Sunday, 23 March 2014

Practice for random numbers

This tutorial provides a brief introduction to the random number functions that come as part of the C++ standard library, namely rand() and srand().
rand() and RAND_MAX
The C++ standard library includes a pseudo random number generator for generating random numbers. In order to use it we need to include the <cstdlib> header. To generate a random number we use the rand() function. This will produce a result in the range 0 to RAND_MAX, where RAND_MAX is a constant defined by the implementation.
Here's a piece of code that will generate a single random number:

#include <cstdlib>
#include <iostream>
using namespace std;
int main()
{
int random_integer = rand();
cout << random_integer << endl;
}

The value of RAND_MAX varies between compilers and can be as low as 32767, which would give a range from 0 to 32767 for rand(). To find out the value of RAND_MAX for your compiler run the following small piece of code:
#include <cstdlib>
#include <iostream>
using namespace std;
int main()
{
cout << "The value of RAND_MAX is " << RAND_MAX << endl;
}

srand()

The pseudo random number generator produces a sequence of numbers that gives the appearance of being random, when in fact the sequence will eventually repeat and is predictable.
We can seed the generator with the srand() function. This will start the generator from a point in the sequence that is dependent on the value we pass as an argument. If we seed the generator once with a variable value, for instance the system time, before our first call of rand() we can generate numbers that are random enough for simple use (though not for serious statistical purposes).
In our earlier example the program would have generated the same number each time we ran it because the generator would have been seeded with the same default value each time. The following code will seed the generator with the system time then output a single random number, which should be different each time we run the program.

#include <cstdlib>
#include <ctime>
#include <iostream>
using namespace std;
int main()
{
srand((unsigned)time(0));
int random_integer = rand();
cout << random_integer << endl;
}

Don't make the mistake of calling srand() every time you generate a random number; we only usually need to call srand() once, prior to the first call to rand().

Generating a number in a specific range
If we want to produce numbers in a specific range, rather than between 0 and RAND_MAX, we can use the modulo operator. It's not the best way to generate a range but it's the simplest. If we use rand()%n we generate a number from 0 to n-1. By adding an offset to the result we can produce a range that is not zero based. The following code will produce 20 random numbers from 1 to 10:

#include <cstdlib>
#include <ctime>
#include <iostream>
using namespace std;
int main()
{
srand((unsigned)time(0));
int random_integer;
for(int index=0; index<20; index++){
random_integer = (rand()%10)+1;
cout << random_integer << endl;
}
}

A better method, though slightly more complicated, is given below. This overcomes problems that are sometimes experienced with some types of pseudo random number generator that might be supplied with your compiler. As before, this will output 20 random numbers from 1 to 10.
#include <iostream>
#include <ctime>
#include <cstdlib>
using namespace std;
int main()
{
srand((unsigned)time(0));
int random_integer;
int lowest=1, highest=10;
int range=(highest-lowest)+1;
for(int index=0; index<20; index++){
random_integer = lowest+int(range*rand()/(RAND_MAX + 1.0));
cout << random_integer << endl;
}
}

If you need to use a pseudo random number generator for anything even remotely serious you should avoid the simple generator that comes with your compiler and use something more sophisticated instead. That said, rand() still has its place and you may find it useful.

my question is, for the functions on choosing random numbers in a specific range, what should i do to make the cout one by one?
As in, like the function given above, it gives the whole 20 outputs at once, but what i would like to do is to get the output one by one, how could i do that?
and let's say i have a range from 2 to N, what should i do to get the output only from 2 to N and not 0 to N?because what's given in the previous thread is a function to choose from 0 to N.
thank you :D

