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Data Structures and Algorithms


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A guide to Data Structures and Algorithms

A guide to Data Structures and Algorithms

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  • Note: by the above definition, a “good” algorithm may still be unusable if it requires too much time/space to solve the problem (i.e. if the algorithm is intractable).
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    • 1. Data Structures and AlgorithmsSnehal
    • 2. 2learn ...... how to design “good” algorithms and datastructures... how to evaluate the performance of algorithms... how to program basic algorithms and datastructuresGoals
    • 3. 3learn ...... how to solve the most common algorithmicproblems, such assearching a data collectionsorting dataexploring a graph/networktext processingGoals
    • 4. 4Michael T. Goodrich, Roberto Tamassia:Algorithm Design: Foundations, Analysis,and Internet Examples.John Wiley & Sons, Inc., 2001.Mark Allen Weiss:Data Structures and Algorithm Analysisin Java.2nd edition, Addision Wesley, 2007.Literature
    • 5. 5Thomas H. Cormen, Charles E. Leiserson,Ronald L. Rivest, Clifford Stein:Introduction to Algorithms.3rd edition, The MIT Press, 2009.Donald E. Knuth:The Art of Computer Programming.Vol. 1: Fundamental Algorithms.Vol. 3: Sorting and Searching.Addision Wesley, 1997/98.Literature
    • 6. 6• an algorithm is a step-by-step procedure forsolving a problem in a finite amount of time andspace• an algorithm is “good” if it is correct and solves theproblem in lowest time/space known for thatproblemAlgorithmsInput Algorithm Output
    • 7. 7• a program is a description of an algorithm in aprogramming language• a program repesents exactly one algorithm• an algorithm represents a multitude of programs• writing a good program requires designing a goodalgorithmNo algorithm, no program!Programs
    • 8. 8Problem – Algorithm - ProgramProblemAlgorithm 1 Algorithm 2Program 21Program 22. . .. . .. . .. . .. . .
    • 9. 9[ 1] int mod(int a, int b) {[ 2] /* Requirements (input): a: a>=0; b: b>0 */[ 3] /* Guarantee (output): r: a=t*b + r and 0<r<=b */[ 4] /* (1) Declaration */[ 5] int r;[ 6] /* (2) Initialization */[ 7] r=a;[ 8] /* (3) Iteration start */[ 9] while (r>=b) {[10] /* (4) Problem reduction */[11] r=r-b;[12] /* (5) Iteration end */[13] }[14] /* (6) Output formation */[15] return(r);[16] }Iteration
    • 10. 10[ 1] int mod(int a, int b) {[ 2] /* Requirements (input): a: a>=0; b: b>0 */[ 3] /* Guarantee (output): r: a=t*b + r and 0<r<=b */[ 4] /* (1) Declaration */[ 5] int r;[ 6] /* (2) Initialization */[ 7] r=a;[ 8] /* (3) Trivial case */[ 9] if (r<b) return(r);[10] /* (4) Problem reduction */[11] r=r-b;[12] /* (5) Recursion step */[13] return(mod(r,b));[14] }Recursion
    • 11. 11• elementary types (in Java):–logical type: boolean–integer type: int, short, byte, long–floating point type: float, double–character type: char• composed data types (concrete data structures):–arrays, e.g., int[], char[]–records/structs (not available in Java)–listsData Types
    • 12. 12• an abstract data type (ADT) is an abstraction of aconcrete data structure• an ADT specifies:–data stored (auxiliary data, inclusive)–operations on the data–error conditions associated with operations• an ADT abstracts from the implementation of thedata and operationsAbstract Data Types
    • 13. 13• a class is an ADT implementation in an OOPL• an instance of an ADT (or a class) has anoperational life span, during which a state (anelement of the ADT„s data set) is always beingassigned to the object• methods of an ADT are programs manipulating thestate of an object• a state of an object can only be manipulated byADT methods (encapsulation)Objects
    • 14. 14• ADT modeling a simple stock trading system• the data stored are buy/sell orders• the operations supported are:–Order buy(Stock st, Shares sh, Price p)–Order sell(Stock st, Shares sh, Price p)–void cancel(Order)• error conditions are:–buy/sell a nonexistent stock–cancel a nonexistent orderExample of an Abstract Data Type