2.  FUNDAMENTALS OF ALGORITHMS.  FUNDAMENTALS OF DATA STRUCTURES.  TREES.  GRAPHS AND THEIR APPLICATIONS.  STORAGE MANAGEMENT.

3.  DATA SRUCTURE Data: Raw facts about an objects. Structure: Way of storing, organising and manipulating data.

4.  Logical (or) Mathematical model of a particular organisation of data.  How the data should be organised.  How the flow of data should be controlled.  How a data structure should be designed.

5.  THREE ACTIVITIES:  Storing,  Accessing,  Manipulating, data in one form to another.

6.  Two types of data structures: they are 1) Primitive data structure. int, char, float. 2) Non-Primitive data structure. arrays, structure and files.

7. TOPICS COVERED: 1)Algorithms. 2)Analysis of algorithm. 3) Analysis of algorithms using data structures. 4) Performance Analysis 4.1) Time Complexity. 4.2) Space Complexity. 4.3) Amortized time Complexity. 5) Asymptotic notation.

8.  1.1 Definition:  An algorithm consists of a set of explicit and unambiguous, finite steps when carrying out for a given set of initial condition,produce corresponding output and terminate in a finite time.

9. 1.2) Characteristics:  Each instruction should be unique and concise.  Each instruction should be relative in nature and should not be repeated infinitely.  Repetition of same tasks should be avoided.  The results should be available to the user after the algorithm terminates.

10.  2.1) Steps to be followed:  Analysis is more reliable than experimentation or testing.  Analysis help to select better algorithms.  Analysis predicts performance.  Analysis identifies scope of improvement of algorithms.

11.  3.1) Problem solving.  3.2) Top-down design.

12.  Part of thinking process.  Describes steps to proceed from a given state to a desired goal state.  3.1.1) Problem solving phases.  3.1.2) Problem solving strategies.

13.  An effective program should be developed by one (or) more users to obtain a solution to a problem is known as problem solving.

14. Program design Problem solving phases Problem specification Analysis& data structure Debugging & testing implementat ion Program correctness Maintenance

15.  Divide and Conquer Method.  Dynamic Programming.  Back tracking.  Brute-force algorithm.

16.  DEFINITION: It is a method for designing the layout for anything that starts with the complete item then breaks it down into smaller and smaller subtasks.

17.  Problem Decomposition.  Collecting information required for each task.  Writing function declaration.  Termination of the algorithm.  The result of top-down design is a tree- like structure.

18. Main task Sub task 1 Sub task 2 Sub task 1(a) Sub task 1(b) Sub task 2(a) Sub task 2(b) Sub task 2(c)

19.  Measured by the amount of resources it uses the time and the spaces. ▪ Time – number of steps. ▪ Space – number of units memory storage.

20.  Time complexity is the amount of time needed by a program to complete its task. It can be divided into two 1) Compile time. 2) Run time.

21.  Three types of time complexity. 1) Worst-case. 2) Average-case. 3) Best-case. 1) Worst-case: The function defined by maximum number of steps taken on any problem of size(n).

22. FORMULA: T(n)=O (f(n)) 2)Average-case: The function defined by average number of steps taken on any problem of size(n). FORMULA: T(n)=theta(f(n))

23. 3) Best-case: The function defined by minimum number of steps taken on any problem of size(n). FORMULA: T(n)=omega((fn))

24.  Amount of memory consumed by the algorithm until it completes its execution. character = 1 unit. Integer = 2 units. Float = 4 units. Three spaces.  Instruction space.  Data space.  Environment space.

25.  NOTATION: A method used to estimate the efficiency of an algorithm. 1)Big-oh notation. 2)Big-omega notation. 3)Big-theta notation. 4)Little -oh notation. 5) Little-omega notation.

26.  5.1) Big-oh notation: O-> Order of. Big-> very large values of “n”. Used to define the worst-case running time of an algorithm. Example: f(n)=O(g(n)) f(n) and g(n) -> positive integer.

27.  5.2) Big-Omega Notation: Used to define the best-case running time of an algorithm. Example: f(n)=Omega(g(n)) f(n) and g(n) -> positive integer.

28.  5.3) Big-Theta Notation: It is in between Big-oh and Big- omega notations. Example: f(n)=Theta(g(n)) f(n) and g(n) -> positive integer.

29.  5.4) Little-Oh Notation: O-> Order of. Little-> very small values of “n”. The growth rate of f(n) is lesser than the growth rate of g(n). Example: f(n)=O(g(n)).

30.  5.5) Little-Omega Notation: The growth rate of f(n) is greater than the growth rate of g(n). Example: f(n)=Omega(g(n)).

31.  Many algorithms are hard to analyze mathematically.  Big-Oh analysis only tells you how it grows with the size of the problem not how efficient of the algorithm is.