How to find the start and the end of sequences automatically in R for rectangles in ggplot

Here is an approach using run length encoding.

library(ggplot2)

df <- data.frame(time  = seq(0.1, 2, 0.1), 
                 speed = c(seq(0.5, 5, 0.5), seq(5, 0.5, -0.5)),
                 type  = c("a", "a", "b", "b", "b", "b", "c", "c", "c", "b", "b", "b", "b", "b", "c", "a", "b", "c", "b", "b"))

# Convert to runlength encoding
rle <- rle(df$type == "b")

# Ignoring the single "b"s
rle$values[rle$lengths == 1 & rle$values] <- FALSE

# Determine starts and ends
starts <- {ends <- cumsum(rle$lengths)} - rle$lengths + 1

# Build a data.frame from the rle
dfrect <- data.frame(
  xmin = df$time[starts],
  # We have to +1 the ends, because the linepieces end at the next datapoint
  # Though we should not index out-of-bounds, so we need to cap at the last end
  xmax = df$time[pmin(ends + 1, max(ends))],
  fill = rle$values
)

This plot gives an idea what we've been doing in the code above:

ggplot() +
  geom_rect(data = dfrect, 
            aes(xmin = xmin, xmax = xmax, ymin = -Inf, ymax = Inf, fill = fill), 
            alpha = 0.4) +
  geom_line(data = df, aes(x = time, y = speed, color = type, group = 1), size = 3)

To get what you want you'd need to filter out the FALSEs.

ggplot() +
  geom_rect(data = dfrect[dfrect$fill,], 
            aes(xmin = xmin, xmax = xmax, ymin = -Inf, ymax = Inf), 
            alpha = 0.4, fill = "yellow") +
  geom_line(data = df, aes(x = time, y = speed, color = type, group = 1), size = 3)

If you are looking for a stat that can calculate this for you, have a look here. Disclaimer: I wrote that function, which does a similar thing to the code I posted above.

Another approach with rle, but using data.table::rleid.

The pivoting idea is from Stefan!

I am sure the pipe could be further shortened somehow

library(tidyverse)
df <- data.frame(
  time = seq(0.1, 2, 0.1),
  speed = c(seq(0.5, 5, 0.5), seq(5, 0.5, -0.5)),
  type = c("a", "a", "b", "b", "b", "b", "c", "c", "c", "b", "b", "b", "b", "b", "c", "a", "b", "c", "b", "b")
)
dfRect <-
  df %>%
  arrange(time, type) %>%
  mutate(id = data.table::rleid(type)) %>%
  group_by(type, id) %>%
  slice(c(1, n())) %>%
  distinct(time, id) %>%
  filter(type == "b" & n() > 1) %>%
  mutate(row = row_number()) %>%
  pivot_wider(names_from = row, names_prefix = "x", values_from = time)

ggplot() +
  geom_rect(
    data = dfRect,
    aes(xmin = x1, xmax = x2, ymin = -Inf, ymax = Inf),
    fill = "yellow", alpha = 0.4
  ) +
  geom_line(data = df, aes(x = time, y = speed, color = type, group = 1), size = 3)

Try this. I added some explanatory comments inside the code:

library(dplyr)
library(tidyr)
library(ggplot2)

df <- data.frame(time  = seq(0.1, 2, 0.1), 
                 speed = c(seq(0.5, 5, 0.5), seq(5, 0.5, -0.5)),
                 type  = c("a", "a", "b", "b", "b", "b", "c", "c", "c", "b", "b", "b", "b", "b", "c", "a", "b", "c", "b", "b"))

dfRect <- df %>% 
  arrange(time, type) %>% 
  # Get start and end of sequences
  mutate(is_b_start = type == "b" & lag(type) != "b",
         is_b_end = type != "b" & lag(type) == "b") %>% 
  filter(is_b_start | is_b_end) %>%
  # Get id of sequences
  mutate(id = cumsum(is_b_start),
         type = ifelse(is_b_start, "min", "max")) %>% 
  select(time, id, type) %>%
  # To wide format gives xmin and xmax for each sequence 
  tidyr::pivot_wider(names_from = type, names_prefix = "x", values_from = time) %>% 
  # In case: Fill last with max time
  tidyr::replace_na(list(xmax = max(df$time)))
  
ggplot() +
  geom_rect(data = dfRect, 
            aes(xmin = xmin, xmax = xmax, ymin = -Inf, ymax = Inf), 
            fill = "yellow", alpha = 0.4) +
  geom_line(data = df, aes(x = time, y = speed, color = type, group = 1), size = 3)

^{Created on 2020-06-21 by the reprex package (v0.3.0)}