Data Structures, Algorithms, and Applications in C++, 2nd Ed. by. Sartaj Sahni. Exercise Solutions. View Solutions. Sartaj Sahni Books Online Store in India. Free Shipping, Cash on delivery at India’s favourite Online Shop – aad ada algorithms computer algorithms daa DOWNLOAD edition Ellis Horowitz FREE PDF Sanguthevar Rajasekaran Sartaj Sahni.

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We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Published by Griffin Asher Pitts Modified over 3 years ago. Algorithms Mashiour Rahman mashiour aiub. Helpful link for Problem Solving: The main things we will learn in this course: To think algorithmically and get the spirit of how algorithms are designed.

To get to know a toolbox of classical algorithms. To learn a number of algorithm design techniques such as divide-and-conquer. To reason in a precise and formal way about the efficiency and the correctness of algorithms. Algorithms are first solved on paper and later keyed in on the computer.

The most important thing is to be simple and precise. Interaction is welcome; ask questions. Additional explanations and examples if desired.

Persian mathematician Mohammed al- Khowarizmi, in Latin became Ny. Euclidean Algorithm, greatest common divisor, B. Organization of data to solve the problem at hand. Algorithm Algorithm Outline, the essence of a computational procedure, step-by-step instructions.

Outline, the essence of a computational procedure, step-by-step instructions. Program Program Implementation of yb algorithm in some programming language. Implementation of an algorithm in some programming language.

Using a computer to help solve problems. Precisely specify the problem. This course is not about: Programming languages Programming languages Computer architecture Computer architecture Software architecture Software architecture Software design and implementation principles Software design and implementation principles Issues concerning small and large scale programming. Issues concerning small and large scale programming.

We will only touch upon the theory of complexity and computability. Infinite number of input instances satisfying the specification. A sorted, non-decreasing sequence of natural numbers. The sequence is of non-zero, finite length: Specification of output as a function of input. Algorithm describes actions on the input instance. There may be many correct algorithms for the same algorithmic problem. Input instance, adhering to the specification Algorithm Output related to the input as required.

An algorithm is a sequence of unambiguous instructions for solving a problem, i. Precisely specify the input and output. Precisely define the problem.

Come up with a simple plan to solve the problem at hand. The plan is language independent. The precise problem specification influences the plan.

## Horowitz and Sahani, Fundamentals of Computer Algorithms, 2ND Edition

Turn the plan into an implementation Turn the plan into an implementation The problem representation data structure influences the implementation. The problem representation data structure influences the implementation. It is important to specify the preconditions and the postconditions of algorithms: The handling of special cases of the input should be described.

Running time Running time Space used Space used Efficiency as a function of the input size: Efficiency as a function of the input size: Number of data elements numbers, points. The number of bits of an input number. It is important to choose the level of detail. Instructions each taking constant timewe usually choose one type of instruction as a characteristic operation that is counted: Arithmetic add, subtract, multiply, etc. Data movement assign Data movement assign Control flow branch, subroutine call, return Control flow branch, subroutine call, return Comparison Comparison Data types — integers, characters, and floats Data types — integers, characters, and floats.

Time to compute the running time as a function of the input size exact analysis. The running time of an algorithm is the sum of the running times of each state-ment.

Often the performance depends on the details of the input not only the length n. This is modeled by t j. In the case of insertion sort the time t j depends on the original sorting of the input array. Often it is sufficient to count the number of iterations of the core innermost part.

No distinction between comparisons, assignments, etc that means roughly the same cost for all of them.

### Notes-4th Semester-ADA | Gec Haveri

Gives precise enough results. In some cases the cost of selected operations dominates all other costs. For inputs of all sizes: Worst case is usually used: It is an upper-bound. In certain application domains e. For some algorithms worst case occurs fairly often- For some algorithms worst case occurs fairly often- The average case is often as bad as the worst case.

The average case is often as bad as the worst case. Finding the average case can be very difficult. Have a left and right bound. Elements to the right of r are bigger than the search element.

In each step reduce the range of the search space by half. How many times the loop is executed? With each execution the difference between l and r is cut in half. Initially the difference is n. The loop stops when the difference sarhaj 0 less than 1. How many times do you have to cut n in half to get 0? Asymptotically more efficient algorithms are best for all but small inputs Asymptotically more efficient algorithms are best for all but small inputs.

Used to describe best-case running times or lower bounds of algorithmic problems. Drop lower order terms and constant factors. Although 50 n log n is O n 5it is expected that an approximation is of the xartaj possible order.

The running time of insertion sort is determined by a nested loop.

Nested loops correspond to summations: Example Example Basis Basis. An algorithm is correct if for any legal input it terminates and produces the desired output. Automatic proof of correctness is not possible. There are practical techniques and rigorous formalisms that help to reason about the correctness of parts of algorithms.

To prove partial correctness we associate a number of assertions statements about the state of the execution with specific checkpoints in the algorithm. Preconditions — assertions that must be valid before the execution of an algorithm or a subroutine INPUT.

Write a pseudocode algorithm to find the two smallest numbers in a sequence of numbers given as an array. We must show three things about loop invariants: A[i] q Ib l: How do you compute 10!? Termination condition determines when and how to stop the recursion. One or more recursive calls. Example for fac 5. The return statement in the if clause terminates the function and, thus, the entire recursion.

The termination condition is never reached. Numbers in the series: