed, ii the number of times a branch was taken, iii the smallest and largest values of all variables. As a minimal requirement, the test data you construct should force every statement to execute and every condition to assume the value true and false at least once.

One thing you have forgotten to do is to document. But why bother to document until the program is entirely finished and correct? Because for each procedure you made some assumptions about its input and output.

If you have written more than a few procedures, then you have already begun to forget what those assumptions were. If you note them down with the code, the problem of getting the procedures to work together will be easier to solve.

The larger the software, the more crucial is the need for documentation. The previous discussion applies to the construction of a single procedure as well as to the writing of a large software system.

Let us concentrate for a while on the question of developing a single procedure which solves a specific task. The design process consists essentially of taking a proposed solution and successively refining it until an executable program is achieved. The initial solution may be expressed in English or some form of mathematical notation.

At this level the formulation is said to be abstract because it contains no details regarding how the objects will be represented and manipulated in a computer.

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If possible the designer attempts to partition the solution into logical subtasks. Each subtask is similarly decomposed until all tasks are expressed within a programming language. This method of design is called the top-down approach. Inversely, the designer might choose to solve different parts of the problem directly in his programming language and then combine these pieces into a complete program. This is referred to as the bottom-up approach. Experience suggests that the top-down approach should be followed when creating a program.

However, in practice it is not necessary to unswervingly follow the method. A look ahead to problems which may arise later is often useful. Underlying all of these strategies is the assumption that a language exists for adequately describing the processing of data at several abstract levels. Let us examine two examples of top-down program development.

Suppose we devise a program for sorting a set of n given by the following 1 distinct integers. One of the simplest solutions is "from those integers which remain unsorted, find the smallest and place it next in the sorted list" This statement is sufficient to construct a sorting program. However, several issues are not fully specified such as where and how the integers are initially stored and where the result is to be placed.

One solution is to store the values in an array in such a way that the i-th integer is stored in the i-th array position, A i 1 i n. We are now ready to give a second refinement of the solution: for i 1 to n do examine A i to A n and suppose the smallest integer is at A j ; then interchange A i and A j.

There now remain two clearly defined subtasks: i to find the minimum integer and ii to interchange it with A i. Eventually A n is compared to the current minimum and we are done. Also, observe that when i becomes greater than q, A Hence, following the last execution of these lines, i. We observe at this point that the upper limit of the for-loop in line 1 can be changed to n - 1 without damaging the correctness of the algorithm. From the standpoint of readability we can ask if this program is good.

Is there a more concise way of describing this algorithm which will still be as easy to comprehend? Substituting while statements for the for loops doesn't significantly change anything.

Also, extra initialization and increment statements would be required. Let us develop another program. We assume that we have n 1 distinct integers which are already sorted and stored in the array A 1:n. By making use of the fact that the set is sorted we conceive of the following efficient method: "let A mid be the middle element.

There are three possibilities. Continue in this way by keeping two pointers, lower and upper, to indicate the range of elements not yet tested. This method is referred to as binary search.

Note how at each stage the number of elements in the remaining set is decreased by about one half. For instance we could replace the while loop by a repeat-until statement with the same English condition. In fact there are at least six different binary search programs that can be produced which are all correct.

There are many more that we might produce which would be incorrect. Part of the freedom comes from the initialization step. Whichever version we choose, we must be sure we understand the relationships between the variables. Below is one complete version. This, combined with the above assertion implies that x is not present.

Unfortunately a complete proof takes us beyond our scope but for those who wish to pursue program proving they should consult our references at the end of this chapter. Recursion We have tried to emphasize the need to structure a program to make it easier to achieve the goals of readability and correctness.

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Actually one of the most useful syntactical features for accomplishing this is the procedure. Given a set of instructions which perform a logical operation, perhaps a very complex and long operation, they can be grouped together as a procedure. Given the input-output specifications of a procedure, we don't even have to know how the task is accomplished, only that it is available. This view of the procedure implies that it is invoked, executed and returns control to the appropriate place in the calling procedure.

