PROBLEM SOLVING TECHNIQUES

Transcription

1 PROBLEM SOLVING TECHNIQUES UNIT I PROGRAMMING TECHNIQUES 1.1 Steps Involved in Computer Programming What is Program? A program is a set of instructions written by a programmer. The program contains detailed instructions and complete procedures for performing the relevant tasks. What is Programming? Programming involves creativity, analytical thinking, knowledge in the language in which coding or the programming is done. Steps Involved in Programming 1. Identify the problem 2. Analyzing the Problem 3. Algorithm design 4. Pseudocode conversion 5. Flowchart 6. Coding 7. Debugging 8. Testing 9. Final output 10. Documentation 1.2 Computer programming: Identify the problem Every program aims at solving the problem for which it has been developed. For example An online banking program solves the problem of transferring money, tracking the transactions, etc., filing your taxes. A word processor solves the problem of document creation. Even a game solves the problem of keeping people entertained. The only way to achieve the goal is to aim in finding the problem involved in achieving it. A program is considered as useful only when it solves the problem. This is the first step to approach any solution.

2 1. Analyzing the Problem Once the problem is being identified and target solution is being outlined. Analysis on the problem has to be carried out. Define whether the problem is a continuation of the existing solution or it is a new problem that has been identified. If the problem arises from an existing solution then its quiet easy for us to start our designing from that point. If its a new problem then we need to look in for the base of the problem and then move further for coding. 2. Algorithm Design In this stage the stepwise procedure involved in arriving at the problem solution is identified and documented in simple English language. It is called as a strategy. These contents are said to be understandable by any person who knows simple English. Example1: Adding two subject marks for one student Algorithm: Step 1. Read the two subject marks that have to be added Step 2. Add the two subject marks and save it inside a variable. Step 3. Write the total. Example2: Adding ten subject marks for one student. Algorithm: Step 1. Initialize a sum variable as zero and subject variable as ten. Step 2. While the number of subjects not equal to zero repeatedly do Step 2.a. Read the corresponding subject mark that has to be added. Step 2.b Compute the current sum by adding along with the previous sum value. Step 3. Write the sum. Example3: Adding ten subject marks for fifty students. Algorithm: Step 1. Initialize a sum variable as zero, subject variable as ten and student variable as fifty. Step 2. While number of students is not equal to zero repeatedly do

3 Step 2.a. While the number of subjects not equal to zero repeatedly do Step 2.a.1. Read the corresponding subject mark that has to be added. value. Step 2.a.2. Compute the current sum by adding along with the previous sum Step 2.b. Write the sum for each student. 3. Pseudocode conversion As the stepwise procedure has been outlined they are easily converted into pseudocode. This helps in the coding the solution in the appropriate programming language. Example1: Adding two subject marks for one student Pseudocode: Var mark1, mark2, sum; read(m1); read(m2); sum=m1+m2; write(sum); Example2: Adding ten subject marks for one student. Pseudocode: Var mark, sum; sum=0; subject=10; While(subject!=0) read(mark); sum = sum +mark; subject --; write(sum)

4 Example 3 : Adding ten subject marks for fifty students. Pseudocode: Var mark, sum, student; sum=0; student=50; subject=10; while(student!=0) While(subject!=0) read(mark); sum = sum +mark; subject --; write(sum) student --; 1.3 FLOW CHART The flowchart is an diagrammatic representation of the work flow. This consists of various shapes for representing the various activities at each step which are connected with an arrow. Therefore this gives a clear picture the procedure involved in reaching the target. Types of flow chart System Flowchart the processing of entire system is shown by the system flow chart. It provides details about the input/output devices, the media being used and the flow of data in the system. Program flowchart the overall steps involved in the program execution including I/O, processing, loops and branching. This provides more illuatated look over the entire system excution compared with the system flowchart.

5 Flowchart Symbols Each symbol in the flow chart represents different activities done in the program. These are the various symbols involved in the flow chart. Each sybols specify the activity inside it and they are connected by the flow lines.

6 Example1 : Adding two suject marks for one student Flow chart: Example2 : Adding ten suject marks for one student. Flow chart:

7 Example3 : Adding ten suject marks for fifty students. Flow Chart: CODING: After the target and the steps has been identified. The coding phase can start. The various factors that should be considered while coding are Identify the users of the computer program Determine the basic system configuration for executing the computer program List the programming skill Select the programming language suitable from the list.

