factorial(3) # same as 3*2*1 which is 6[1] 6factorial(5) # same as 5*4*3*2*1 which is 120[1] 12035 35. while loops
A “while loop” in R is one of several ways to get R to do something over and over again (we’ll discuss other ways later). A relatively straight forward example of code that could be written with a “while loop” is the factorial function (see below). Now, since R has a built-in version of the factorial function, you don’t actually have to write the factorial function yourself. However, it will be instructive to reproduce this function with our own code that uses a while loop - which we do below. In order to understand the example code below, let’s first understand what a factorial is.
35.1 What is the “factorial” of a number?
In math, the factorial of a number is the product of that number and all the positive whole numbers below it. For example:
The factorial of 5 is: 5 × 4 × 3 × 2 × 1 = 120
Mathematicians write factorials using an exclamation point.
For example a mathematician would write 5! to mean 5 × 4 × 3 × 2 × 1 = 120
However, 5! is NOT valid R code. Rather, R has a builtin function, factorial(SOME_NUMBER) that calculates factorials. For example:
35.1.1 factorial is not defined for negative numbers
The concept of a factorial is not defined for negative numbers. When given a negative number, R’s factorial function returns NaN (i.e. R’s special value meaning “not a number”)
factorial(-1) # NaN[1] NaN35.1.2 factorial(0) and factorial(1) are both 1
The factorial of 0 and the factorial of 1 are both defined to be 1.
factorial(0) # defined by mathematicians to be 1[1] 1factorial(1) # defined by mathematicians to be 1[1] 1To learn more about factorials, see this page: https://www.mathsisfun.com/numbers/factorial.html
35.2 Let’s rewrite the factorial function - we’ll use a while loop.
Let’s write a function called myFactorial that reproduces the results of R’s builtin factorial function that was shown above.
The code introduces a new concept - the “while loop”. We’ll explain all of the code below, but first let’s see the full definition of the function and make sure that it works:
myFactorial <- function(num){
if(!is.numeric(num) || trunc(num) != num || length(num) != 1) {
stop("num must be a single positive whole number")
}
if (num < 0) {
return(NaN)
}
answer = 1
while(num > 1) {
answer <- answer * num
num <- num - 1
}
return(answer)
}Some examples of using the myFactorial function:
myFactorial(0) # factorial of 0 is defined to be 1[1] 1myFactorial(1) # factorial of 1 is defined to be 1[1] 1myFactorial(3) # 6, ie. 3 * 2 * 1[1] 6myFactorial(5) # 120 i.e. 5*4*3*2*1[1] 120myFactorial(10) # 3628800 - i.e. 10*9*8*7*6*5*4*3*2*1[1] 3628800myFactorial(100) # 9.332622e+157 - this is a VERY VERY large number (see section on "scientific notation")[1] 9.332622e+157myFactorial(c(1,2,3,4)) # ERROR - only one number in our version of myFactorialError in !is.numeric(num) || trunc(num) != num: 'length = 4' in coercion to 'logical(1)'myFactorial(-1) # NaN[1] NaN35.2.1 Explanation of the code
Let’s go through the myFactorial function in detail. Portions of the code are highlighted with numbers and explained below.
myFactorial <- function(num){
1 if(!is.numeric(num) || trunc(num) != num || length(num) != 1) {
stop("num must be a single positive whole number")
}
2 if (num < 0) {
return(NaN)
}
3 answer = 1
4 while(num > 1) {
answer <- answer * num
num <- num - 1
}
5 return(answer)
}- 1
- make sure that num is just one whole number
- 2
- make sure that num is not negative
- 3
- setup the answer variable - this is necessary to do before the while loop starts
- 4
- the while loop (explinaed in detail below)
- 5
- return the answer
35.2.2 How the while loop works
A while loop looks similar to an if, except that a while loop starts with the word “while” and an if starts with the word “if”.
Similar to an “if”, a “while” has a logical condition in parentheses followed by some code in {curly braces}. (The code in the {curly braces} is called the “body” of the while loop.)
Similar to an “if”, the condition must evaluate to TRUE or FALSE.
Similar to an “if” - when the condition for the while is TRUE - the code in the {curly braces} is executed and when the condition is FALSE, the code in the {curly braces} is NOT executed.
What makes a while different from an if is the following:
o if : when the code in the {curly braces} (i.e. the “body” of the if) finishes, the execution of the code continues with the first line after the body of the “if”
o while : when the code in the {curly braces} (i.e. the “body” of the while) finishes, the entire “while” is repeated - i.e. the condition is checked and if it is still TRUE - the body of the while is done again. This keeps happening as long as the condition is TRUE (i.e. “while” the condition is TRUE). If/when the condition eventually becomes FALSE, the execution of the code continues with the first line after the body of the “while”.
35.3 Terminology: “iteration” , “iterate”
As a while loop executes, the code in the “body” of the while loop may be executed (i.e. run) several times. Each time the code of the body is executed is known as a single “iteration” of the while loop. In general we say that the while loop “iterates over” the code in the body of the loop.
35.4 Using the debugger to understand the code
It is often helpful to use R’s debugger to help understand the code for a loop. Information about how to use R’s debugger is above in the debugger section.
As a quick refresher - to use the debugger, you should first run the code shown above that defines the function myFactorial. Then type the command debugonce(myFactorial) and finally call the function, e.g. myFactorial(5). At that point the debugger should start. To see how the code works, you can repeatedly press the “next” button (or type n). Every time you do so, the code will advance one line. You can use this technique to see what “path” the code takes through ifs and loops. You should pay attention to how the values of the variables in the “Environment” pane change as the code is executed. Tracing through code in this way is one of the best ways to understand how the code works.
35.5 Things to keep in mind when writing while loops
When writing while loops, keep the following in mind:
The condition, which appears in the parentheses, should depend on at least one variable.
In this example, the condition is (num > 1). This particular condition contains one variable, i.e. num. It is very possible for a condition to be more complicated than this and contain more than one variable.
The condition must be true for the code in the body to be executed. The condition must be false for the code in the body to NOT be executed.
The value of the variable(s) in the condition must be setup in the code that appears BEFORE the while.
In this example, the value of num was passed into the function, therefore its value was set before the while loop started.
The code inside the {curly braces} is known as the “body” of the loop.
The code in the body should eventually cause the condition to become false. The most common way to do that is for the body to change the value of a variable in the condition in some way.
In this example, the line : num <- num - 1 changes the value of num by subtracting one from it. If this happens enough times, the value of num will eventually become 1, thus making the condition FALSE.
35.7 Practice with finding errors in loops
# The following is the same exact code as above, without all the
# comments. There are many different subtle errors that can pop up
# when writing while loops. Think about what would happen in each of the
# following situations ..
#
# What would happen in each of the situations listed below?
# To find out, change the code and try it.
#
# For each of the following questions, try to figure out what will happen
# before actually running the code. Then change the code and run it.
# To help you figure out what will happen, keep track of the values of all
# the variables and arguments on a piece of paper.
# Then, every time you "run a line of code in your head" keep track of any
# changes to the variables on the piece of paper.
#
# You can also use the debugger ...
#
# What would happen if ...
# 1. ... instead of "answer=1" the programmer typed "answer=0" ?
# 2. ... instead of "while(num>1)" the programmer typed "while(num<1)" ?
# 3. ... instead of "num<-num+1" the programmer typed "num<-num-1"
# 4. ... the programmer forgot to type the line "num<-num-1" and just left it out?
# 5. ... the programmer wrote the lines "answer<-answer*num" and "num<-num-1"
# in the opposite order, i.e. "num<-num-1" and then "answer<-answer*num"
myFactorial <- function(num){
if (num <0 || !is.numeric(num) || trunc(num) != num || length(num) != 1) {
stop("num must be a single positive whole number")
}
answer = 1
while(num > 1) {
answer <- answer * num
num <- num - 1
}
return(answer)
}
myFactorial(4)[1] 24#debugonce(myFactorial)
myFactorial(4) # The result SHOULD BE 24[1] 24myFactorial(100)[1] 9.332622e+15735.9 More practice finding errors in loops
