Data Frame Manipulation with tidyr

Overview

Teaching: 30 min
Exercises: 15 min

Questions

How can I change the layout of a data frame?

Objectives

To understand the concepts of ‘longer’ and ‘wider’ data frame formats and be able to convert between them with tidyr.

Researchers often want to reshape their data frames from ‘wide’ to ‘longer’ layouts, or vice-versa. The ‘long’ layout or format is where:

each column is a variable
each row is an observation

In the purely ‘long’ (or ‘longest’) format, you usually have 1 column for the observed variable and the other columns are ID variables.

For the ‘wide’ format each row is often a site/subject/patient and you have multiple observation variables containing the same type of data. These can be either repeated observations over time, or observation of multiple variables (or a mix of both). You may find data input may be simpler or some other applications may prefer the ‘wide’ format. However, many of R’s functions have been designed assuming you have ‘longer’ formatted data. This tutorial will help you efficiently transform your data shape regardless of original format.

Diagram illustrating the difference between a wide versus long layout of a data frame

Long and wide data frame layouts mainly affect readability. For humans, the wide format is often more intuitive since we can often see more of the data on the screen due to its shape. However, the long format is more machine readable and is closer to the formatting of databases. The ID variables in our data frames are similar to the fields in a database and observed variables are like the database values.

Getting started

First install the packages if you haven’t already done so (you probably installed dplyr in the previous lesson):

#install.packages("tidyr")
#install.packages("dplyr")

Load the packages

library("tidyr")
library("dplyr")

First, lets look at the structure of our original gapminder data frame:

str(gapminder)

'data.frame':	1704 obs. of  6 variables:
 $ country  : chr  "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
 $ year     : int  1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
 $ pop      : num  8425333 9240934 10267083 11537966 13079460 ...
 $ continent: chr  "Asia" "Asia" "Asia" "Asia" ...
 $ lifeExp  : num  28.8 30.3 32 34 36.1 ...
 $ gdpPercap: num  779 821 853 836 740 ...

Challenge 1

Is gapminder a purely long, purely wide, or some intermediate format?

Solution to Challenge 1

The original gapminder data.frame is in an intermediate format. It is not purely long since it had multiple observation variables (pop,lifeExp,gdpPercap).

Sometimes, as with the gapminder dataset, we have multiple types of observed data. It is somewhere in between the purely ‘long’ and ‘wide’ data formats. We have 3 “ID variables” (continent, country, year) and 3 “Observation variables” (pop,lifeExp,gdpPercap). This intermediate format can be preferred despite not having ALL observations in 1 column given that all 3 observation variables have different units. There are few operations that would need us to make this data frame any longer (i.e. 4 ID variables and 1 Observation variable).

While using many of the functions in R, which are often vector based, you usually do not want to do mathematical operations on values with different units. For example, using the purely long format, a single mean for all of the values of population, life expectancy, and GDP would not be meaningful since it would return the mean of values with 3 incompatible units. The solution is that we first manipulate the data either by grouping (see the lesson on dplyr), or we change the structure of the data frame. Note: Some plotting functions in R actually work better in the wide format data.

From wide to long format with pivot_longer()

Until now, we’ve been using the nicely formatted original gapminder dataset, but ‘real’ data (i.e. our own research data) will never be so well organized. Here let’s start with the wide formatted version of the gapminder dataset.

Download the wide version of the gapminder data from here and save it in your data folder.

We’ll load the data file and look at it. Note: we don’t want our continent and country columns to be factors, so we use the stringsAsFactors argument for read.csv() to disable that.

gap_wide <- read.csv("data/gapminder_wide.csv", stringsAsFactors = FALSE)
str(gap_wide)

