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- 1. Thinking in Data Structures Tushar B Kute http://www.tusharkute.com
- 2. Data Structure ● What is the "Data Structure" ? – – ● Ways to represent data. In a general sense, any data representation is a data structure. Example: An integer more typically, a data structure is meant to be an organization for a collection of data items. Why data structure ? – – Have proven correct algorithms – ● To design and implement large-scale computer system The art of programming How to master in data structure ? – practice, discuss, and think www.tusharkute.com 2
- 3. Need of data structures ● Data structures organize data – ● More powerful computers – ● ● More efficient programs. More complex applications. More complex applications demand more calculations. Complex computing tasks are unlike our everyday experience. www.tusharkute.com 3
- 4. List of data structures ● Static – – Stack – ● Array Queue Dynamic – Linked list – Tree – Graph www.tusharkute.com 4
- 5. Choosing a data structure int p[10], i=0; int *p, i=0; while(1) while(1) { { scanf(“%d”, &p[i]); i++; } scanf(“%d”, &p[i]); i++; } www.tusharkute.com 5
- 6. System life cycle ● Summary – ● Requirements – ● RADRCV What inputs, functions, and outputs. Analysis – Break the problem down into manageable pieces. – Top-down approach. – Bottom-up approach. www.tusharkute.com 6
- 7. System life cycle ● Design – ● Refinement and Coding – ● Create abstract data types and the algorithm specifications, language independent. Determining data structures and algorithms. Verification – Developing correctness proofs, testing the program, and removing errors. www.tusharkute.com 7
- 8. Efficiency ● A solution is said to be efficient if it solves the problem within its resource constraints. – – ● Space Time The cost of a solution is the amount of resources that the solution consumes. www.tusharkute.com 8
- 9. Data Structure philosophy ● ● ● Each data structure has costs and benefits. Rarely is one data structure better than another in all situations. A data structure requires: – – ● space for each data item it stores, time to perform each basic operation, Programming effort. www.tusharkute.com 9
- 10. Data structure philosophy ● ● ● Each problem has constraints on available space and time. Only after a careful analysis of problem characteristics can we know the best data structure for the task. Bank example: – Start account: a few minutes – Transactions: a few seconds – Close account: overnight www.tusharkute.com 10
- 11. Example. for(a=0; a>10; a++) //loop-1 { printf(“Hello World...”); } for(a=0; a<10; a++) //loop-2 { printf(“Hello World...”); } www.tusharkute.com 11
- 12. Example. for(a=0; a<=10; a++) //loop-3 { printf(“Hello World...”); } for(a=0; a!=10; a++) //loop-4 { printf(“Hello World...”); } www.tusharkute.com 12
- 13. Example: check for prime number flag=0; for(a=2;a<num;a++) { if(num%a==0) flag=1; } if(flag==1) printf(“Number is not prime.”); else printf(“Number is prime.”); www.tusharkute.com 13
- 14. Refinement-1 flag=0; for(a=2;a<num;a++) { if(num%a==0) { flag=1; break; } } if(flag==1) printf(“Number is not prime.”); else www.tusharkute.com printf(“Number is prime.”); 14
- 15. Refinement-2 flag=0; for(a=2;a<num/2;a++) { if(num%a==0) { flag=1; break; } } if(flag==1) printf(“Number is not prime.”); else www.tusharkute.com printf(“Number is prime.”); 15
- 16. Refinement-3 for(a=2;a<num/2;a++) { if(num%a==0) break; } if(a==(num/2)) printf(“Number is prime.”); else printf(“Number is not prime.”); www.tusharkute.com 16
- 17. Example: swapping of two numbers, Way-1 a=13, b=29; temp = a; a = b; b = temp; www.tusharkute.com 17
- 18. Way-2 a=13, b=29; a = a + b; a = a – b; b = a – b; www.tusharkute.com 18
- 19. Way-3 a=13, b=29; a = a ^ b; b = a ^ b; a = a ^ b; or a^=b^=a^=b; www.tusharkute.com 19
- 20. Worst / Average / Best case ● Worst-case running time of an algorithm – The longest running time for any input of size n – An upper bound on the running time for any input – Guarantee that the algorithm will never take longer Example: Sort a set of numbers in increasing order; and the data is in decreasing order – The worst case can occur fairly often – E.g. in searching a database for a particular piece of information ● ● Best-case running time – ● Sort a set of numbers in increasing order; and the data is already in increasing order Average-case running time – May be difficult to define what “average” means www.tusharkute.com 20
- 21. Example: searching in database ● Best case: O(1) ● Worst case: O(n) ● Average case: O(n/2) www.tusharkute.com 21
- 22. Running time of algorithms ● Bounds are for the algorithms, rather than programs – ● Programs are just implementations of an algorithm, and almost always the details of the program do not affect the bounds Bounds are for algorithms, rather than problems – A problem can be solved with several algorithms, some are more efficient than others www.tusharkute.com 22
- 23. Describing algorithms ● Natural language – – ● English, Chinese Instructions must be definite and effectiveness. Graphic representation – Flowchart Work well only if the algorithm is small and simple. Pseudo language ● ● – Readable Instructions must be definite and effectiveness. Combining English and C ● ● – Simple and Tough task to do. www.tusharkute.com 23
- 24. Algorithm and programs ● Algorithm: a method or a process followed to solve a problem. – ● An algorithm takes the input to a problem (function) and transforms it to the output. – ● A recipe: The algorithm gives us a “recipe” for solving the problem by performing a series of steps, where each step is completely understood. A mapping of input to output. A problem can be solved by many algorithms. www.tusharkute.com 24
- 25. A problem can have many solutions ● For example, the problem of sorting can be solved by the following algorithms: – Insertion sort – Bubble sort – Selection sort – Shell sort – Merge sort – Radix sort – Merge sort – Quick sort www.tusharkute.com 25
- 26. Algorithm properties ● An algorithm possesses the following properties: – – It must be composed of a series of concrete steps. – There can be no ambiguity as to which step will be performed next. – It must be composed of a finite number of steps. – ● It must be correct. It must terminate. A computer program is an instance, or concrete representation, for an algorithm in some programming language. www.tusharkute.com 26
- 27. Thank you This presentation is created using LibreOffice Impress 3.6.2.2 www.tusharkute.com 27