What this fails to stress is the fact that procedures may call themselves direct recursion before they are done or they may call other procedures which again invoke the calling procedure indirect recursion.

These recursive mechanisms are extremely powerful, but even more importantly, many times they can express an otherwise complex process very clearly. For these reasons we introduce recursion here. Most students of computer science view recursion as a somewhat mystical technique which only is useful for some very special class of problems such as computing factorials or Ackermann's function.

This is unfortunate because any program that can be written using assignment, the if-then-else statement and the while statement can also be written using assignment, if-then-else and recursion. Of course, this does not say that the resulting program will necessarily be easier to understand. One of the simplest solutions is "from those integers which remain unsorted, find the smallest and place it next in the sorted list" This statement is sufficient to construct a sorting program.

However, several issues are not fully specified such as where and how the integers are initially stored and where the result is to be placed. One solution is to store the values in an array in such a way that the i-th integer is stored in the i-th array position, A i 1 i n.

We are now ready to give a second refinement of the solution: for i 1 to n do examine A i to A n and suppose the smallest integer is at A j ; then interchange A i and A j. There now remain two clearly defined subtasks: i to find the minimum integer and ii to interchange it with A i. Eventually A n is compared to the current minimum and we are done.

Also, observe that when i becomes greater than q, A Hence, following the last execution of these lines, i. We observe at this point that the upper limit of the for-loop in line 1 can be changed to n - 1 without damaging the correctness of the algorithm. From the standpoint of readability we can ask if this program is good.

Is there a more concise way of describing this algorithm which will still be as easy to comprehend? Substituting while statements for the for loops doesn't significantly change anything. Also, extra initialization and increment statements would be required.

Let us develop another program. We assume that we have n 1 distinct integers which are already sorted and stored in the array A 1:n. By making use of the fact that the set is sorted we conceive of the following efficient method: "let A mid be the middle element.

There are three possibilities. Continue in this way by keeping two pointers, lower and upper, to indicate the range of elements not yet tested. This method is referred to as binary search. Note how at each stage the number of elements in the remaining set is decreased by about one half.

For instance we could replace the while loop by a repeat-until statement with the same English condition. In fact there are at least six different binary search programs that can be produced which are all correct. There are many more that we might produce which would be incorrect. Part of the freedom comes from the initialization step. Whichever version we choose, we must be sure we understand the relationships between the variables.

Below is one complete version. This, combined with the above assertion implies that x is not present. Unfortunately a complete proof takes us beyond our scope but for those who wish to pursue program proving they should consult our references at the end of this chapter.

Recursion We have tried to emphasize the need to structure a program to make it easier to achieve the goals of readability and correctness. Actually one of the most useful syntactical features for accomplishing this is the procedure.

Given a set of instructions which perform a logical operation, perhaps a very complex and long operation, they can be grouped together as a procedure. Given the input-output specifications of a procedure, we don't even have to know how the task is accomplished, only that it is available. This view of the procedure implies that it is invoked, executed and returns control to the appropriate place in the calling procedure.

## Fundamentals of Data Structures - Ellis Horowitz, Sartaj Sahni.pdf

What this fails to stress is the fact that procedures may call themselves direct recursion before they are done or they may call other procedures which again invoke the calling procedure indirect recursion. These recursive mechanisms are extremely powerful, but even more importantly, many times they can express an otherwise complex process very clearly.

For these reasons we introduce recursion here.

Most students of computer science view recursion as a somewhat mystical technique which only is useful for some very special class of problems such as computing factorials or Ackermann's function.

This is unfortunate because any program that can be written using assignment, the if-then-else statement and the while statement can also be written using assignment, if-then-else and recursion. Of course, this does not say that the resulting program will necessarily be easier to understand.

