Here are some basic exercises on loops and applying functions to data structures:
12.5.1 Exercise 1
Fibonacci loop and functions
- Look up the term Fibonacci numbers (e.g., on Wikipedia) and use a
forloop to create a numeric vector of the first 25 Fibonacci numbers (for a series of numbers starting with
Hint: The series of Fibonacci numbers was previously introduced in our discussion of recursion (see Section 11.4.1). We are now looking for an iterative definition, but the underlying processes are quite similar. Essentially, the recursive definition resulted in an implicit loop, whereas we now explicitly define the iteration.
forloop into a
fibonacci()function that returns a numeric vector of the first
nFibonacci numbers. Test your function for
fibonacci(n = 25).
fibonacci()function to also accept the first two elements (
e2) as inputs to the series and then create the first
nFibonacci numbers given these initial elements. Test your function for
fibonacci(e1 = 1, e2 = 3, n = 25).
12.5.2 Exercise 2
Looping for divisors
- Write a
forloop that prints out all positive divisors of the number 1000.
N %% x == 0 to test whether
x is a divisor of
How many iterations did your loop require? Could you achieve the same results with fewer iterations?
divisors()function that uses a
forloop to return a numeric vector containing all positive divisors of a natural number
Hint: Note that we do not know the length of the resulting vector.
divisors()function to answer the question: Does the number 1001 have fewer or more divisors than the number 1000?
divisors()function and another
forloop to answer the question: Which prime numbers exist between the number 111 and the number 1111?
Hint: A prime number (e.g., 13) has only two divisors: The number 1 and the number itself.
12.5.3 Exercise 3
Let’s revisit our favorite randomizing devices one more time:
In this exercise, we will use
whileloops to repeatedly call an existing function.
Throwing dice in loops
Implement a function
my_dice()that uses the base R function
sample()to simulate a throw of a dice (i.e., yielding an integer from 1 to 6 with equal probability).
Add an argument
N(for the number of throws) to your function and modify it by using a
forloop to throw the dice
Ntimes, and returning a vector of length
Nthat shows the results of the
- Use a
whileloop to throw
my_dice(N = 1)until you throw the number 6 twice in a row and show the sequence of all throws up to this point.
Hint: Given a sequence
i-th element is
Hence, the last element of
- Use your solution of 3. to conduct a simulation that addresses the following question:
- How many times on average do we need to throw
my_dice(1)to obtain the number 6 twice in a row?
Hint: Use a
for loop to run your solution to 3. for
T = 10000 times and store the length of the individual
throws in a numeric vector.
This exercise shows how loops can be used to generate and collect multiple outputs. This can sometimes replace vector arguments to functions. However, as R is optimized for vectors, using loops rather than vectors is not generally recommended.
12.5.4 Exercise 4
Mapping functions to data
Write code that uses a function of the base R
apply or purrr
map family of functions to:
- Compute the mean of every column in
- Determine the type of each column in
- Compute the number of unique values in each column of
- Generate 10 random normal numbers for each of
μ = −100, 0, and 100.
12.5.5 Exercise 5
In this exercise, we will standardize an entire table of data (using a
for loop, an
apply(), and a
We will first write a utility function that achieves the desired transformation for a vector and then compare and contrast different ways of applying this function to a table of data.
In case you are not familiar with the notion of a z score or standard score, look up these terms (e.g., on Wikipedia).
Write a function called
z_transthat takes a vector
vas input and returns the z-transformed (or standardized) values as output if
vis numeric and returns
vunchanged if it is non-numeric.
