1. CSC 107 - Programming for Science Lecture 22: Random Numbers & Macros

2. Question of the Day On a game show you’re given the choice of three doors: Behind one door is a car; behind the others, goats. After you pick a door, the host, opens another door which has a goat. He then asks, "Do you change your selection?” Should you?

3. Proving This Solution After 1 experiments ---------------------- Sticking it out: 100.00% correct Switching doors: 0.00% correct After 1000 experiments ---------------------- Sticking it out: 34.10% correct Switching doors: 68.20% correct After 1000000 experiments ---------------------- Sticking it out: 33.40% correct Switching doors: 66.72% correct

4. Pseudo-random Numbers Computers are stupid & only follow orders  Cannot be random or do unexpected things Algorithm generates sequence of integers  No correlation between numbers in sequence  (One hopes) Sequence should be very long Numbers completely predictable  Just have to know the algorithm  Or wait long enough to see patterns repeat

5. Pseudo-random Numbers

6. Seeding Pseudo-random number generators rely upon a seed  Value used to start sequence of random numbers A seed always yields identical sequence of random numbers  Useful for testing & debugging code  Bad when comparing runs Usually seed with current time: srand(times(NULL));

7. rand() Pre-defined function  Prototype in stdlib.h Generates integer between 0 & RAND_MAX  RAND_MAX also from stdlib.h To generate a random number…  … between 0 - 5: (rand() % 6)  … between 5 - 10: (rand() % 6) + 5  … between -5 - 0: (rand() % 6) - 5  … between -25 - 25: (rand() % 51) - 25

8. Results For Staying correct = 0 for (i = 0; i < experiments; i++) { guess = rand() % 3 solution = rand() % 3 if (guess == solution) { correct += 1; } pct = correct /((double)experiments) * 100;

9. Results For Switching correct = 0 for (i = 0; i < experiments; i++) { guess = rand() % 3 solution = rand() % 3 if (guess != solution) { /* Other incorrect solution revealed, so switch to correct solution */ correct += 1; } pct = correct /((double)experiments) * 100;

10. Warning!!!! Many systems have bad rand() versions  Generates random numbers, …  … but randomness limited to largest digits So, remainders will not be that random  Recommend that they not be used Instead round random decimal numbers  Decimal numbers use those largest digits

11. Random Decimal Numbers No function generates random decimals  Just use rand() / (RAND_MAX + 0.0) To generate random decimal number…  … between 0 - 1: rand()/(RAND_MAX+0.0)  … between 0 - 5: rand()/(RAND_MAX+0.0)*5  … between -5 - 0: rand()/(RAND_MAX+0.0)*-5  … between -25 - 25: (rand()/(RAND_MAX+0.0)*50)-25

12. Symbolic Constants Pre-processor replaces name with value  Compiler only sees the constant value  Programmer only sees the name  Makes code far easier to read, write, debug Names traditionally in all CAPITAL letters

13. What You Write And Work With #define PI 3.1415962 #define AVOGADRO 6.022E23 #define MY_SHOE_SIZE 10.5 #define DUMB_EXAMPLE MY_SHOE_SIZE area = PI * (r * r); printf(“%lf”, MY_SHOE_SIZE); printf(“%lf”, DUMB_EXAMPLE);

14. #define AVOGADRO 6.022E23 #define MY_SHOE_SIZE 10.5 #define DUMB_EXAMPLE MY_SHOE_SIZE area = 3.1415962 * (r * r); printf(“%lf”, MY_SHOE_SIZE); printf(“%lf”, DUMB_EXAMPLE); #define MY_SHOE_SIZE 10.5 #define DUMB_EXAMPLE MY_SHOE_SIZE area = 3.1415962 * (r * r); printf(“%lf”, MY_SHOE_SIZE); printf(“%lf”, DUMB_EXAMPLE); #define DUMB_EXAMPLE 10.5 area = 3.1415962 * (r * r); printf(“%lf”, 10.5); printf(“%lf”, DUMB_EXAMPLE); area = 3.1415962 * (r * r); printf(“%lf”, 10.5); printf(“%lf”, 10.5); What The Compiler Sees #define PI 3.1415962 #define AVOGADRO 6.022E23 #define MY_SHOE_SIZE 10.5 #define DUMB_EXAMPLE MY_SHOE_SIZE area = 3.1415962 * (r * r); printf(“%lf”, MY_SHOE_SIZE); printf(“%lf”, DUMB_EXAMPLE);

15. Macros Powerful cousins of symbolic constants Shares similar traits with their relatives  Begin with #define  Must be only code on line (and fit one 1 line)  Name usually in all CAPITAL  Text replaced before compilation But can use parameters Value should be placed in parenthesis

16. Creating a Macro Macro can be very simple #define RAND_DEC (rand()/(RAND_MAX+0.0)) Macros can also take parameters #define SQUARED(x) (x * x) #define VELOCITY(init,a,t) (init+(a*t)) #define RAND_X(x) (rand() % x) #define RAND_RNG(lo,hi) ((rand()%(hi- lo))+lo) #define MAX(x,y) ((x > y) ? x : y) Parameters replaced during compilation  This will cause problems in code, be careful!

17. What You Write And Work With #define RAND_DEC (rand()/(RAND_MAX+0.0)) #define RAND_RNG(lo,hi) ((rand()%(hi- lo))+lo) #define MAX(x,y) ((x > y)? x : y) int i = RAND_RNG(4, 7); double rnd = RAND_DEC; int j = 6; printf(“%lf”, rnd); printf(“%d”, MAX(i, j++));

18. What the Compiler Sees #define RAND_RNG(lo,hi) ((rand()%(hi- lo))+lo) #define MAX(x,y) ((x > y)? x : y) int i = RAND_RNG(4, 7); double rnd = (rand()/(RAND_MAX+0.0)); int j = 6; printf(“%lf”, rnd); printf(“%d”, MAX(i, j++)); #define MAX(x,y) ((x > y)? x : y) int i = ((rand()%(7-4))+4); double rnd = (rand()/(RAND_MAX+0.0)); int j = 6; printf(“%lf”, rnd); printf(“%d”, MAX(i, j++)); int i = ((rand()%(7-4))+4); double rnd = (rand()/(RAND_MAX+0.0)); int j = 6; printf(“%lf”, rnd); printf(“%d”, (i > j++)? i : j++);

19. Your Turn Try doing following problems on your own

20. For Next Lecture Continue programming assignment #2  Now due next Wednesday – 11/01/06 Finish week #9 weekly assignment