riddler-circular-table.Rmd

---
title: "Untitled"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## R Markdown

0 is you, 1 is the person to your right, 19 is the person to your left

```{r}
library(tidyverse)
library(scales)
theme_set(theme_light())

cumsum(sample(c(1, -1), 20, replace = TRUE)) %% 20

sim_full <- crossing(trial = 1:10000,
                     step = 1:1200) %>%
  mutate(direction = sample(c(1, -1), n(), replace = TRUE)) %>%
  group_by(trial) %>%
  mutate(position = cumsum(direction)) %>%
  ungroup() %>%
  crossing(table_size = c(5, 10, 20, 30)) %>%
  mutate(seat = position %% table_size)

sim <- sim_full %>%
  distinct(table_size, trial, seat, .keep_all = TRUE) %>%
  filter(seat != 0)
```

```{r}
by_seat <- sim %>%
  group_by(table_size, trial) %>%
  mutate(is_last = row_number() == table_size - 1) %>%
  group_by(table_size, seat) %>%
  summarize(avg_step = mean(step),
            pct_last = mean(is_last),
            avg_length_last = mean(step[is_last]))

by_seat %>%
  ggplot(aes(seat, avg_step, color = factor(table_size))) +
  geom_line() +
  expand_limits(y = 0) +
  labs(x = "Seat",
       y = "Average # of steps to reach this seat",
       color = "Table size")

by_seat %>%
  ggplot(aes(seat, pct_last, color = factor(table_size))) +
  geom_line() +
  geom_hline(aes(yintercept = 1 / (table_size - 1), color = factor(table_size)),
             lty = 2) +
  scale_y_continuous(labels = percent) +
  expand_limits(y = 0) +
  labs(x = "Seat",
       y = "% this is the last seat to get cranberry sauce",
       color = "Table size")

by_seat %>%
  mutate(seat = seat - 1) %>%
  group_by(table_size) %>%
  summarize(mod = list(lm(avg_step ~ I(seat ^ 2) + seat)),
            td = map(mod, broom::tidy)) %>%
  unnest(td)

# - seat ^ 2 + 20 * seat - .22

# Maximum is (table_size / 2) ^ 2

sim %>%
  ggplot(aes(step)) +
  geom_histogram() +
  facet_wrap(~ seat, scales = "free_y") +
  labs(x = "Step on which this seat gets the cranberry sauce")

last_steps <- sim %>%
  group_by(trial) %>%
  slice(19) %>%
  ungroup() %>%
  select(table_size, trial, last_step = step, last_seat = seat)

last_steps %>%
  filter(table_size == 20,
         last_seat %in% c(1, 5, 10, 15))
  inner_join(sim_full, by = c("trial") %>%
  filter(step <= last_step) %>%
  ggplot(aes(step, position, group = trial)) +
  geom_line() +
  facet_wrap(~ last_seat)
```