Random Numbers

Intro
This tutorial provides a brief introduction to the random number functions that come as part of the C++ standard library, namely rand() and srand().
rand() and RAND_MAX
The C++ standard library includes a pseudo random number generator for generating random numbers. In order to use it we need to include the <cstdlib> header. To generate a random number we use the rand() function. This will produce a result in the range 0 to RAND_MAX, where RAND_MAX is a constant defined by the implementation.
Here's a piece of code that will generate a single random number:
  1. #include <cstdlib>
  2. #include <iostream>
  3. using namespace std;
  4. int main()
  5. {
  6. int random_integer = rand();
  7. cout << random_integer << endl;
  8. }
The value of RAND_MAX varies between compilers and can be as low as 32767, which would give a range from 0 to 32767 for rand(). To find out the value of RAND_MAX for your compiler run the following small piece of code:
  1. #include <cstdlib>
  2. #include <iostream>
  3. using namespace std;
  4. int main()
  5. {
  6. cout << "The value of RAND_MAX is " << RAND_MAX << endl;
  7. }
srand()
The pseudo random number generator produces a sequence of numbers that gives the appearance of being random, when in fact the sequence will eventually repeat and is predictable.
We can seed the generator with the srand() function. This will start the generator from a point in the sequence that is dependent on the value we pass as an argument. If we seed the generator once with a variable value, for instance the system time, before our first call of rand() we can generate numbers that are random enough for simple use (though not for serious statistical purposes).
In our earlier example the program would have generated the same number each time we ran it because the generator would have been seeded with the same default value each time. The following code will seed the generator with the system time then output a single random number, which should be different each time we run the program.
  1. #include <cstdlib>
  2. #include <ctime>
  3. #include <iostream>
  4. using namespace std;
  5. int main()
  6. {
  7. srand((unsigned)time(0));
  8. int random_integer = rand();
  9. cout << random_integer << endl;
  10. }
Don't make the mistake of calling srand() every time you generate a random number; we only usually need to call srand() once, prior to the first call to rand().
Generating a number in a specific range
If we want to produce numbers in a specific range, rather than between 0 and RAND_MAX, we can use the modulo operator. It's not the best way to generate a range but it's the simplest. If we use rand()%n we generate a number from 0 to n-1. By adding an offset to the result we can produce a range that is not zero based. The following code will produce 20 random numbers from 1 to 10:
  1. #include <cstdlib>
  2. #include <ctime>
  3. #include <iostream>
  4. using namespace std;
  5. int main()
  6. {
  7. srand((unsigned)time(0));
  8. int random_integer;
  9. for(int index=0; index<20; index++){
  10. random_integer = (rand()%10)+1;
  11. cout << random_integer << endl;
  12. }
  13. }
A better method, though slightly more complicated, is given below. This overcomes problems that are sometimes experienced with some types of pseudo random number generator that might be supplied with your compiler. As before, this will output 20 random numbers from 1 to 10.
  1. #include <iostream>
  2. #include <ctime>
  3. #include <cstdlib>
  4. using namespace std;
  5. int main()
  6. {
  7. srand((unsigned)time(0));
  8. int random_integer;
  9. int lowest=1, highest=10;
  10. int range=(highest-lowest)+1;
  11. for(int index=0; index<20; index++){
  12. random_integer = lowest+int(range*rand()/(RAND_MAX + 1.0));
  13. cout << random_integer << endl;
  14. }
  15. }
Conclusion
If you need to use a pseudo random number generator for anything even remotely serious you should avoid the simple generator that comes with your compiler and use something more sophisticated instead. That said, rand() still has its place and you may find it useful.