'data.frame':	142 obs. of  38 variables:
 $ continent     : chr  "Africa" "Africa" "Africa" "Africa" ...
 $ country       : chr  "Algeria" "Angola" "Benin" "Botswana" ...
 $ gdpPercap_1952: num  2449 3521 1063 851 543 ...
 $ gdpPercap_1957: num  3014 3828 960 918 617 ...
 $ gdpPercap_1962: num  2551 4269 949 984 723 ...
 $ gdpPercap_1967: num  3247 5523 1036 1215 795 ...
 $ gdpPercap_1972: num  4183 5473 1086 2264 855 ...
 $ gdpPercap_1977: num  4910 3009 1029 3215 743 ...
 $ gdpPercap_1982: num  5745 2757 1278 4551 807 ...
 $ gdpPercap_1987: num  5681 2430 1226 6206 912 ...
 $ gdpPercap_1992: num  5023 2628 1191 7954 932 ...
 $ gdpPercap_1997: num  4797 2277 1233 8647 946 ...
 $ gdpPercap_2002: num  5288 2773 1373 11004 1038 ...
 $ gdpPercap_2007: num  6223 4797 1441 12570 1217 ...
 $ lifeExp_1952  : num  43.1 30 38.2 47.6 32 ...
 $ lifeExp_1957  : num  45.7 32 40.4 49.6 34.9 ...
 $ lifeExp_1962  : num  48.3 34 42.6 51.5 37.8 ...
 $ lifeExp_1967  : num  51.4 36 44.9 53.3 40.7 ...
 $ lifeExp_1972  : num  54.5 37.9 47 56 43.6 ...
 $ lifeExp_1977  : num  58 39.5 49.2 59.3 46.1 ...
 $ lifeExp_1982  : num  61.4 39.9 50.9 61.5 48.1 ...
 $ lifeExp_1987  : num  65.8 39.9 52.3 63.6 49.6 ...
 $ lifeExp_1992  : num  67.7 40.6 53.9 62.7 50.3 ...
 $ lifeExp_1997  : num  69.2 41 54.8 52.6 50.3 ...
 $ lifeExp_2002  : num  71 41 54.4 46.6 50.6 ...
 $ lifeExp_2007  : num  72.3 42.7 56.7 50.7 52.3 ...
 $ pop_1952      : num  9279525 4232095 1738315 442308 4469979 ...
 $ pop_1957      : num  10270856 4561361 1925173 474639 4713416 ...
 $ pop_1962      : num  11000948 4826015 2151895 512764 4919632 ...
 $ pop_1967      : num  12760499 5247469 2427334 553541 5127935 ...
 $ pop_1972      : num  14760787 5894858 2761407 619351 5433886 ...
 $ pop_1977      : num  17152804 6162675 3168267 781472 5889574 ...
 $ pop_1982      : num  20033753 7016384 3641603 970347 6634596 ...
 $ pop_1987      : num  23254956 7874230 4243788 1151184 7586551 ...
 $ pop_1992      : num  26298373 8735988 4981671 1342614 8878303 ...
 $ pop_1997      : num  29072015 9875024 6066080 1536536 10352843 ...
 $ pop_2002      : int  31287142 10866106 7026113 1630347 12251209 7021078 15929988 4048013 8835739 614382 ...
 $ pop_2007      : int  33333216 12420476 8078314 1639131 14326203 8390505 17696293 4369038 10238807 710960 ...

Diagram illustrating the wide format of the gapminder data frame

To change this very wide data frame layout back to our nice, intermediate (or longer) layout, we will use one of the two available pivot functions from the tidyr package. To convert from wide to a longer format, we will use the pivot_longer() function. pivot_longer() makes datasets longer by increasing the number of rows and decreasing the number of columns, or ‘lengthening’ your observation variables into a single variable.

Diagram illustrating how pivot longer reorganizes a data frame from a wide to long format

gap_long <- gap_wide %>%
  pivot_longer(
    cols = c(starts_with('pop'), starts_with('lifeExp'), starts_with('gdpPercap')),
    names_to = "obstype_year", values_to = "obs_values"
  )
str(gap_long)

tibble [5,112 × 4] (S3: tbl_df/tbl/data.frame)
 $ continent   : chr [1:5112] "Africa" "Africa" "Africa" "Africa" ...
 $ country     : chr [1:5112] "Algeria" "Algeria" "Algeria" "Algeria" ...
 $ obstype_year: chr [1:5112] "pop_1952" "pop_1957" "pop_1962" "pop_1967" ...
 $ obs_values  : num [1:5112] 9279525 10270856 11000948 12760499 14760787 ...

Here we have used piping syntax which is similar to what we were doing in the previous lesson with dplyr. In fact, these are compatible and you can use a mix of tidyr and dplyr functions by piping them together.

