CSci 162

Lecture 7

Martin van Bommel

Random Numbers

• Until now, all programs have behaved deterministically - completely predictable and repeatable based on input values

• Some applications (e.g. games) require unpredictable behavior - nondeterministic

• One method for nondeterminism die toss where one of several outcomes possible

Random Numbers

• Number is random if there is no way to determine in advance what value it will have among a set of equally probable possibilites

• E.g. on a standard unloaded die– random number between 1 and 6 equally possible

• Cannot generate number randomly on computer– uses deterministic behavior

Pseudo-random Numbers

• Use a deterministic procedure to generate “random” numbers

• Numbers must appear random– behave like random numbers statistically– be sufficiently difficult to predict in advance

• Random numbers generated by an algorithmic process by a computer are called pseudo-random numbers

Pseudo-random number in C++

• <cstdlib> includes function rand and constant RAND_MAX

• prototype int rand();• generates pseudo-random number between 0 and RAND_MAX, inclusive

• Value of RAND_MAX depends on system• Ours uses 32 767 but your program should not

rely on a given value but on the symbolic constant

Using “rand” to flip a coin

• Want to use the result of rand that is a number between 0 and RAND_MAX to generate Heads or Tails

• Useif (rand() <= RAND_MAX / 2) cout << ”Heads”;else cout << ”Tails”;

Wrong Method to flip a coin

• Why not use:if (rand() % 2 == 0) cout << ”Heads”;etc.

• No guarantee of distribution of even and odd numbers, only even distribution along the range 0 to RAND_MAX

Using “rand” to Roll a Dieint RollDie(void){ if (rand() < RAND_MAX / 6) return 1;if (rand() < RAND_MAX*2/6) return 2;if (rand() < RAND_MAX*3/6) return 3;if (rand() < RAND_MAX*4/6) return 4;if (rand() < RAND_MAX*5/6) return 5;return 6;

}• Unfortunately uses new value of “rand” in each

“if”, thus losing original.

Using “rand” to Roll a Die (2)int RollDie(){ int r = rand();if (r < RAND_MAX / 6) return 1;if (r < RAND_MAX*2/6) return 2;if (r < RAND_MAX*3/6) return 3;if (r < RAND_MAX*4/6) return 4;if (r < RAND_MAX*5/6) return 5;return 6;

}• Unfortunately RAND_MAX*2/6 gives strange value due to

integer arithmetic• Better to use RAND_MAX/6.0*2.0

Generalize the Problem

• Want a function to choose random number between two values, inclusive int RandomInteger(int low, int high);

• Four-step process1. Normalize rand to number d where 0 <= d < 12. Scale d by multiplying by size of desired range3. Truncate number back to an integer4. Translate integer so range begins at lower bound

RandomInteger

int RandomInteger(int low, int high){ int k; double d;

d = rand() / ((double) RAND_MAX + 1.0); k = (int) (d * (high - low + 1)); return (low + k);}