CS221

Random Numbers

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 a real roulette wheel are

random Writing a program with predictable values doesn't make for a

very interesting roulette game We want to simulate randomness in the computer!

What about computerized slot machines?

Computers and Random Numbers

Computers are “deterministic” machines Computers are not capable of true

randomness 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

Advantage of Psuedo-Randomness

It would be difficult to debug programs that use truly random numbers (can’t recreate error cases on demand)

By providing the same start-value (seed) to the generator, the same sequence results on each run and error cases can be observed

When you are through debugging, you can use a different seed each time. Often, this is done by using the system clock

Random #s in C++

The <cstdlib> header file should be included 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)

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

#include <cstdlib> //req'd for srand and rand#include <iostream> //req'd for cout and cinusing namespace std;

int main(){ double avg = 0.0; int i, minX = 30, maxX = 50; int randVal, seed; 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);}

srand() is usually called onlyone time to start a sequence

rand() is called each time apseudo-random numberis needed

Enter seed: 1242464041404332383142Avg of 10000: 39.9971

Enter seed: 165238324343364834483149Avg of 10000: 40.0484

Enter seed: 1242464041404332383142Avg of 10000: 39.9971

Note: Same seed = same sequence = same results

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 C++'s random number generator has a period of 232

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

//include iostream, cstdlib, and cmathint main(){ long int stopX; srand(100); stopX = (long int)pow(2, 32) - 1; long int li;

cout << "RANDOM #" << rand() << endl; cout << "RANDOM #" << rand() << endl; for (li = 0; li < stopX; li++) rand(); cout << "RANDOM #" << rand() << endl; cout << "RANDOM #" << rand() << endl; for (li = 0; li < stopX; li++) rand(); cout << "RANDOM #" << rand() << endl; cout << "RANDOM #" << rand() << endl; return (0);}

RANDOM #12662RANDOM #23392RANDOM #12662RANDOM #23392RANDOM #12662RANDOM #23392

While the pattern DOESrepeat, there are about 4.3 billion "random"numbers generatedin the pattern.(This program took about29 minutes of time to run)

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

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

#include <cstdlib> //req'd for srand and rand#include <iostream> //req'd for cout and cin#include <time.h> //req’d for timeusing namespace std;

int main(){ double avg = 0.0; int i, minX = 30, maxX = 50; int randVal, seed; srand( time(NULL) );

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);}

srand() is usually called onlyone time to start a sequence

Using the clock to seed thegenerator instead of user input

rand() is called each time apseudo-random numberis needed