Hint: Remember that
z <- (v - mean(v)) / sd(v)), but beware that
# Load data: <- ds4psy::falsePosPsy_all # from ds4psy package falsePosPsy # falsePosPsy <- readr::read_csv("http://rpository.com/ds4psy/data/falsePosPsy_all.csv") # online falsePosPsy#> # A tibble: 78 x 19 #> study ID aged aged365 female dad mom potato when64 kalimba cond #> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> #> 1 1 1 6765 18.5 0 49 45 0 0 1 control #> 2 1 2 7715 21.1 1 63 62 0 1 0 64 #> 3 1 3 7630 20.9 0 61 59 0 1 0 64 #> 4 1 4 7543 20.7 0 54 51 0 0 1 control #> 5 1 5 7849 21.5 0 47 43 0 1 0 64 #> 6 1 6 7581 20.8 1 49 50 0 1 0 64 #> 7 1 7 7534 20.6 1 56 55 0 0 1 control #> 8 1 8 6678 18.3 1 45 45 0 1 0 64 #> 9 1 9 6970 19.1 0 53 51 1 0 0 potato #> 10 1 10 7681 21.0 0 53 51 0 1 0 64 #> # … with 68 more rows, and 8 more variables: root <dbl>, bird <dbl>, #> # political <dbl>, quarterback <dbl>, olddays <dbl>, feelold <dbl>, #> # computer <dbl>, diner <dbl>
- Use an appropriate
mapfunction to to create a single vector that — for each column in
falsePosPsy— indicates whether or not it is a numeric variable?
Hint: The function
is.numeric() tests whether a vector is numeric.
Use this vector to select only the numeric columns of
falsePosPsyinto a new tibble
forloop to apply your
fpp_numericto standardize all of its columns:
Turn your resulting data structure into a tibble
out_1and print it.
- Repeat the task of 2. (i.e., applying
z_trans()to all numeric columns of
falsePosPsy) by using the base R
applyfunction, rather than a
forloop. Save and print your resulting data structure as a tibble
Hint: Remember to set the
MARGIN argument to apply
z_trans() over all columns, rather than rows.
- Repeat the task of 2. and 3. (i.e., applying
z_trans()to all numeric columns of
falsePosPsy) by using an appropriate version of a
mapfunction from the purrr package. Save and print your resulting data structure as a tibble
Hint: Note that the desired output structure is a rectangular data table, which is also a list.
all.equalto verify that your results of 2., 3. and 4. (i.e.,
out_3) are all equal.
Hint: If a tibble
t1 lacks variable names, you can add those of another tibble
t2 by assigning
names(t1) <- names(t2).
12.5.6 Exercise 6
Cumulative savings revisited
In Exercise 2 of Chapter 1: Basic R concepts and commands, we computed the cumulative sum of an initial investment amount
a = 1000, given an annual interest rate of
int of .1%, and an annual rate of inflation
inf of 2%, after a number of
n full years (e.g.,
n = 10):
# Task parameters: <- 1000 # initial amount: $1000 a <- .1/100 # annual interest rate of 0.1% int <- 2/100 # annual inflation rate 2% inf <- 10 # number of yearsn
Our solution in Chapter 1 consisted in an arithmetic formula which computes a new
total based on the current task parameters:
# Previous solution (see Exercise 2 of Chapter 1): <- a * (1 + int - inf)^n total total#>  825.4487
Given our new skills about writing loops and functions (from Chapter 11), we can solve this task in a variety of ways. This exercise illustrates some differences between loops, a function that implements the formula, and a vector-based solution. Although all these approaches solve the same problem, they differ in important ways.
- Write a
forloop that iteratively computes the current value of your investment after each of
1:nyears (with \(n \geq 1\)).
Hint: Express the new value of your investment
a as a function of its current value
a and its change based on
int in each year.
- Write a function
nas its arguments, and directly computes and returns the cumulative total after
Hint: Translate the arithmetic solution (shown above) into a function that directly computes the new total. Use sensible default values for your function.
forloop that iteratively calls your function
compute_value()for every year
Check whether your
compute_value()function also works for a vector of year values
n. Then discuss the differences between the solutions to Exercise 6.1, 6.3, and 6.4.
This concludes our basic exercises on loops and applying functions to data structures.