(This article was first published on Jkunst - R category , and kindly contributed to R-bloggers)
Have you read Visualizing Algorithms by Mike Bostock? It's a pure gold post.
In that post Mike show a static representation of a sort algorith and obvious it will fun to replicate that image
with ggplot. So here we go.
We need some sorts algorihms. In this link you can
see some algorithms.
We start with Insertion Sort:
insertion_sort_steps <- function(x = sample(1:15)){
msteps <- matrix(data = x, ncol = length(x))
for (i in 2:length(x)) {
j <- i
while ((j > 1) && (x[j] < x[j - 1])) {
temp <- x[j]
x[j] <- x[j - 1]
x[j - 1] <- temp
j <- j - 1
msteps <- rbind(msteps, as.vector(x))
}
}
msteps
}
Now to test it and see what the function do:
set.seed(12345)
x <- sample(seq(4))
x
## [1] 3 4 2 1
msteps <- insertion_sort_steps(x)
as.data.frame(msteps)
| V1 | V2 | V3 | V4 |
|---|---|---|---|
| 3 | 4 | 2 | 1 |
| 3 | 2 | 4 | 1 |
| 2 | 3 | 4 | 1 |
| 2 | 3 | 1 | 4 |
| 2 | 1 | 3 | 4 |
| 1 | 2 | 3 | 4 |
Every row is a step in sort the algorithm (a partial sort). This matrix is a hard to plot so
we need a nicer structure. We can transform the matrix to a data_frame
with the information of every position of every element in each step.
sort_matix_to_df <- function(msteps){
df <- as.data.frame(msteps, row.names = NULL)
names(df) <- seq(ncol(msteps))
df_steps <- df %>%
tbl_df() %>%
mutate(step = seq(nrow(.))) %>%
gather(position, element, -step) %>%
arrange(step)
df_steps
}
And we apply this function to the previous steps matrix.
df_steps <- sort_matix_to_df(msteps)
head(df_steps, 10)
| step | position | element |
|---|---|---|
| 1 | 1 | 3 |
| 1 | 2 | 4 |
| 1 | 3 | 2 |
| 1 | 4 | 1 |
| 2 | 1 | 3 |
| 2 | 2 | 2 |
| 2 | 3 | 4 |
| 2 | 4 | 1 |
| 3 | 1 | 2 |
| 3 | 2 | 3 |
The next step will be plot the data frame.
plot_sort <- function(df_steps, size = 5, color.low = "#D1F0E1", color.high = "#524BB4"){
ggplot(df_steps,
aes(step, position, group = element, color = element, label = element)) +
geom_path(size = size, alpha = 1, lineend = "round") +
scale_colour_gradient(low = color.low, high = color.high) +
coord_flip() +
scale_x_reverse() +
theme(legend.position = "none")
}
Now compare this:
as.data.frame(msteps)
| V1 | V2 | V3 | V4 |
|---|---|---|---|
| 3 | 4 | 2 | 1 |
| 3 | 2 | 4 | 1 |
| 2 | 3 | 4 | 1 |
| 2 | 3 | 1 | 4 |
| 2 | 1 | 3 | 4 |
| 1 | 2 | 3 | 4 |
With:
plot_sort(df_steps, size = 6) + geom_text(color = "white", size = 4)
It works, so we can now scroll!
sample(seq(70)) %>%
insertion_sort_steps() %>%
sort_matix_to_df() %>%
plot_sort(size = 2.2)
Now try with other sort algorithms:
Bubble sort:
bubble_sort_steps <- function(x = sample(1:15)){
msteps <- matrix(data = x, ncol = length(x))
for (i in 1:(length(x) - 1)) {
for (j in 1:(length(x) - 1)) {
if (x[j] > x[j + 1]) {
temp <- x[j]
x[j] <- x[j + 1]
x[j + 1] <- temp
}
msteps <- rbind(msteps, as.vector(x))
}
}
msteps
}
Selection sort:
selection_sort_steps <- function(x = sample(1:15)){
msteps <- matrix(data = x, ncol = length(x))
for (i in 1:(length(x) - 1)) {
smallsub <- i
for (j in (i + 1):(length(x) - 0)) { # Is not '- 1' like website
if (x[j] < x[smallsub]) {
smallsub <- j
}
}
temp <- x[i]
x[i] <- x[smallsub]
x[smallsub] <- temp
msteps <- rbind(msteps, as.vector(x))
}
msteps
}
And test with a longer vector:
n <- 50
x <- sample(seq(n))
big_df <- rbind(
x %>% selection_sort_steps() %>% sort_matix_to_df() %>% mutate(sort = "Selection Sort"),
x %>% insertion_sort_steps() %>% sort_matix_to_df() %>% mutate(sort = "Insertion Sort"),
x %>% bubble_sort_steps() %>% sort_matix_to_df() %>% mutate(sort = "Bubble Sort")
)
head(big_df)
| step | position | element | sort |
|---|---|---|---|
| 1 | 1 | 3 | Selection Sort |
| 1 | 2 | 31 | Selection Sort |
| 1 | 3 | 47 | Selection Sort |
| 1 | 4 | 49 | Selection Sort |
| 1 | 5 | 24 | Selection Sort |
| 1 | 6 | 7 | Selection Sort |
big_df %>%
group_by(sort) %>%
summarise(steps = n())
| sort | steps |
|---|---|
| Bubble Sort | 120100 |
| Insertion Sort | 30700 |
| Selection Sort | 2500 |
ggplot(big_df,
aes(step, position, group = element, color = element, label = element)) +
geom_path(size = 0.8, alpha = 1, lineend = "round") +
scale_colour_gradient(low = "#c21500", high = "#ffc500") + # http://uigradients.com/#Kyoto
facet_wrap(~sort, scales = "free_x", ncol = 1) +
theme(legend.position = "none",
strip.background = element_rect(fill = "transparent", linetype = 0),
strip.text = element_text(size = 8))
Or we can plot vertical using the viridis package:
ggplot(big_df,
aes(position, step, group = element, color = element, label = element)) +
geom_path(size = 1, alpha = 1, lineend = "round") +
scale_colour_gradientn(colours = viridis_pal()(n)) +
facet_wrap(~sort, scales = "free_y", nrow = 1) +
scale_y_reverse() +
theme(legend.position = "none",
strip.background = element_rect(fill = "transparent", linetype = 0),
strip.text = element_text(size = 8))
And that's it. If you write/implement another sort algorithm in this way let me know to view it ;).
Some bonus content :D.
References:
- http://bost.ocks.org/mike/algorithms/
- http://faculty.cs.niu.edu/~hutchins/csci230/sorting.htm
- http://corte.si/posts/code/visualisingsorting/
- http://uigradients.com/#Kyoto
- http://algs4.cs.princeton.edu/21elementary/
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