Systematic Programming - Revision history

Davrot: /* Examples of Program Development */

2025-10-20T10:32:05Z

Examples of Program Development

← Older revision		Revision as of 10:32, 20 October 2025
Line 62:		Line 62:
	The task our example program has to solve is the calculation of all prime numbers in the interval from <math display="inline">1</math> to <math display="inline">N</math>. Reminder: a prime number is a natural number that is only divisible without remainder by itself and by <math display="inline">1</math>. <math display="inline">1</math> itself is no prime number.		The task our example program has to solve is the calculation of all prime numbers in the interval from <math display="inline">1</math> to <math display="inline">N</math>. Reminder: a prime number is a natural number that is only divisible without remainder by itself and by <math display="inline">1</math>. <math display="inline">1</math> itself is no prime number.

	The simplest method to determine whether <math ~~display="inline"~~>i</math>is a prime number is the following: One tries every divisor from 2 to<math display="inline">i-1</math>. If a divisor is found that divides without remainder, then <math display="inline">i</math>is no prime number. This so called ‘brute-force’-ansatz (leads to an end, but is not very smart) can be easily implemented in a program. We check, in a loop, whether for a particular number <math display="inline">i</math>a divisor can be found. If this is the case, a so-called flag is set (a variable, that is either<math display="inline">0</math>or<math display="inline">1</math>and signal, whether a certain event occurred). If the flag is not set after the loop is finished, no divisor has been found and the number is remembered as a prime number. If the flag is not set, the program does nothing. After this, the next number<math display="inline">i+1</math>is scrutinized and so forth until all natural numbers until<math display="inline">N</math>have been tested. The latter will also be done in a loop. Figure 5.1 shows the flow chart, the following gives the correspondent Python code: <syntaxhighlight lang="python"># TASK:		The simplest method to determine whether <math>i</math>is a prime number is the following: One tries every divisor from 2 to <math display="inline">i-1</math>. If a divisor is found that divides without remainder, then <math display="inline">i</math>is no prime number. This so called ‘brute-force’-ansatz (leads to an end, but is not very smart) can be easily implemented in a program. We check, in a loop, whether for a particular number <math display="inline">i</math>a divisor can be found. If this is the case, a so-called flag is set (a variable, that is either<math display="inline">0</math>or<math display="inline">1</math>and signal, whether a certain event occurred). If the flag is not set after the loop is finished, no divisor has been found and the number is remembered as a prime number. If the flag is not set, the program does nothing. After this, the next number<math display="inline">i+1</math>is scrutinized and so forth until all natural numbers until<math display="inline">N</math>have been tested. The latter will also be done in a loop. Figure 5.1 shows the flow chart, the following gives the correspondent Python code: <syntaxhighlight lang="python"># TASK:
	# ========		# ========
	# find all prime numbers between 1 and N and save them		# find all prime numbers between 1 and N and save them

Davrot: /* Examples of Program Development */

2025-10-20T10:31:38Z

Examples of Program Development

Davrot: Created page with "Questions to [mailto:davrot@uni-bremen.de David Rotermund] ''By Jan Wiersig, modified by Udo Ernst and translated into English by Daniel Harnack. David Rotermund replaced the Matlab code with Python code.'' Computers are at the same time incredibly fast and incredibly stupid. They will do exactly what they were told, but usually not what you want. To change this or even prevent it from happening, second to the thorough knowledge of the syntax of a programming language..."

2025-10-14T14:28:05Z

Created page with "Questions to [mailto:davrot@uni-bremen.de David Rotermund] ''By Jan Wiersig, modified by Udo Ernst and translated into English by Daniel Harnack. David Rotermund replaced the Matlab code with Python code.'' Computers are at the same time incredibly fast and incredibly stupid. They will do exactly what they were told, but usually not what you want. To change this or even prevent it from happening, second to the thorough knowledge of the syntax of a programming language..."