# The following is the same function again, this time without the comments.
#
# For each of the following questions, try to figure out what will happen
# before actually running the code. Then change the code and run it.
# To help you figure out what will happen, keep track of the values of all the variables
# and arguments on a piece of paper. Every time you "run a line of code in
# your head" keep track of any changes to the variables on the piece
# of paper. You can also use the debugger ...
#
# What would happen if ...
# 1. ... instead of "divisor <- 2" the programmer typed "divisor <- 1" ?
# 2. ... instead of "while(divisor<num)" the programmer typed "while(divisor>num)" ?
# 3. ... instead of "while(divisor<num)" the programmer typed "while(divisor<=num)" ?
# 4. ... the line "divisor<-divisor+1" was mistakenly left out?
# 5. ... the line "divisor<-divisor+1" was inside the body of the if?
# 6. ... the line "divisor<-divisor+1" was before the if instead of after the if?
# 7. ... the line "divisor<-divisor+1" was before the if instead of after the if ...
# and instead of "divisor <- 2" the programmer typed "divisor <- 1" ?
# 8. ... the programmer forgot to type the last line "return(TRUE)".
# 9. ... instead of "while(divisor<num)" the programmer typed "while(divisor<num/2)" ?
# 10. ... instead of "while(divisor<num)" the programmer typed "while(divisor<sqrt(num))" ?
is.prime <- function( num ) {
if (num < 2){
return(FALSE)
}
divisor <- 2
while ( divisor < num ) {
if (num %% divisor == 0){
return(FALSE)
}
divisor <- divisor + 1
}
return(TRUE)
}
is.prime(35)[1] FALSEis.prime(37)[1] TRUE35.10 There are MANY ways to write the same function
#----------------------------------------------------
# Another way to write the same function.
#
# This version has a single return statement at the end of the function.
# Some people argue that this style is "cleaner" and
# easier to understand when reading the code.
#----------------------------------------------------
is.prime2 <- function( num ) {
answer <- TRUE # assume answer is TRUE unless we find out otherwise
if (num < 2){
answer <- FALSE
} else {
divisor <- 2
while ( divisor < num ) {
if (num %% divisor == 0){
answer <- FALSE
}
divisor <- divisor + 1
}
}
return(answer)
}
is.prime2(35) # FALSE[1] FALSEis.prime2(37) # TRUE[1] TRUE# check to make sure that both versions return the same values
#all(sapply(1:100,is.prime) == sapply(1:100,is.prime2)) # TRUE35.11 another example - divisors(num)
#--------------------------------------------------
# Write a function to find all divisors of a number
# (assume that num is a positive whole number)
#--------------------------------------------------
divisors <- function(num){
if (!is.numeric(num) || trunc(num)!=num || num<1 || length(num)!=1){
stop("num must be a single positive whole number")
}
# This is the variable we will return at the end of the function.
answer <- 1 # 1 is a divisor of all positive whole numbers
divisor <- 2
while(divisor <= num){
if (num %% divisor == 0){
answer <- c(answer, divisor) # add another number to the answer
}
divisor <- divisor + 1
}
return(answer)
}
#debugonce(divisors)
divisors(12)[1] 1 2 3 4 6 12divisors(15)[1] 1 3 5 15divisors(36)[1] 1 2 3 4 6 9 12 18 36divisors(100)[1] 1 2 4 5 10 20 25 50 100divisors(101) # this is prime, only divisors are 1 and 101[1] 1 101#divisors(15485863) # This will take a few seconds.
#divisors(67867979) # This will take a few seconds.
#divisors(67867970) # This will take a few seconds.35.12 more efficient version
#-------------------------------------
# a more efficient version
#-------------------------------------
divisors.faster <- function(num){
if (!is.numeric(num) || trunc(num)!=num || num<1 || length(num)!=1){
stop("num must be a single positive whole number")
}
answer <- c(1,num) # changed this line
divisor <- 2
while(divisor <= sqrt(num)){ # changed this line (why?)
if (num %% divisor == 0){
answer <- c(answer, divisor)
answer <- c(answer, num/divisor) # added this line (why?)
}
divisor <- divisor + 1
}
answer <- sort(unique(answer)) # added this line (why?)
return(answer)
}
#debugonce(divisors.faster)
divisors.faster(36)[1] 1 2 3 4 6 9 12 18 36divisors.faster(12)[1] 1 2 3 4 6 12divisors.faster(10)[1] 1 2 5 10divisors.faster(97)[1] 1 97divisors.faster(100)[1] 1 2 4 5 10 20 25 50 100divisors.faster(15485863) # much faster now!!![1] 1 15485863divisors.faster(15485864) # much faster now!!! [1] 1 2 4 8 31 41 62 82
[9] 124 164 248 328 1271 1523 2542 3046
[17] 5084 6092 10168 12184 47213 62443 94426 124886
[25] 188852 249772 377704 499544 1935733 3871466 7742932 15485864divisors.faster(67867979) # much faster now!!![1] 1 67867979divisors.faster(67867970) # much faster now!!![1] 1 2 5 10 6786797 13573594 33933985 67867970# check to see that both functions are equivalent
#all ( divisors.faster(15485864) == divisors(15485864) ) # TRUE if all nums are the same35.13 More practice - mysum(NUMS) blastoff(SECONDS)