Wednesday, 19 March 2014

Reserved words

The syntax rules (or grammar) of C++ define certain symbols to have a unique meaning within a C++ program. These symbols, the reserved words, must not be used for any other purposes. The reserved words already used are int and void. All reserved words are in lower-case letters. The table below lists the reserved words of C++. C++ Reserved Words
andand_eqasmautobitand
bitorboolbreakcasecatch
charclassconstconst_castcontinue
defaultdeletedodoubledynamic_cast
elseenumexplicitexportextern
falsefloatforfriendgoto
ifinlineintlongmutable
namespacenewnotnot_eqoperator
oror_eqprivateprotectedpublic
registerreinterpret_castreturnshortsigned
sizeofstaticstatic_caststructswitch
templatethisthrowtruetry
typedeftypeidtypenameunionunsigned
usingvirtualvoidvolatilewchar_t
whilexorxor_eq
Some of these reserved words may not be treated as reserved by older compilers. However you would do well to avoid their use. Other compilers may add their own reserved words. Typical are those used by Borland compilers for the PC, which add nearfarhugecdecl, and pascal.
Notice that main is not a reserved word. However, this is a fairly technical distinction, and for practical purposes you are advised to treat maincin, and cout as if they were reserved as well.

Variables, Types and Expressions

This document is part of the HTML publication "An Introduction to the Imperative Part of C++" The original version was produced by Rob Miller at Imperial College London, September 1996. Version 1.1 (modified by David Clark at Imperial College London, September 1997) Version 1.2 (modified by Bob White at Imperial College London, September 1998) Version 1.3, 1.4, 2.0, ..., 2.12 (modified by William Knottenbelt at Imperial College London, September 1999-September 2013) 2. Variables, Types and Expressions 2.1 Identifiers As we have seen, C++ programs can be written using many English words. It is useful to think of words found in a program as being one of three types: Reserved Words. These are words such as if, int and else, which have a predefined meaning that cannot be changed. Here's a more complete list. Library Identifiers. These words are supplied default meanings by the programming environment, and should only have their meanings changed if the programmer has strong reasons for doing so. Examples are cin, cout and sqrt (square root). Programmer-supplied Identifiers. These words are "created" by the programmer, and are typically variable names, such as year_now and another_age. An identifier cannot be any sequence of symbols. A valid identifier must start with a letter of the alphabet or an underscore ("_") and must consist only of letters, digits, and underscores. (BACK TO COURSE CONTENTS) 2.2 Data Types Integers C++ requires that all variables used in a program be given a data type. We have already seen the data type int. Variables of this type are used to represent integers (whole numbers). Declaring a variable to be of type int signals to the compiler that it must associate enough memory with the variable's identifier to store an integer value or integer values as the program executes. But there is a (system dependent) limit on the largest and smallest integers that can be stored. Hence C++ also supports the data types short int and long int which represent, respectively, a smaller and a larger range of integer values than int. Adding the prefix unsigned to any of these types means that you wish to represent non-negative integers only. For example, the declaration unsigned short int year_now, age_now, another_year, another_age; reserves memory for representing four relatively small non-negative integers. Some rules have to be observed when writing integer values in programs: Decimal points cannot be used; although 26 and 26.0 have the same value, "26.0" is not of type "int". Commas cannot be used in integers, so that (for example) 23,897 has to be written as "23897". Integers cannot be written with leading zeros. The compiler will, for example, interpret "011" as an octal (base 8) number, with value 9. (BACK TO COURSE CONTENTS) Real numbers Variables of type "float" are used to store real numbers. Plus and minus signs for data of type "float" are treated exactly as with integers, and trailing zeros to the right of the decimal point are ignored. Hence "+523.5", "523.5" and "523.500" all represent the same value. The computer also accepts real numbers in floating-point form (or "scientific notation"). Hence 523.5 could be written as "5.235e+02" (i.e. 5.235 x 10 x 10), and -0.0034 as "-3.4e-03". In addition to "float", C++ supports the types "double" and "long double", which give increasingly precise representation of real numbers, but at the cost of more computer