1. CSci 162 Lecture 7 Martin van Bommel

2. 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

3. 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

4. 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

5. Pseudo-random number in C++ 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

6. 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 Use if (rand() <= RAND_MAX / 2) cout << ”Heads”; else cout << ”Tails”;

7. 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

8. Using “rand” to Roll a Die int 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.

9. 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

10. Generalize the Problem Want a function to choose random number between two values, inclusive int RandomInteger(int low, int high); Four-step process 1. Normalize rand to number d where 0 <= d < 1 2. Scale d by multiplying by size of desired range 3. Truncate number back to an integer 4. Translate integer so range begins at lower bound

11. 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); }