We first provide to pivot_longer() a vector of column names that will be pivoted into longer format. We could type out all the observation variables, but as in the select() function (see dplyr lesson), we can use the starts_with() argument to select all variables that start with the desired character string. pivot_longer() also allows the alternative syntax of using the - symbol to identify which variables are not to be pivoted (i.e. ID variables).

The next arguments to pivot_longer() are names_to for naming the column that will contain the new ID variable (obstype_year) and values_to for naming the new amalgamated observation variable (obs_value). We supply these new column names as strings.

Diagram illustrating the long format of the gapminder data

gap_long <- gap_wide %>%
  pivot_longer(
    cols = c(-continent, -country),
    names_to = "obstype_year", values_to = "obs_values"
  )
str(gap_long)

tibble [5,112 × 4] (S3: tbl_df/tbl/data.frame)
 $ continent   : chr [1:5112] "Africa" "Africa" "Africa" "Africa" ...
 $ country     : chr [1:5112] "Algeria" "Algeria" "Algeria" "Algeria" ...
 $ obstype_year: chr [1:5112] "gdpPercap_1952" "gdpPercap_1957" "gdpPercap_1962" "gdpPercap_1967" ...
 $ obs_values  : num [1:5112] 2449 3014 2551 3247 4183 ...

That may seem trivial with this particular data frame, but sometimes you have 1 ID variable and 40 observation variables with irregular variable names. The flexibility is a huge time saver!

Now obstype_year actually contains 2 pieces of information, the observation type (pop,lifeExp, or gdpPercap) and the year. We can use the separate() function to split the character strings into multiple variables

gap_long <- gap_long %>% separate(obstype_year, into = c('obs_type', 'year'), sep = "_")
gap_long$year <- as.integer(gap_long$year)

Challenge 2

Using gap_long, calculate the mean life expectancy, population, and gdpPercap for each continent. Hint: use the group_by() and summarize() functions we learned in the dplyr lesson

Solution to Challenge 2

gap_long %>% group_by(continent, obs_type) %>%
   summarize(means=mean(obs_values))

`summarise()` has grouped output by 'continent'. You can override using the
`.groups` argument.

# A tibble: 15 × 3
# Groups:   continent [5]
  continent obs_type       means
  <chr>     <chr>          <dbl>
Africa    gdpPercap     2194. 
Africa    lifeExp         48.9
Africa    pop        9916003. 
Americas  gdpPercap     7136. 
Americas  lifeExp         64.7
Americas  pop       24504795. 
Asia      gdpPercap     7902. 
Asia      lifeExp         60.1
Asia      pop       77038722. 
Europe    gdpPercap    14469. 
Europe    lifeExp         71.9
Europe    pop       17169765. 
Oceania   gdpPercap    18622. 
Oceania   lifeExp         74.3
Oceania   pop        8874672. 

From long to intermediate format with pivot_wider()

It is always good to check work. So, let’s use the second pivot function, pivot_wider(), to ‘widen’ our observation variables back out. pivot_wider() is the opposite of pivot_longer(), making a dataset wider by increasing the number of columns and decreasing the number of rows. We can use pivot_wider() to pivot or reshape our gap_long to the original intermediate format or the widest format. Let’s start with the intermediate format.

The pivot_wider() function takes names_from and values_from arguments.

To names_from we supply the column name whose contents will be pivoted into new output columns in the widened data frame. The corresponding values will be added from the column named in the values_from argument.

gap_normal <- gap_long %>%
  pivot_wider(names_from = obs_type, values_from = obs_values)
dim(gap_normal)

[1] 1704    6

dim(gapminder)

[1] 1704    6

names(gap_normal)

[1] "continent" "country"   "year"      "gdpPercap" "lifeExp"   "pop"

names(gapminder)

[1] "country"   "year"      "pop"       "continent" "lifeExp"   "gdpPercap"

Now we’ve got an intermediate data frame gap_normal with the same dimensions as the original gapminder, but the order of the variables is different. Let’s fix that before checking if they are all.equal().

gap_normal <- gap_normal[, names(gapminder)]
all.equal(gap_normal, gapminder)