memory. Type Casting Sometimes it is important to guarantee that a value is stored as a real number, even if it is in fact a whole number. A common example is where an arithmetic expression involves division. When applied to two values of type int, the division operator "/" signifies integer division, so that (for example) 7/2 evaluates to 3. In this case, if we want an answer of 3.5, we can simply add a decimal point and zero to one or both numbers - "7.0/2", "7/2.0" and "7.0/2.0" all give the desired result. However, if both the numerator and the divisor are variables, this trick is not possible. Instead, we have to use a type cast. For example, we can convert "7" to a value of type double using the expression "static_cast(7)". Hence in the expression answer = static_cast(numerator) / denominator the "/" will always be interpreted as real-number division, even when both "numerator" and "denominator" have integer values. Other type names can also be used for type casting. For example, "static_cast(14.35)" has an integer value of 14. (BACK TO COURSE CONTENTS) Characters Variables of type "char" are used to store character data. In standard C++, data of type "char" can only be a single character (which could be a blank space). These characters come from an available character set which can differ from computer to computer. However, it always includes upper and lower case letters of the alphabet, the digits 0, ... , 9, and some special symbols such as #, £, !, +, -, etc. Perhaps the most common collection of characters is the ASCII character set (see for example Savitch, Appendix 3 or just click here). Character constants of type "char" must be enclosed in single quotation marks when used in a program, otherwise they will be misinterpreted and may cause a compilation error or unexpected program behaviour. For example, "'A'" is a character constant, but "A" will be interpreted as a program variable. Similarly, "'9'" is a character, but "9" is an integer. There is, however, an important (and perhaps somewhat confusing) technical point concerning data of type "char". Characters are represented as integers inside the computer. Hence the data type "char" is simply a subset of the data type "int". We can even do arithmetic with characters. For example, the following expression is evaluated as true on any computer using the ASCII character set: '9' - '0' == 57 - 48 == 9 The ASCII code for the character '9' is decimal 57 (hexadecimal 39) and the ASCII code for the character '0' is decimal 48 (hexadecimal 30) so this equation is stating that 57(dec) - 48(dec) == 39(hex) - 30(hex) == 9 It is often regarded as better to use the ASCII codes in their hexadecimal form. However, declaring a variable to be of type "char" rather than type "int" makes an important difference as regards the type of input the program expects, and the format of the output it produces. For example, the program #include using namespace std; int main() { int number; char character; cout << "Type in a character:\n"; cin >> character; number = character; cout << "The character '" << character; cout << "' is represented as the number "; cout << number << " in the computer.\n"; return 0; } Program 2.2.1 produces output such as Type in a character: 9 The character '9' is represented as the number 57 in the computer. We could modify the above program to print out the whole ASCII table of characters using a "for loop". The "for loop" is an example of a repetition statement - we will discuss these in more detail later. The general syntax is: for (initialisation; repetition_condition ; update) { Statement1; ... ... StatementN; } C++ executes such statements as follows: (1) it executes the initialisation statement. (2) it checks to see if repetition_condition is true. If it isn't, it finishes with the "for loop" completely. But if it is, it executes each of the statements Statement1 ... StatementN in turn, and then executes the expression update. After this, it goes back to the beginning of step (2) again. We can also 'manipulate' the output to produce the hexadecimal code. Hence to print out the ASCII table, the program above can be modified to: #include using namespace std; int main() { int number; char character; for (number = 32 ; number <= 126 ; number = number + 1) { character = number; cout << "The character '" << character; cout << "' is represented as the number "; cout << dec << number << " decimal or " < #include using namespace std; int main() { float number; cout << "Type in a real number.\n"; cin >> number; cout.setf(ios::fixed); // LINE 10 cout.precision(2); cout << "The square root of " << number << " is approximately "; cout << sqrt(number) << ".\n"; return 0; } Program 2.3.1 This produces the output Type in a real number. 