Day 4

Part 1

Given two ranges of numbers, we need to find how many ranges have a complete overlap.

library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.0      ✔ purrr   0.3.5 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.2.1      ✔ stringr 1.4.1 
✔ readr   2.1.3      ✔ forcats 0.5.2 
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

data <- read_csv("2022-12-4_assets/input.txt", col_names = FALSE)

Rows: 1000 Columns: 2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): X1, X2

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

elf_ranges <- 
  data |>
  separate(
    X1, 
    into = c("elf1_start", "elf1_end"),
    convert = TRUE
  ) |>
  separate(
    X2,
    into = c("elf2_start", "elf2_end"),
    convert = TRUE
  )

For two ranges of numbers, they overlap if

x1   .....   x2
   y1  .......  y2
   
x1 <= y2
y1 <= x2

overlaps <- 
  elf_ranges |>
  filter(elf1_start <= elf2_end,
         elf2_start <= elf1_end)

I think I have to use disjunction to find complete containment? Either

x1 .......... x2
   y1 ... y2
   
x1 <= y1 & x2 >= y2 || y1 <= x1 & y2 >= x2

overlaps |>
  filter((elf1_start <= elf2_start & elf1_end >= elf2_end) | 
           (elf2_start <= elf1_start & elf2_end >= elf1_end)) |>
  nrow()

[1] 441

Part 2

Hah! Got the number of overlaps first!

overlaps |> nrow()

[1] 861

Just for Fun

library(showtext)

Loading required package: sysfonts

Loading required package: showtextdb

library(ggdark)
library(scales)

Attaching package: 'scales'

The following object is masked from 'package:purrr':

    discard

The following object is masked from 'package:readr':

    col_factor

library(khroma)

font_add_google(name = "Mountains of Christmas", family = "christmas")
showtext_auto()

theme_set(dark_theme_gray() + 
            theme(title = element_text(family = "christmas", size = 20)))

Inverted geom defaults of fill and color/colour.
To change them back, use invert_geom_defaults().

overlaps |>
  rowwise() |>
  mutate(overlap_start = max(c(elf1_start, elf2_start)),
         overlap_end = min(c(elf1_end, elf2_end)),
         overlap_df = map2(overlap_start, overlap_end, ~tibble(position = .x:.y))) |>
  select(overlap_df) |>
  unnest(overlap_df) |>
  ggplot(aes(position))+
    stat_bin(binwidth = 1,
             aes(y = after_stat(count), 
                 fill = after_stat(count))) +
    stat_density(aes(y = after_stat(count),
                     linewidth = after_stat(count)), 
                 geom = "path")+
    scale_fill_oslo(guide = "none")+
    scale_linewidth(guide = "none")+
    labs(title = "overlap by position")

Figure 1: Degree of overlap by position