[1] "Attributes: < Component \"class\": Lengths (3, 1) differ (string compare on first 1) >"
[2] "Attributes: < Component \"class\": 1 string mismatch >"                                
[3] "Component \"country\": 1704 string mismatches"                                         
[4] "Component \"pop\": Mean relative difference: 1.634504"                                 
[5] "Component \"continent\": 1212 string mismatches"                                       
[6] "Component \"lifeExp\": Mean relative difference: 0.203822"                             
[7] "Component \"gdpPercap\": Mean relative difference: 1.162302"                           

head(gap_normal)

# A tibble: 6 × 6
  country  year      pop continent lifeExp gdpPercap
  <chr>   <int>    <dbl> <chr>       <dbl>     <dbl>
1 Algeria  1952  9279525 Africa       43.1     2449.
2 Algeria  1957 10270856 Africa       45.7     3014.
3 Algeria  1962 11000948 Africa       48.3     2551.
4 Algeria  1967 12760499 Africa       51.4     3247.
5 Algeria  1972 14760787 Africa       54.5     4183.
6 Algeria  1977 17152804 Africa       58.0     4910.

head(gapminder)

      country year      pop continent lifeExp gdpPercap
Afghanistan 1952  8425333      Asia  28.801  779.4453
Afghanistan 1957  9240934      Asia  30.332  820.8530
Afghanistan 1962 10267083      Asia  31.997  853.1007
Afghanistan 1967 11537966      Asia  34.020  836.1971
Afghanistan 1972 13079460      Asia  36.088  739.9811
Afghanistan 1977 14880372      Asia  38.438  786.1134

We’re almost there, the original was sorted by country, then year.

gap_normal <- gap_normal %>% arrange(country, year)
all.equal(gap_normal, gapminder)

[1] "Attributes: < Component \"class\": Lengths (3, 1) differ (string compare on first 1) >"
[2] "Attributes: < Component \"class\": 1 string mismatch >"                                

That’s great! We’ve gone from the longest format back to the intermediate and we didn’t introduce any errors in our code.

Now let’s convert the long all the way back to the wide. In the wide format, we will keep country and continent as ID variables and pivot the observations across the 3 metrics (pop,lifeExp,gdpPercap) and time (year). First we need to create appropriate labels for all our new variables (time*metric combinations) and we also need to unify our ID variables to simplify the process of defining gap_wide.

gap_temp <- gap_long %>% unite(var_ID, continent, country, sep = "_")
str(gap_temp)

tibble [5,112 × 4] (S3: tbl_df/tbl/data.frame)
 $ var_ID    : chr [1:5112] "Africa_Algeria" "Africa_Algeria" "Africa_Algeria" "Africa_Algeria" ...
 $ obs_type  : chr [1:5112] "gdpPercap" "gdpPercap" "gdpPercap" "gdpPercap" ...
 $ year      : int [1:5112] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
 $ obs_values: num [1:5112] 2449 3014 2551 3247 4183 ...

gap_temp <- gap_long %>%
    unite(ID_var, continent, country, sep = "_") %>%
    unite(var_names, obs_type, year, sep = "_")
str(gap_temp)

tibble [5,112 × 3] (S3: tbl_df/tbl/data.frame)
 $ ID_var    : chr [1:5112] "Africa_Algeria" "Africa_Algeria" "Africa_Algeria" "Africa_Algeria" ...
 $ var_names : chr [1:5112] "gdpPercap_1952" "gdpPercap_1957" "gdpPercap_1962" "gdpPercap_1967" ...
 $ obs_values: num [1:5112] 2449 3014 2551 3247 4183 ...

Using unite() we now have a single ID variable which is a combination of continent,country,and we have defined variable names. We’re now ready to pipe in pivot_wider()

gap_wide_new <- gap_long %>%
  unite(ID_var, continent, country, sep = "_") %>%
  unite(var_names, obs_type, year, sep = "_") %>%
  pivot_wider(names_from = var_names, values_from = obs_values)
str(gap_wide_new)

