1. 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

2. 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

3. 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

4. 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 but your program should not rely on a given value but on the symbolic constant

5. 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”;

6. 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

7. 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.

8. 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

9. 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

10. 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); }

11. Random Problem? Running randtest twice gives same values
Why? rand function always returns same sequence of values on every execution
Why? So program behavior is repeatable for debugging
But - want non-deterministic behavior
Can modify behavior

12. Seeding Random Numbers
Initial value for random number generator same each time program is run
Next value depends on previous
Change initial value, change behavior
Function srand in stdlib allows seed
Using time from time.h allows “random” seed
srand( (int) time(NULL));
Provide operation in interface

13. Header files and implementation files
Example Random
Two steps:
Create an interface - random.h
Write implementation - random.cpp

14. Interface Contents Documentation on use Function prototypes
Constant definitions
Type definitions (later)
Three lines
at top: #ifndef _name_h #define _name_h
at end: #endif

15. Preliminary random.h #ifndef _random_h #define _random_h
/* Function: RandomInteger
* Usage: n = RandomInteger(low,high); *
* This function returns a random integer
* in the range low to high, inclusive. */
int RandomInteger(int low, int high);
#endif

16. Preliminary random.cpp
#include <stdlib> #include ”random.h” int RandomInteger(int low, int high) { int k; double d; d = rand() / ((double) RAND_MAX + 1); k = (int) (d * (high - low + 1)); return (low + k); }

17. Preliminary Client
/* Filename: randtest.cpp */ #include <iostream> #include ”random.h” int main(void) { int i; for (i = 0; i < 10; i++) cout << RandomInteger(1,6) << endl; return (0); }