#include pps/lrblib.tc
#include pps/library.tc

// socks.try.tc.2 - lrb - 6/28/23

[
This program simulates the drawing of single socks from a bureau. You
specify the number of different colors of socks you have. You continue
to draw single socks until you have two pairs. e.g. two whites and two
blues, or four whites. It can been shown that the worst case for c
colors and f feet is 2f+(c-1)(f-1) socks. If you have 3 colors and 2
feet, you need to draw 6 socks to guarantee you have two pair. You need
to draw 19 socks if you have 16 colors to guarantee you have two pair.

The average number of socks you draw to get your two pair is
substantially fewer than the number that will guarantee you have two
pair. e.g. the average is about 9 when there are 16 colors.

We now support bipeds, quadrupeds, fleas, spiders, centipedes, tripedes, etc.
]

int debug,nc,sims,ap

d [debug=1;main]

test [
 debug=1
 nc=2;sims=300;ap=6;last=seed=31
 printf "%c%ccolors=%d sims=%d feet=%d seed=%d%c",10,10,nc,sims,ap,seed,10
 main
 sak
 nc=3;sims=300;ap=6;last=seed=27
 printf "%c%ccolors=%d sims=%d feet=%d seed=%d%c",10,10,nc,sims,ap,seed,10
 main
 sak
 nc=4;sims=300;ap=6;last=seed=141
 printf "%c%ccolors=%d sims=%d feet=%d seed=%d%c",10,10,nc,sims,ap,seed,10
 main
 sak
 ]

main [
 int fa(5000),sa(5000),sp,msp,mpc,i,j,total,x // 1/5,7,9/23
 int pairs;pairs=2 // 1/9/23
 char foo(20),bar(20),pair(500) // 1/14/23
 msp=0 // initialize max socks picked
 printf "%csocks.try.tc.2 - lrb - 6/28/23%c",10,10
 if nc==0 [
  printf "%cNumber of colors (between 2 and 16) : ",10;nc=gn
  printf "%cNumber of simulations (1 to 1000) : ",10;sims=gn
  printf "%cNumber of feet (humans 2, dogs 4, fleas 6, spiders 8, centipedes 100) : ",10
  ap=gn
  printf "%cSeed the random number generator with some odd number (e.g. 271) : ",10
  last=seed=gn
  ]
 printf "%cCalculating ...%c",10,10 // 1/9/23
 char time(20) // 1/9/23
 cdate time // 1/9/23
 printf "%cstart time : %s%c%c",10,time,10,10 // 1/9/23
 while i<sims [ // 1/9/23
  mpc=0;j=1
  while j<=nc [sa(j)=0;j=j+1]
  sp=0
  while mpc<pairs [ // loop while matched pair count is less than pairs - 1/9/23
   sp=sp+1 // bump socks picked
   x=random(1,nc)
   sa(x)=sa(x)+1 // add 1 to a random bucket
   j=1
   while j<=nc [
    if (sa(j)==ap) [ // when pair found
     mpc=mpc+1;sa(j)=0 // bump matched pair count, clear bucket
     break // and get out
     ]
    j=j+1
    ]
   ]
  if sp>msp msp=sp // update max socks picked
  fa(sp)=fa(sp)+1 // update frequency array
  total=total+sp // keep track of total socks pulled
  if debug printf "%d ",i
  i=i+1
  ]
 printf "%c%cNumber of simulations was %d",10,10,sims // 1/9/23
 printf "%c%cAverage number of socks picked was %d",10,10,total/sims;dpf total%sims,sims,5 // 1/9/23
 printf "%c%c",10,10
 j=pairs*ap // 1/9/23
 while j<=msp [
  if fa(j) [
   printf "%d,%d ",j,fa(j)
   itoa j,foo
   itoa fa(j),bar
   strcat pair,foo;strcat pair,",";strcat pair,bar;strcat pair," "
   ]
  j=j+1
  ]
 printf "%c%cThe worst-case scenario is %d%c",10,10,pairs*ap+(ap-1)*(nc-1),10 // 1/9/23
 cdate time
 printf "%cstop time : %s%c",10,time,10 // 1/9/23
 char tcbuff(40),os(30);int linux // 1/11/23
 getproperty "pps/version.prop", "os =", tcbuff, 40, "..."
 strcpy os, tcbuff
 if (index(os, strlen(os), "Linux", 5)) linux = 1
 if linux [
  ]
 else [
  ]
 ]