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same output. But it is possible to generate numbers that appear to be randomly generated; i.e., numbers that are uniformly distributed within a given interval and for which there is no discernible pattern. Such numbers are called pseudo-random numbers. The Standard C header file <cstdlib> defines the function rand() which generates pseudo-random integers in the range 0 to RAND_MAX, which is a constant that is also defined in <cstdlib>. Each time the rand() function is called, it generates another unsigned integer in this range. EXAMPLE 4.26 Generating Pseudo-Random Numbers
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This program uses the rand() function to generate pseudo-random numbers: #include <cstdlib> // defines the rand() function and RAND_MAX const #include <iostream> using namespace std;
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int main() { // prints pseudo-random numbers: for (int i = 0; i < 8; i++) cout << rand() << endl; cout << "RAND_MAX = " << RAND_MAX << endl; } 1103527590 377401575 662824084 1147902781 2035015474 368800899 1508029952 486256185 RAND_MAX = 2147483647 1103527590 377401575 662824084 1147902781 2035015474 368800899 1508029952 486256185 RAND_MAX = 2147483647
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On each run, the computer generates 8 unsigned integers that are uniformly distributed in the interval 0 to RAND_MAX, which is 2,147,483,647 on this computer. Unfortunately each run produces the same sequence of numbers. This is because they are generated from the same seed.
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Each pseudo-random number is generated from the previously generated pseudo-random number by applying a special number crunching function that is defined internally. The first pseudo-random number is generated from an internally defined variable, called the seed for the sequence. By default, this seed is initialized by the computer to be the same value every time the program is run. To overcome this violation of pseudo-randomness, we can use the srand() function to select our own seed.
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EXAMPLE 4.27 Setting the Seed Interactively
This program is the same as the one in Example 4.26 except that it allows the pseudo-random number generator s seed to be set interactively: #include <cstdlib> // defines the rand() and srand() functions #include <iostream> using namespace std;
int main() { // prints pseudo-random numbers: unsigned seed; cout << "Enter seed: "; cin >> seed; srand(seed); for (int i = 0; i < 8; i++) cout << rand() << endl; } Enter seed: 0 12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 Enter seed: 1 1103527590 377401575 662824084 1147902781 2035015474 368800899 1508029952 486256185 Enter seed: 12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793
// initializes the seed
The line srand(seed) assigns the value of the variable seed to the internal seed used by the rand() function to initialize the sequence of pseudo-random numbers that it generates. Different seeds produce different results. Note that the seed value 12345 used in the third run of the program is the first number generated by rand() in the first run. Consequently the first through seventh numbers generated in the third run are the same as the second through eighth numbers generated in the first run. Also note that the sequence generated in the second run is the same as the one produced in Example 4.26. This suggests that, on this computer, the default seed value is 1.
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The problem of having to enter a seed value interactively can be overcome by using the computer s system clock. The system clock keeps track of the current time in seconds. The time() function defined in the header file <ctime> returns the current time as an unsigned integer. This then can be used as the seed for the rand() function. EXAMPLE 4.28 Setting the Seed from the System Clock
This program is the same as the one in Example 4.27 except that it sets the pseudo-random number generator s seed from the system clock. Note: if your compiler does not recognize the <ctime> header, then use the pre-standard <time.h> header instead. #include <cstdlib> // defines the rand() and srand() functions #include <ctime> // defines the time() function #include <iostream> //#include <time.h> // use this if <ctime> is not recognized using namespace std; int main() { // prints pseudo-random numbers: unsigned seed = time(NULL); // uses the system clock cout << "seed = " << seed << endl; srand(seed); // initializes the seed for (int i = 0; i < 8; i++) cout << rand() << endl; } Here are two runs using a UNIX workstation running a Motorola processor: seed = 808148157 1877361330 352899587 1443923328 1857423289 200398846 1379699551 1622702508 715548277 seed = 808148160 892939769 1559273790 1468644255 952730860 1322627253 1305580362 844657339 440402904 On the first run, the time() function returns the integer 808,148,157 which is used to seed the random number generator. The second run is done 3 seconds later, so the time() function returns the integer 808,148,160 which generates a completely different sequence. Here are two runs using a Windows PC running an Intel processor:
In many simulation programs, one needs to generate random integers that are uniformly distributed in a given range. The next example illustrates how to do that.
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