8 Identify the users of the computer program If the user of the program is suppose to be the programmer itself. The programmer can frame the program as he or she want it to be. If the user is a person who is no way connected to the programmer. Then the programmer must know the exact expectation of the user. Determine the basic system configuration for executing the computer program The system configuration includes hardware configuration and software configuration. The hardware configuration includes the RAM size, hard disk size, Processor and the various other devices which are used for the program execution. The software configuration includes the type of Operating System, Editor used, Software used for execution,etc., The language in which the program can be written should be listed. List the programming skill When designing any program, list out the programming skill available for your team. Some programming languages may not be suitable for the system configuration, some may not be suitable for getting the expected output. All these factors must be considered and eliminate the program which is not suitable from the list. Select the programming language suitable from the list Out of all the programming languages listed the selection can be made on the number of lines of code. Some programming languages have certain predefined functions for the some activities. Minimal number lines in the codes helps to understand, maintain and debug the code easily. There are various other criteria that can also be added while selecting the programming language. This is either based on the programmer who is going to code the program or the user who are going to use the program. Debugging After the coding is of executable form. It is run several times manually inorder to remove the errors that has been occurred while typing the code. The program execution done manually is called dry run. This process is continued until the code become error less.

9 Testing The testing of the codes are done after the completion of the entire coding. There are three types of data that has to be considered while testing the codes they are usual, unusual and invalid data. These type of datas are given to check the behaviour of the code. If it results in an unexpected way then the code has to be corrected accordingly. This phase aims in providing the best output with any type of input given to the system. Final Output This is the last stage in which the programmer has to show the full efficiency of the program. The exact output expected by the user should be provided. Documentation This is similar to a manual that is been generated for any electronic product.this type of manual is also necessary for the software that is being coded too. This helps the user and the programmer to know about the product and helps in long term maintance. The procedure of usin There are two types of documentation User Manual provides the overall information about how to operate the program and what are the do s and dont s in the program. The steps that has to be carried out when a problem has occured is given in detail. Technical Manual contains the technical information about the program. This is used to get technical details of the program, when the system is not working properly or requires modifications. This is used for long term maintanace of the system. 1.4 THE EFFICIENCY OF ALGORITHMS Efficiency is naturally tied in with the design, implementation, and analysis of algorithms. It is considered based on the usage of the resources. The common measures used to find the efficiency are Time Complexity : It is the amount of cpu time required by a program to execute. Time complexity is the sum of the following components: Compile time The time taken for the compilation of the program.

10 Runtime or Execution time - The time taken for the execution of the program. The optimized code will take less time to get executed. Time complexity T(P) = c + Tp c Compile time Tp Run time or execution time Space Complexity It is the amount of memory required to execute a program. Space complexity is the sum of the following components: Instruction space: algorithm code,data space: input & output data. Due to the high cost of the computing resources it is always desirable to design algorithms that are very economical in the use of CPU time and memory. To design an efficient algorithm the following points to be considered. Redundant computations Referencing array elements Inefficiency due to late termination Early detection of desired output conditions Trading storage for efficiency gains Redundant computations To improve the efficiency of algorithm redundant calculations should be avoided. The effects of redundant computations are most serious when they are embedded within a loop that must be executed many times. Recalculating expression that remains constant throughout the loop is the most common mistake. x=0; for (i=0;i<n;i++) x=x+2 y=(a*a+c)*x+b*b*x write( the value of y=,y) In the above example the expressions (a*a*a+c) and (b*b) remains constant throughout the loop. So this unnecessary multiplications and additions can be removed out of the loop. a=a*a+c; b=b*b;

11 x=0; for(i=0;i<n;i++) x=x+2; y=a*x+b*x; write( the value of y=,y); Referencing array elements Arrays are processed by iterative constructs. Redundant computations can also easily creep into array processing if care is not exercised. For example, consider the two versions of an algorithm for finding maximum and its position in an array. Version 1 p=1 for(i=2;i<n;i++) if(a[i]>a[p] then p=i max=a[p] Version 2 p=1 max=a[1] for(i=2;i<n;i++) if(a[i]>a[p] max=a[i] p=i The version2 implementation would normally be preferred because of the conditional test a[i]>max. It is more efficient because to use the variable max only one memory reference instruction is required, whereas a[p] requires two memory references and an additional operation to locate the correct value for use in the test. Also max variable makes it clearer what task is to be accomplished. Inefficiency due to late termination Next inefficiency is more tests are done than are required to solve the problem. For example, in an alphabetical ordered list of names we are searching a name using linear search. All the names are examined in the inefficient implementation. We are looking for the

12 name flip, then as soon as the name flop encountered an efficient algorithm concludes flip is not in the list. Early detection of desired output conditions We must include additional conditions to detect the conditions for early termination. For example, a bubble sort might be used to sort a set of data that is almost in sorted order. The algorithm will have the data in sorted order long before the loop termination condition is met. It is desirable to terminate the sort as soon as it is established that the data is already sorted. To do this check whether there have been any exchanges in the current pass of the inner loop. If there have been no exchanges in the current pass the data must be sorted and so early termination can be applied. Trading storage for efficiency gains Computing has meant calculating results and then storing those results for later use. Storing large volumes of rarely used data waste spaces, making it a very expensive strategy. In the tradeoff, what usually happens is we recomputed or save some intermediate results and avoid having to do a lot of unnecessary testing and computation later on. Summary: Factors which are decided efficiency of algorithm Eliminate redundant calculations of the expression inside the loop. Remove temporary assignments. Include additional conditions to detect the conditions for early termination Tradeoff unnecessary storage 1.5 ANALYSIS OF ALGORITHM Algorithm Step-by-step procedure for solving a problem. problem solving method for Implementation. well-defined procedure that takes set of values as input and produces set of values as output. Example : the sorting problem Input: sequence A of n numbers a 1, a 2,... a n.