200 The square root of 200.00 is approximately 14.14. whereas replacing line 10 with "cout.setf(ios::scientific)" produces the output: Type in a real number. 200 The square root of 2.00e+02 is approximately 1.41e+01. We can also include tabbing in the output using a statement such as "cout.width(20)". This specifies that the next item output will have a width of at least 20 characters (with blank space appropriately added if necessary). This is useful in generating tables. However the C++ compiler has a default setting for this member function which makes it right justified. In order to produce output left-justified in a field we need to use some fancy input and output manipulation. The functions and operators which do the manipulation are to be found in the library file iomanip (old header style iomanip.h) and to do left justification we need to set a flag to a different value (i.e. left) using the setiosflags operator: #include #include #include using namespace std; int main() { int number; cout << setiosflags ( ios :: left ); cout.width(20); cout << "Number" << "Square Root\n\n"; cout.setf(ios::fixed); cout.precision(2); for (number = 1 ; number <= 10 ; number = number + 1) { cout.width(20); cout << number << sqrt( (double) number) << "\n"; } return 0; } Program 2.3.2 This program produces the output Number Square Root 1 1.00 2 1.41 3 1.73 4 2.00 5 2.24 6 2.45 7 2.65 8 2.83 9 3.00 10 3.16 (In fact, the above programs work because "cout" is an identifier for an object belonging to the class "stream", and "setf(...)", "precision(...)" and "width(...)" are member functions of "stream". Don't worry too much about this for now - you will learn more about objects, classes and member functions later in the object-oriented part of the course.) (BACK TO COURSE CONTENTS) 2.4 Declarations, Constants and Enumerations As we have already seen, variables have to be declared before they can be used in a program, using program statements such as float number; Between this statement and the first statement which assigns "number" an explicit value, the value contained in the variable "number" is arbitrary. But in C++ it is possible (and desirable) to initialise variables with a particular value at the same time as declaring them. Hence we can write double PI = 3.1415926535; Furthermore, we can specify that a variable's value cannot be altered during the execution of a program with the reserved word "const": Enumerations Constants of type "int" may also be declared with an enumeration statement. For example, the declaration enum { MON, TUES, WED, THURS, FRI, SAT, SUN }; is shorthand for const int MON = 0; const int TUES = 1; const int WED = 2; const int THURS = 3; const int FRI = 4; const int SAT = 5; const int SUN = 6; By default, members of an "enum" list are given the values 0, 1, 2, etc., but when "enum" members are explicitly initialised, uninitialised members of the list have values that are one more than the previous value on the list: enum { MON = 1, TUES, WED, THURS, FRI, SAT = -1, SUN }; In this case, the value of "FRI" is 5, and the value of "SUN" is 0. (BACK TO COURSE CONTENTS) Where to put Constant and Variable Declarations Generally speaking, it is considered good practice to put constant declarations before the "main" program heading, and variable declarations afterwards, in the body of "main". For example, the following is part of a program to draw a circle of a given radius on the screen and then print out its circumference: (There is no need to type in this program) #include using namespace std; const float PI = 3.1415926535; const float SCREEN_WIDTH = 317.24; int drawCircle(float diameter); /* this is a "function prototype" */ int main() { float radius = 0; cout << "Type in the radius of the circle.\n"; cin >> radius; drawCircle(radius * 2); cout.setf(ios::fixed); cout.precision(2); cout << "The circumference of a circle of radius " << radius; cout << " is approximately " << 2 * PI * radius << ".\n"; return 0; } int drawCircle(float diameter) { float radius = 0; if (diameter > SCREEN_WIDTH) radius = SCREEN_WIDTH / 2.0; else radius = diameter / 2.0; ... ... } After the definition of "main()", this program includes a definition of the function "drawCircle(...)", the details of which need not concern us here (we can simply think of "drawCircle(...)" as a function like "sqrt(...)"). But notice that although both "main()" and "drawCircle(...)" use the identifier "radius", this refers to a different variable in "main()" than in "drawCircle(...)". Had a variable "radius" been declared before the "main" program heading, it would have been a public or global variable. In this case, and assuming there was no other variable declaration inside the function "drawCircle(...)", if "drawCircle(...)" had assigned it the value "SCREEN_WIDTH / 2.0", "main()" would have subsequently printed out the wrong value for the circumference of the circle. We say that the (first) variable "radius" is local to the main part of the program, or has the function main as its scope. In contrast, it usually makes sense to make constants such as "PI" and "SCREEN_WIDTH" global, i.e. available to every function. In any case, notice that the program above incorporates the safety measure of echoing the input. In other words, the given value of "radius" is printed on the screen again, just before the circumference of the circle is output. (BACK TO COURSE CONTENTS) 2.5 Assignments and Expressions Shorthand Arithmetic Assignment Statements We have already seen how programs can include variable assignments such as number = number + 1; Since it is often the case that variables are assigned a new value in function of their old value, C++ provides a shorthand notation. Any of the operators "+" (addition), "-" (subtraction), "*" (multiplication), "/" (division) and "%" (modulus) can be prefixed to the assignment operator (=), as in the following examples (mostly copied from Savitch, Section 2.3): Example: number += 1; total -= discount; bonus *= 2; time /= rush_factor; change %= 100; amount *= count1 + count2; Equivalent to: number = number + 1; total = total - discount; bonus = bonus * 2; time = time / rush_factor; change = change % 100; amount = amount * (count1 + count2); The first of the above examples may written in even shorter form. Using the increment operator "++", we may simply write number++; The operator "++" may also be used as a prefix operator: ++number; but care must be taken, since in some contexts the prefix and postfix modes of use have different effects. For example, the program fragment x = 4; y = x++; results in "x" having the value 5 and "y" having the value 4, whereas x = 4; y = ++x; results in both variables having value 5. This is because "++x" increments the value of "x" before its value is used, whereas "x++" increments the value afterwards. There is also an operator "--", which decrements variables by 1, and which can also be used in prefix or postfix form. In general, assignment statements have a value equal to the value of the left hand side after the assignment. Hence the following is a legal expression which can be included in a program and which might be either evaluated as true or as false: (y = ++x) == 5 It can be read as the assertion: "after x is incremented and its new value assigned to y, y's value is equal to 5". (BACK TO COURSE CONTENTS) Boolean Expressions and Operators Intuitively, we think of expressions such as "2 < 7", "1.2 != 3.7" and "6 >= 9" as evaluating to "true" or "false" ("!=" means "not equal to"). Such expressions can be combined using the logical operators "&&" ("and"), "||" ("or") and "!" ("not"), as in the following examples: Expression: (6 <= 6) && (5 < 3) (6 <= 6) || (5 < 3) (5 != 6) (5 < 3) && (6 <= 6) || (5 != 6) (5 < 3) && ((6 <= 6) || (5 != 6)) !((5 < 3) && ((6 <= 6) || (5 != 6))) True or False: false true true true false true The fourth of these expressions is true because the operator "&&" has a higher precedence than the operator "||". You can check the relative precedence of the different C++ operators in a C++ programming manual or text book (see for example Savitch, Appendix 2). But if in doubt use ( ) parentheses, which in any case often make the program easier to read. Compound Boolean expressions are typically used as the condition in "if statements" and "for loops". For example: ... ... if (total_test_score >= 50 && total_test_score < 65) cout << "You have just scraped through the test.\n"; ... ... Once again, there is an important technical point concerning Boolean expressions. In C++, "true" is represented simply as any non-zero integer, and "false" is represented as the value 0. This can lead to errors. For example, it is quite easy to type "=" instead of "==". Unfortunately, the program fragment ... ... if (number_of_people = 1) cout << "There is only one person.\n"; ... ... will always result in the message "There is only one person" being output to the screen, even if the previous value of the variable "number_of_people" was not 1. (BACK TO COURSE CONTENTS) 2.6 Summary In this lecture we have discussed variables in more detail. We have seen how variables are always of a particular data type, and have listed different ways in which variables may be temporarily or permanently assigned values. We have also seen how new values of various types can be generated by the use of operators. The material here is also covered in more detail in Savitch, Chapter 2, and Sections 4.2 and 4.5. Exercises