VIEWS: 13 PAGES: 13 POSTED ON: 8/31/2011
Random Numbers Adopted From EE/CS 498 Andrew Morgan University of Michigan 1 Random Numbers Random numbers are often very important in programming Suppose you are writing a program to play the game of roulette The numbers that come up on the roulette wheel are random Writing a program such that the numbers that come up the same every time doesn't make for a very interesting roulette game What about computerized slot machines? 2 Computers and Random Numbers Computers are “deterministic” machines Computers can not generate truly "random" numbers Instead, pseudo-random numbers are used Pseudo-random numbers are generated using a mathematical formula There is a pattern in pseudo-random numbers The pattern is nearly impossible to observe 3 Advantage of Psuedo-Randomness It is difficult to debug programs that use truly random numbers By providing the same start-value (seed) to the generator, the same sequence results When you are through debugging, you can use a different seed each time. Often, this is done by using a portion of the system clock 4 Random #s in C++ The <cstdlib> header file should be includedd Functions provided: void srand(unsigned int seed); This function sets the seed for the random number generator to the value of the seed parameter int rand(); This function generates and returns an integer value in the range 0..RAND_MAX (which is a defined constant in cstdlib) 5 Random #s in C++ srand() is usually only called ONE time rand() is called every time a random number is desired If you want a number between 0 and N val = rand() % (N+1) If you want a number with a range M..N val = rand() % (N-M+1) + M 6 #include <cstdlib> //req'd for srand and rand #include <iostream> //req'd for cout and cin using namespace std; srand() is usually called only one time to start a sequence int main() { double avg = 0.0; rand() is called each time a int i, minX = 30, maxX = 50; pseudo-random number int randVal, seed; is needed cout << "Enter seed: "; cin >> seed; srand(seed); for (i = 0; i < 10; i++) { randVal = rand() % (maxX - minX + 1) + minX; cout << randVal << endl; } for (i = 0; i < 10000; i++) { avg += rand() % (maxX - minX + 1) + minX; } avg = avg / 10000; cout << "Avg of 10000: " << avg << endl; return (0); } 7 Enter seed: 12 Enter seed: 1652 Enter seed: 12 42 38 42 46 32 46 40 43 40 41 43 41 40 36 40 43 48 43 32 34 32 38 48 38 31 31 31 42 49 42 Avg of 10000: 39.9971 Avg of 10000: 40.0484 Avg of 10000: 39.9971 Note: Same seed = same sequence = same results 8 C++ Random # Generator The C++ random number generator DOES produce a repeating sequence of pseudo- random numbers The "period" of the generator is so large, though, that it is not usually a problem The "period" of a random number generator is how large the pattern that repeats is 32 C++'s random number generator has a period of 2 rand() will re-start the same repeating sequence after generating about 4.3 billion random numbers This is large enough for most applications requiring random number generation 9 //include iostream, cstdlib, and cmath int main() RANDOM #12662 { RANDOM #23392 long int stopX; srand(100); RANDOM #12662 stopX = (long int)pow(2, 32) - 1; RANDOM #23392 long int li; RANDOM #12662 RANDOM #23392 cout << "RANDOM #" << rand() << endl; cout << "RANDOM #" << rand() << endl; for (li = 0; li < stopX; li++) rand(); While the pattern DOES cout << "RANDOM #" << rand() << endl; repeat, there are about cout << "RANDOM #" << rand() << endl; 4.3 billion "random" for (li = 0; li < stopX; li++) rand(); numbers generated cout << "RANDOM #" << rand() << endl; in the pattern. cout << "RANDOM #" << rand() << endl; (This program took about return (0); 29 minutes of time to run) } 10 Using Time to Seed the Generator If you hard code the seed or allow the user to enter a seed, simulated randomness is lost Most programmers use the “time” function to seed the generator This lessens the probability that a user can determine the pattern of psuedo-random numbers 11 Using Time to Seed the Generator Must include the <time.h> library Provides function “time( )” Calling function “time( )” time( NULL ) Returns the current time from the system clock Expressed in number of seconds elapsed since 00:00 hours, Jan 1, 1970 UTC 12 #include <cstdlib> //req'd for srand and rand #include <iostream> //req'd for cout and cin #include <time.h> //req’d for time srand() is usually called only using namespace std; one time to start a sequence int main() { Using the clock to seed the double avg = 0.0; generator instead of user input int i, minX = 30, maxX = 50; int randVal, seed; rand() is called each time a srand( time(NULL) ); pseudo-random number for (i = 0; i < 10; i++) is needed { randVal = rand() % (maxX - minX + 1) + minX; cout << randVal << endl; } for (i = 0; i < 10000; i++) { avg += rand() % (maxX - minX + 1) + minX; } avg = avg / 10000; cout << "Avg of 10000: " << avg << endl; return (0); } 13