However, there are many instances when this will be the case. When is recursion an appropriate mechanism for algorithm exposition? One instance is when the problem itself is recursively defined. Given a set of n 1 elements the problem is to print all possible permutations of this set. It is easy to see that given n elements there are n! A simple algorithm can be achieved by looking at the case of four elements a,b,c,d. The answer is obtained by printing i a followed by all permutations of b,c,d ii b followed by all permutations of a,c,d iii c followed by all permutations of b,a,d iv d followed by all permutations of b,c,a The expression "followed by all permutations" is the clue to recursion.

It implies that we can solve the problem for a set with n elements if we had an algorithm which worked on n - 1 elements. A is a character string e.

## Guy blelloch dblp

Then try to do one or more of the exercises at the end of this chapter which ask for recursive procedures. We will see several important examples of such structures, especially lists in section 4.

Another instance when recursion is invaluable is when we want to describe a backtracking procedure. But for now we will content ourselves with examining some simple, iterative programs and show how to eliminate the iteration statements and replace them by recursion. This may sound strange, but the objective is not to show that the result is simpler to understand nor more efficient to execute.

The main purpose is to make one more familiar with the execution of a recursive procedure. Suppose we start with the sorting algorithm presented in this section.

To rewrite it recursively the first thing we do is to remove the for loops and express the algorithm using assignment, if-then-else and the go-to statement. Every place where a ''go to label'' appears, we replace that statement by a call of the procedure associated with that label. This gives us the following set of three procedures. Procedure MAXL2 is also directly reculsive.

These two procedures use eleven lines while the original iterative version was expressed in nine lines; not much of a difference. Notice how in MAXL2 the fourth parameter k is being changed. The effect of increasing k by one and restarting the procedure has essentially the same effect as the for loop.

Now let us trace the action of these procedures as they sort a set of five integers When a procedure is invoked an implicit branch to its beginning is made. The parameter mechanism of the procedure is a form of assignment. In section 4. Also in that section are several recursive procedures, followed in some cases by their iterative equivalents. Rules are also given there for eliminating recursion. There are many criteria upon which we can judge a program, for instance: i Does it do what we want it to do?

The above criteria are all vitally important when it comes to writing software, most especially for large systems. Though we will not be discussing how to reach these goals, we will try to achieve them throughout this book with the programs we write.

Hopefully this more subtle approach will gradually infect your own program writing habits so that you will automatically strive to achieve these goals. There are other criteria for judging programs which have a more direct relationship to performance. These have to do with computing time and storage requirements of the algorithms. Performance evaluation can be loosely divided into 2 major phases: a a priori estimates and b a posteriori testing.

Both of these are equally important. First consider a priori estimation. We would like to determine two numbers for this statement. The first is the amount of time a single execution will take; the second is the number of times it is executed.

## Ebook – (DS) Fundamentals Of Data Structures – Ellis Horowitz & Sartaj Sahni

The product of these numbers will be the total time taken by this statement. One of the hardest tasks in estimating frequency counts is to choose adequate samples of data. It is impossible to determine exactly how much time it takes to execute any command unless we have the following information: i the machine we are executing on: ii its machine language instruction set; iii the time required by each machine instruction; iv the translation a compiler will make from the source to the machine language.

It is possible to determine these figures by choosing a real machine and an existing compiler. Another approach would be to define a hypothetical machine with imaginary execution times , but make the times reasonably close to those of existing hardware so that resulting figures would be representative. Neither of these alternatives seems attractive. Chat to ask more. Paper II. This app provides an easy to use interface to download and use notes from VTU professors.

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VTUsouls is a platform created for students, from students where you can get all the updates regarding VTU and all study materials of ccn notes vtu semesters and streams.But prior experience is definitely helpful and the time to build the third compiler was less than one fifth that for the first one.

Data Structures for Sets Rajeev Raman This happens to industrial programmers as well. Also in that section are several recursive procedures, followed in some cases by their iterative equivalents. Chat to ask more. He written notes for many subjects in Electronics of 3rd, 4th, 5th, 6th, 7th, 8th, Semester. All books are in clear copy here, and all files are secure so don't worry about it. However, we assume that this statement is used in conjunction with some test within S which will cause an exit.

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