tibble [142 × 37] (S3: tbl_df/tbl/data.frame)
 $ ID_var        : chr [1:142] "Africa_Algeria" "Africa_Angola" "Africa_Benin" "Africa_Botswana" ...
 $ gdpPercap_1952: num [1:142] 2449 3521 1063 851 543 ...
 $ gdpPercap_1957: num [1:142] 3014 3828 960 918 617 ...
 $ gdpPercap_1962: num [1:142] 2551 4269 949 984 723 ...
 $ gdpPercap_1967: num [1:142] 3247 5523 1036 1215 795 ...
 $ gdpPercap_1972: num [1:142] 4183 5473 1086 2264 855 ...
 $ gdpPercap_1977: num [1:142] 4910 3009 1029 3215 743 ...
 $ gdpPercap_1982: num [1:142] 5745 2757 1278 4551 807 ...
 $ gdpPercap_1987: num [1:142] 5681 2430 1226 6206 912 ...
 $ gdpPercap_1992: num [1:142] 5023 2628 1191 7954 932 ...
 $ gdpPercap_1997: num [1:142] 4797 2277 1233 8647 946 ...
 $ gdpPercap_2002: num [1:142] 5288 2773 1373 11004 1038 ...
 $ gdpPercap_2007: num [1:142] 6223 4797 1441 12570 1217 ...
 $ lifeExp_1952  : num [1:142] 43.1 30 38.2 47.6 32 ...
 $ lifeExp_1957  : num [1:142] 45.7 32 40.4 49.6 34.9 ...
 $ lifeExp_1962  : num [1:142] 48.3 34 42.6 51.5 37.8 ...
 $ lifeExp_1967  : num [1:142] 51.4 36 44.9 53.3 40.7 ...
 $ lifeExp_1972  : num [1:142] 54.5 37.9 47 56 43.6 ...
 $ lifeExp_1977  : num [1:142] 58 39.5 49.2 59.3 46.1 ...
 $ lifeExp_1982  : num [1:142] 61.4 39.9 50.9 61.5 48.1 ...
 $ lifeExp_1987  : num [1:142] 65.8 39.9 52.3 63.6 49.6 ...
 $ lifeExp_1992  : num [1:142] 67.7 40.6 53.9 62.7 50.3 ...
 $ lifeExp_1997  : num [1:142] 69.2 41 54.8 52.6 50.3 ...
 $ lifeExp_2002  : num [1:142] 71 41 54.4 46.6 50.6 ...
 $ lifeExp_2007  : num [1:142] 72.3 42.7 56.7 50.7 52.3 ...
 $ pop_1952      : num [1:142] 9279525 4232095 1738315 442308 4469979 ...
 $ pop_1957      : num [1:142] 10270856 4561361 1925173 474639 4713416 ...
 $ pop_1962      : num [1:142] 11000948 4826015 2151895 512764 4919632 ...
 $ pop_1967      : num [1:142] 12760499 5247469 2427334 553541 5127935 ...
 $ pop_1972      : num [1:142] 14760787 5894858 2761407 619351 5433886 ...
 $ pop_1977      : num [1:142] 17152804 6162675 3168267 781472 5889574 ...
 $ pop_1982      : num [1:142] 20033753 7016384 3641603 970347 6634596 ...
 $ pop_1987      : num [1:142] 23254956 7874230 4243788 1151184 7586551 ...
 $ pop_1992      : num [1:142] 26298373 8735988 4981671 1342614 8878303 ...
 $ pop_1997      : num [1:142] 29072015 9875024 6066080 1536536 10352843 ...
 $ pop_2002      : num [1:142] 31287142 10866106 7026113 1630347 12251209 ...
 $ pop_2007      : num [1:142] 33333216 12420476 8078314 1639131 14326203 ...

Challenge 3

Take this 1 step further and create a gap_ludicrously_wide format data by pivoting over countries, year and the 3 metrics? Hint this new data frame should only have 5 rows.
Solution to Challenge 3
gap_ludicrously_wide <- gap_long %>%
   unite(var_names, obs_type, year, country, sep = "_") %>%
   pivot_wider(names_from = var_names, values_from = obs_values)

