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Introduction to Data Structures 1 Course Name : Data Structure (CSI 221) Course Teacher : Md. Zakir Hossain Lecturer, Dept. of Computer Science Stamford University Bangladesh Class Schedule : Tuesday Thursday : 11:45 am - 1:00 pm : 1:00 pm – 2.15 pm Marks Distribution : Attendance - 10% Assignment – (5%+5%) Class Test - (10% +10%) Midterm - 30% Final - 30% --------------------------------Total 2 - 100% Course Outline 1. Concepts and examples 2. Elementary data objects 3. Elementary data structures 4. Arrays 5. Lists 6. Stacks 7. Queues 8. Graphs 9. Trees 10.Sorting and searching 11.Hash techniques 3 Books 1. “Theory and Problems of Data Structures” by Seymour Lipschutz, McGraw-Hill, ISBN 0-07-038001-5. 4 Elementary Data Organization • Data are simply values or sets of values. • Collection of data are frequently organized into a hierarchy of fields, records and files. • This organization of data may not complex enough to maintain and efficiently process certain collections of data. • For this reason, data are organized into more complex type of structures called Data Structures. Data Structures Data Structures The logical or mathematical model of a particular organization of data is called a data structure. Types of Data Structure 1. Linear Data Structure Example: Arrays, Linked Lists, Stacks, Queues 2. Nonlinear Data Structure Example: Trees, Graphs Array A B C A D E F Tree B D Figure: Linear and nonlinear structures 6 C E F Choice of Data Structures The choice of data structures depends on two considerations: 1. It must be rich enough in structure to mirror the actual relationships of data in the real world. 2. The structure should be simple enough that one can effectively process data when necessary. 10 20 30 40 50 60 70 80 Figure 2: Array with 8 items 7 10 20 40 30 50 60 70 Figure 3: Tree with 8 nodes Data Structure Operations 1. Traversing: Accessing each record exactly once so that certain items in the record may be processed. 2. Searching: Finding the location of the record with a given key value. 3. Inserting: Adding a new record to the structure. 4. Deleting: Removing a record from the structure. 5. Sorting: Arranging the records in some logical order. 6. Merging: Combing the records in two different sorted files into a single sorted file. 8 Algorithms It is a well-defined set of instructions used to solve a particular problem. Example: Write an algorithm for finding the location of the largest element of an array Data. Largest-Item (Data, N, Loc) 1. set k:=1, Loc:=1 and Max:=Data[1] 2. while k<=N repeat steps 3, 4 3. If Max < Data[k] then Set Loc:=k and Max:=Data[k] 4. Set k:=k+1 5. write: Max and Loc 6. 9 exit Complexity of Algorithms • The complexity of an algorithm M is the function f(n) which gives the running time and/or storage space requirement of the algorithm in terms of the size n of the input data. • Two types of complexity 1. Time Complexity 2. Space Complexity 10 O-notation - A function f(n)=O(g(n)) if there are positive constants c and n0 such that f(n)<=c.g(n) for all n>= n0. - When f(n)=O(g(n)), it is guaranteed that f(n) grows at a rate no faster than g(n). So g(n) is an upper bound on f(n). Example: (a) f(n) = 3n+2 Here f(n) <= 5n for n>=1 So, f(n) = O(n). (b) f(n) = 3n2-2 Here f(n) < 3n2 for n>=1 So, f(n) = O(n2). 11 Some rules related to asymptotic notation Rule-1 If fa(n) = O(ga(n)) and fb(n) = O((gb(n)) then (a) fa(n)+fb(n) = max(O(ga(n)),O(gb(n)) (b) fa(n) * fb(n) = O(ga(n) * gb(n)) Rule-2 If f(n) is a polynomial of degree k, then f(n) = Θ(nk). Rule-3 Logkn = O(n) for any constant. 12 Typical Growth Rates Function Name c Constant logn Logarithmic log2n Log-squared n Linear nlogn n2 Quadratic n3 Cubic 2n Exponential 13