# Visualizing sort algorithms with ggplot2

Just learning ggplot2 with inspiration from looking at Sorting Algorithms by Mike Bostock

ggplot2
data-visualization
Author

Joshua Kunst Fuentes

Published

September 25, 2015

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 algorithm and obvious it will fun to replicate that image with ggplot2 so here we go.

We need some sorts algorithms. In this link you can see some algorithms.

Code

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:

Code
set.seed(12345)

x <- sample(seq(4))

x
[1] 2 3 4 1
Code
msteps <- insertion_sort_steps(x)

as.data.frame(msteps)
V1 V2 V3 V4
1  2  3  4  1
2  2  3  1  4
3  2  1  3  4
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.

Code
sort_matix_to_df <- function(msteps){

df <- as.data.frame(msteps, row.names = NULL)

names(df) <- seq(ncol(msteps))

df_steps <- df %>%

mutate(step = seq(nrow(.))) %>%
gather(position, element, -step) %>%
arrange(step)

df_steps

}

And we apply this function to the previous steps matrix.

Code
df_steps <- sort_matix_to_df(msteps)

# A tibble: 10 × 3
step position element
<int> <chr>      <int>
1     1 1              2
2     1 2              3
3     1 3              4
4     1 4              1
5     2 1              2
6     2 2              3
7     2 3              1
8     2 4              4
9     3 1              2
10     3 2              1

The next step will be plot the data frame.

Code
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() +

theme(legend.position = "none")

}

Now compare this:

Code
V1 V2 V3 V4
1  2  3  4  1
2  2  3  1  4
3  2  1  3  4
4  1  2  3  4

With:

Code
plot_sort(df_steps, size = 6) +
geom_text(color = "white", size = 4)

It works, so we can now scroll!

Code
sample(seq(50)) %>%
insertion_sort_steps() %>%
sort_matix_to_df() %>%
plot_sort(size = 2.0)

Now try with other sort algorithms:

Bubble sort:

Code
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:

Code
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

}

Now test with a longer vector:

Code
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")
)

# A tibble: 6 × 4
step position element sort
<int> <chr>      <int> <chr>
1     1 1             10 Selection Sort
2     1 2             43 Selection Sort
3     1 3             27 Selection Sort
4     1 4             34 Selection Sort
5     1 5             44 Selection Sort
6     1 6             35 Selection Sort
Code
big_df %>%
group_by(sort) %>%
summarise(steps = n())
# A tibble: 3 × 2
sort            steps
<chr>           <int>
1 Bubble Sort    120100
2 Insertion Sort  32100
3 Selection Sort   2500
Code

big_df,
aes(step, position, group = element, color = element, label = element)
) +
geom_path(size = 0.8, alpha = 1, lineend = "round") +
facet_wrap(~sort, scales = "free_x", ncol = 1) +

legend.position = "none",
strip.background = element_rect(fill = "transparent", linetype = 0),
strip.text = element_text(size = 8)
)

Or we can plot vertically using the viridis palette from the viridis package :

Code

big_df,
aes(position, step, group = element, color = element, label = element)
) +
geom_path(size = 1, alpha = 1, lineend = "round") +
facet_wrap(~sort, scales = "free_y", nrow = 1) +

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 ;).

References:

1. http://bost.ocks.org/mike/algorithms/
2. http://faculty.cs.niu.edu/~hutchins/csci230/sorting.htm
3. http://corte.si/posts/code/visualisingsorting/
5. http://algs4.cs.princeton.edu/21elementary/

## Citation

BibTeX citation:
@online{kunstfuentes2015,
author = {Joshua Kunst Fuentes},
title = {Visualizing Sort Algorithms with Ggplot2},
date = {2015-09-25},
url = {https://jkunst.com/blog/posts/2015-09-25-visualizing-sort-algorithms-with-ggplot2},
langid = {en}
}