Now we have a great ‘wide’ format data frame, but the ID_var could be more usable, let’s separate it into 2 variables with separate()

gap_wide_betterID <- separate(gap_wide_new, ID_var, c("continent", "country"), sep="_")
gap_wide_betterID <- gap_long %>%
    unite(ID_var, continent, country, sep = "_") %>%
    unite(var_names, obs_type, year, sep = "_") %>%
    pivot_wider(names_from = var_names, values_from = obs_values) %>%
    separate(ID_var, c("continent","country"), sep = "_")
str(gap_wide_betterID)

tibble [142 × 38] (S3: tbl_df/tbl/data.frame)
 $ continent     : chr [1:142] "Africa" "Africa" "Africa" "Africa" ...
 $ country       : chr [1:142] "Algeria" "Angola" "Benin" "Botswana" ...
 $ gdpPercap_1952: num [1:142] 2449 3521 1063 851 543 ...
 $ gdpPercap_1957: num [1:142] 3014 3828 960 918 617 ...
 $ gdpPercap_1962: num [1:142] 2551 4269 949 984 723 ...
 $ gdpPercap_1967: num [1:142] 3247 5523 1036 1215 795 ...
 $ gdpPercap_1972: num [1:142] 4183 5473 1086 2264 855 ...
 $ gdpPercap_1977: num [1:142] 4910 3009 1029 3215 743 ...
 $ gdpPercap_1982: num [1:142] 5745 2757 1278 4551 807 ...
 $ gdpPercap_1987: num [1:142] 5681 2430 1226 6206 912 ...
 $ gdpPercap_1992: num [1:142] 5023 2628 1191 7954 932 ...
 $ gdpPercap_1997: num [1:142] 4797 2277 1233 8647 946 ...
 $ gdpPercap_2002: num [1:142] 5288 2773 1373 11004 1038 ...
 $ gdpPercap_2007: num [1:142] 6223 4797 1441 12570 1217 ...
 $ lifeExp_1952  : num [1:142] 43.1 30 38.2 47.6 32 ...
 $ lifeExp_1957  : num [1:142] 45.7 32 40.4 49.6 34.9 ...
 $ lifeExp_1962  : num [1:142] 48.3 34 42.6 51.5 37.8 ...
 $ lifeExp_1967  : num [1:142] 51.4 36 44.9 53.3 40.7 ...
 $ lifeExp_1972  : num [1:142] 54.5 37.9 47 56 43.6 ...
 $ lifeExp_1977  : num [1:142] 58 39.5 49.2 59.3 46.1 ...
 $ lifeExp_1982  : num [1:142] 61.4 39.9 50.9 61.5 48.1 ...
 $ lifeExp_1987  : num [1:142] 65.8 39.9 52.3 63.6 49.6 ...
 $ lifeExp_1992  : num [1:142] 67.7 40.6 53.9 62.7 50.3 ...
 $ lifeExp_1997  : num [1:142] 69.2 41 54.8 52.6 50.3 ...
 $ lifeExp_2002  : num [1:142] 71 41 54.4 46.6 50.6 ...
 $ lifeExp_2007  : num [1:142] 72.3 42.7 56.7 50.7 52.3 ...
 $ pop_1952      : num [1:142] 9279525 4232095 1738315 442308 4469979 ...
 $ pop_1957      : num [1:142] 10270856 4561361 1925173 474639 4713416 ...
 $ pop_1962      : num [1:142] 11000948 4826015 2151895 512764 4919632 ...
 $ pop_1967      : num [1:142] 12760499 5247469 2427334 553541 5127935 ...
 $ pop_1972      : num [1:142] 14760787 5894858 2761407 619351 5433886 ...
 $ pop_1977      : num [1:142] 17152804 6162675 3168267 781472 5889574 ...
 $ pop_1982      : num [1:142] 20033753 7016384 3641603 970347 6634596 ...
 $ pop_1987      : num [1:142] 23254956 7874230 4243788 1151184 7586551 ...
 $ pop_1992      : num [1:142] 26298373 8735988 4981671 1342614 8878303 ...
 $ pop_1997      : num [1:142] 29072015 9875024 6066080 1536536 10352843 ...
 $ pop_2002      : num [1:142] 31287142 10866106 7026113 1630347 12251209 ...
 $ pop_2007      : num [1:142] 33333216 12420476 8078314 1639131 14326203 ...

all.equal(gap_wide, gap_wide_betterID)

[1] "Attributes: < Component \"class\": Lengths (1, 3) differ (string compare on first 1) >"
[2] "Attributes: < Component \"class\": 1 string mismatch >"                                

There and back again!

Other great resources

Key Points

Use the tidyr package to change the layout of data frames.

Use pivot_longer() to go from wide to longer layout.

Use pivot_wider() to go from long to wider layout.

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Data Frame Manipulation with tidyr

Overview

Getting started

Challenge 1

Solution to Challenge 1