Show changes

← Older revision		Revision as of 10:31, 20 October 2025
Line 26:		Line 26:

	* Which steps have to be carried out dependent on a specific condition? Always when a distinction of cases is due, program code will be executed only under certain conditions. For example the absolute value of a number <math display="inline">x</math> is found by multiplying it with <math display="inline">-1</math> – but only if x is negative! Another example: the e-mail client on your computer will only retrieve emails from a mail-server in case they do not already exist as local copies on your hard drive (avoiding unnecessary operation).		* Which steps have to be carried out dependent on a specific condition? Always when a distinction of cases is due, program code will be executed only under certain conditions. For example the absolute value of a number <math display="inline">x</math> is found by multiplying it with <math display="inline">-1</math> – but only if x is negative! Another example: the e-mail client on your computer will only retrieve emails from a mail-server in case they do not already exist as local copies on your hard drive (avoiding unnecessary operation).
	* Which steps demand user interaction or an informative feedback? Some steps might need the confirmation of the user prior to their execution. For example a program that formats your hard disk should ask you before it starts running.		*Which steps demand user interaction or an informative feedback? Some steps might need the confirmation of the user prior to their execution. For example a program that formats your hard disk should ask you before it starts running.

	Feedback is also important if errors occur during the execution of the program – for example when dividing a number by <math display="inline">0</math>.		Feedback is also important if errors occur during the execution of the program – for example when dividing a number by <math display="inline">0</math>.
Line 43:		Line 43:
	* Replace every sub-step by at least one program command		* Replace every sub-step by at least one program command
	* Unexpectedly complex sub-steps should be further broken down		* Unexpectedly complex sub-steps should be further broken down
	* Adhere to the syntax of commands and expressions		*Adhere to the syntax of commands and expressions

	For this, it is mandatory to use the help function! – especially for beginners or when changing to another programming language. Every command has to be unambiguous, so the computer can understand what you want it to do.		For this, it is mandatory to use the help function! – especially for beginners or when changing to another programming language. Every command has to be unambiguous, so the computer can understand what you want it to do.
Line 62:		Line 62:
	The task our example program has to solve is the calculation of all prime numbers in the interval from <math display="inline">1</math> to <math display="inline">N</math>. Reminder: a prime number is a natural number that is only divisible without remainder by itself and by <math display="inline">1</math>. <math display="inline">1</math> itself is no prime number.		The task our example program has to solve is the calculation of all prime numbers in the interval from <math display="inline">1</math> to <math display="inline">N</math>. Reminder: a prime number is a natural number that is only divisible without remainder by itself and by <math display="inline">1</math>. <math display="inline">1</math> itself is no prime number.

	The simplest method to determine whether <math display="inline">i</math> is a prime number is the following: One tries every divisor from 2 to <math display="inline">i-1</math>. If a divisor is found that divides without remainder, then <math display="inline">i</math> is no prime number. This so called ‘brute-force’-ansatz (leads to an end, but is not very smart) can be easily implemented in a program. We check, in a loop, whether for a particular number <math display="inline">i</math> a divisor can be found. If this is the case, a so-called flag is set (a variable, that is either <math display="inline">0</math> or <math display="inline">1</math> and signal, whether a certain event occurred). If the flag is not set after the loop is finished, no divisor has been found and the number is remembered as a prime number. If the flag is not set, the program does nothing. After this, the next number <math display="inline">i+1</math> is scrutinized and so forth until all natural numbers until <math display="inline">N</math> have been tested. The latter will also be done in a loop. Figure 5.1 shows the flow chart, the following gives the correspondent Python code:<syntaxhighlight lang="python"># TASK:		The simplest method to determine whether <math display="inline">i</math>is a prime number is the following: One tries every divisor from 2 to<math display="inline">i-1</math>. If a divisor is found that divides without remainder, then <math display="inline">i</math>is no prime number. This so called ‘brute-force’-ansatz (leads to an end, but is not very smart) can be easily implemented in a program. We check, in a loop, whether for a particular number <math display="inline">i</math>a divisor can be found. If this is the case, a so-called flag is set (a variable, that is either<math display="inline">0</math>or<math display="inline">1</math>and signal, whether a certain event occurred). If the flag is not set after the loop is finished, no divisor has been found and the number is remembered as a prime number. If the flag is not set, the program does nothing. After this, the next number<math display="inline">i+1</math>is scrutinized and so forth until all natural numbers until<math display="inline">N</math>have been tested. The latter will also be done in a loop. Figure 5.1 shows the flow chart, the following gives the correspondent Python code: <syntaxhighlight lang="python"># TASK:
	# ========		# ========
	# find all prime numbers between 1 and N and save them		# find all prime numbers between 1 and N and save them