13 Output: reordering of A in increasing value. Good Algorithms possess the following qualities and capabilities: 1. They are simple but powerful and general solutions. 2. They can be easily understood by others, that is, the implementation is clear and concise without being "tricky". 3. They can be easily modified if necessary. 4. They are correct for clearly defined situations. 5. They are able to be understood on a number of levels. 6. They are economical in the use of computer time, computer storage and peripherals. 7. They are documented well enough to be used by others who do not have a detailed knowledge of their inner workings. 8. They are not depent on being run on a particular computer. 9. They are able to be used as a subprocedure for other problems. 10. The solution is pleasing and satisfying to its designer-a product that the designer feels proud to have created. Computational complexity With increasing n the relative difference in the cost of a computation is enormous for these two extremes. Table: Computational cost as a function of problem size for a range of computational complexities log 2 n n n log 2 n n 2 n 3 2 n > >> >> , >> Algorithm analysis : determine the time/space required by an algorithm Goals:

14 minimize time minimize space Pseudo-code is a structured description of an algorithm, not as formal as a programming language. Example: find the maximum element of an array. Algorithm Max(A,n) Input: an array A sorting n integers. Output: maximum element in A 1. max=a[1] 2. for i=0 to n do 3. if max<a[i] then max=a[i] Primitive operations arithmetic operations (+,_,*,/) comparisons indexing,etc. The order notation A standard notation has been developed to represent functions which bound the computing time for algorithms. It is an order notation and its usually referred to as the O- notation. An algorithm in which the dominant mechanism is executed cn 2 times for c,a constant, and n the problem size, is said to have an order n 2 complexity which is written as O(n 2). A function g(n) is O(f(n)) provided there is a constant c for which the relationship g(n)< cf(n) holds for all values of n that are finite and positive. Worst case vs. average case Usually measure worst case complexity. crucial importance in some applications. often algorithms will better worst case performance have worse average case performance in practice. 1.6 STEP-COUNT METHOD The operation-count method omits accounting for the time spent on all but the chosen operation The step-count method count for all the time spent in all parts of the program

15 A program step is loosely defined to be a syntactically or semantically meaningful segment of a program for which the execution time is indepent of the instance characteristics. 100 adds, 100 subtracts, 1000 multiples can be counted as one step. However, n adds cannot be counted as one step. steps/execution (s/e) for (int i = 1; i < n; i++) 1 { 0 // insert a[i] into a[0:i-1] 0 int t = a[i]; 1 int j; 0 for (j = i - 1; j >= 0 && t < a[j]; j--) 1 a[j + 1] = a[j]; 1 a[j + 1] = t; 1 } 0 s/e frequency for (int i = 1; i < n; i++) 1 n-1 { 0 0 // insert a[i] into a[0:i-1] 0 0 int t = a[i]; 1 n-1 int j; 0 0 for (j = i - 1; j >= 0 && t < a[j]; j--) 1 (n-1)n/2 a[j + 1] = a[j]; 1 (n-1)n/2 a[j + 1] = t; 1 n-1 } 0 n-1 Total step counts = (n-1)+0+0+(n-1)+0+(n-1)n/2+(n-1)n/2 + (n-1) + (n-1) = n 2 + 3n 4

16 1.7 OPERATION COUNT One way to estimate the time complexity of a program or method is to select one or more operations, such as add, multiply, and compare, and to determine how many of each is done. The success of this method deps on our ability to identify the operations that contribute most to the time complexity. Pick an instance characteristic n, n = the number of elements in case of insertion sort. Determine count as a function of this instance characteristic. for (int i = 1; i < n; i++) for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; How many comparisons are made? The number of compares deps on a[]s and t as well as on n. Worst case count = maximum count Best case count = minimum count Average count Worst Case Operation Count for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a = [1,2,3,4] and t = 0 a = [1,2,3,4,,i] and t = 0 4 compares i compares for (int i = 1; i < n; i++) for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; total compares = (n-1) = (n-1)n/2

17 QUESTIONS FOR PRACTICE 1. Draw a flowchart to implement area of triangle. 2. Write an algorithm to count the numbers greater than 25 in a list of numbers. 3. Write an algorithm to find the minimum number in a list of elements. 4. Write an algorithm and draw the flowchart to find the sum of first n numbers. 5. Write an algorithm and draw its flowchart to convert Farenheit temperature to Celsius.