Simulation of Riddler Gym

gistfile1.txt

hi!

Thank you again for taking a look -- I'm trying to improve my simulation skills and curious where I might have the logic or intuition wrong with this riddler exercise

```{r}
library(tidyverse)


total_minutes <- 3*180

incremental_minutes <- total_minutes*.01

gym <- function(){

  
  # create grid  of gym participants -- everyone's ID correspondents to the   # % of time they spend in the gym
  
  grid <- tibble(
  id=1:100
  ,availability=id/100
  ,total_gym_availability=total_minutes
  ,participant_minutes=total_minutes*availability
  )


simulation <- grid %>% 
  rowwise() %>% 
  mutate(
    avail_time=total_minutes-participant_minutes # available time window to participate
    ,avail_increments=avail_time/participant_minutes # the chunk they can participate
    ,start_time=sample(c(1:avail_increments),1)*incremental_minutes # random gym entry time within the window
    ,exit_time=min(start_time+participant_minutes,total_minutes) # when they leave the gym
    ,total_duration=exit_time-start_time # total time in gym
    ,check_ratio=total_duration/total_minutes # validate total time by proportion
  ) %>% 
  mutate(
    timeframe=list(seq.int(from=1,to=total_minutes,by = 1)) # create timeframe minute by minute
  ) %>% 
  unnest(timeframe) %>% 
  ungroup() %>% 
  mutate(
    gym_indicator= # indicator for when a participant was in the gym by timeframe
      case_when(
        start_time<=timeframe&timeframe<=exit_time~1
        ,TRUE~0
      )
  ) %>% 
  select(id,availability,timeframe,gym_indicator)


# extract the time window of when 'I' went to the gym
window <- simulation %>% 
  filter(
  id==50
  ,gym_indicator==1
  ) %>% 
  pull(timeframe) 

# filter those gym goers that are in the gym at the same time as me
paricipants_in_gym <- simulation %>% 
  filter(
    timeframe==min(window) & gym_indicator==1 #those participants that were there at the start of my time window and pull their ID numbers
    ,id!=50
  ) %>% pull(id)

# to validate the window range of the gym goe

# simulation %>% 
#   pivot_wider(
#     names_from = timeframe
#     ,values_from = gym_indicator
#     ,names_repair = janitor::make_clean_names
#   ) %>% 
#   relocate(id,availability,tidyselect::num_range("x",1:100)) %>% 
#   view()

# of everyone in the gym, sample at random who I meet first and check if there rank is over 50

results <- sample(paricipants_in_gym,1,replace = TRUE)>50


# returns a TRUE if over 50 and FALSE if under 50
return(results)


}


# replicate simulation 1000 times and take average of outcome
# runs slow -- probably many better ways to speed this up

out <- replicate(1000,gym())


mean(out)
```

fixed error