###############################################################################
# The next two "QUESTIONS" (i.e. to write the "mysum" and "blastoff" functions)
# do not present any new concepts. They are just additional examples.
###############################################################################
#----------------------------------------------------------
# QUESTION
# Write a function that simulates the sum function
#
# mysum = function( nums )
#
# nums is expected to be a numeric vector
# mysum should return the sum of all the numbers in nums
# DO NOT USE THE SUM FUNCTION
#----------------------------------------------------------
mysum = function( nums ){
theSum = nums[1]
position = 2
while(position <= length(nums)){
theSum = theSum + nums[position]
position = position + 1
}
theSum # return the answer
}
mysum(c(10,20,5)) # 35[1] 35mysum(10) # 10[1] 10# Note that the following returns NA, which makes sense because a sum
# is not applicable (i.e. Not Available) if there are no numbers specified.
mysum( numeric(0) ) [1] NA# You should use the debugger to understand why we get NA.
#
# debugonce(mysum)
mysum( numeric(0) ) [1] NA#-------------------------------------------------------------------
# The following is a SLIGHTLY different version of the function.
# In this version we returned a sum of 0 when the numeric vector
# is an empty vector. This is also a reasonable answer.
#-------------------------------------------------------------------
mysum = function( nums ){
theSum = 0 # this line changed
position = 1 # this line changed
while(position <= length(nums)){
theSum = theSum + nums[position]
position = position + 1
}
theSum # return the answer
}
mysum(c(10,20,5)) # 35[1] 35mysum(character(0)) # 0[1] 0#---------------------------------------------------------
# QUESTION
#
# Write a function
#
# countdown = function(from)
#
# that counts down as shown below. There should be 1 second
# pause between each line of output HINT: use Sys.sleep(1)
#
# > countdown(5)
# T minus 5 seconds
# T minus 4 seconds
# T minus 3 seconds
# T minus 2 seconds
# T minus 1 second
# BLASTOFF!!!
#
# > countdown(3)
# T minus 3 seconds
# T minus 2 seconds
# T minus 1 second
# BLASTOFF!!!
#
# > countdown(0)
# BLASTOFF!!!
#-----------------------------------------------------------
###########.
# ANSWER
###########.
countdown = function(from){
while(from > 0){
if(from == 1){
cat("T minus", from, "second\n")
} else {
cat("T minus", from, "seconds\n")
}
Sys.sleep(1)
from = from - 1
}
cat("BLASTOFF!!!")
}
countdown(5)T minus 5 seconds
T minus 4 seconds
T minus 3 seconds
T minus 2 seconds
T minus 1 second
BLASTOFF!!!#countdown(3)
#countdown(0)35.14 Random numbers : runif()
####################################################################
####################################################################
##
## Generating random numbers
##
## - runif : returns a random number
## - set.seed(SOME_WHOLE_NUMBER) : resets the random number generator
## - sample
##
####################################################################
####################################################################
# There are several different functions that are built into R for
# generating "random numbers". These are useful for "simulations"
# e.g. to generate random
# View the help pages by typing:
#
# ?runif
# ?set.seed
# ?sample
#--------------------------------------------------------------
#
# runif
#
# runif stands for "Random number from a UNIForm distribution
#
#--------------------------------------------------------------
runif(1) # one random number between 0 and 1 (not including 0.0 or 1.0)[1] 0.5955975runif(1) # another random number between 0 and 1 (not including 0.0 or 1.0)[1] 0.6974013runif(3) # three random numbers between 0 and 1[1] 0.08113108 0.80810731 0.20745448runif(3, min=0, max=100) # three random numbers between 0 and 100[1] 19.26440 38.41008 45.59523runif(3, min=500, max=505) # three random numbers between 500 and 505[1] 502.9197 502.5152 504.1375trunc(runif(25, min=1, max=11)) # 25 random whole numbers between 1 and 10 [1] 9 9 8 4 10 6 7 2 1 8 4 7 9 2 4 10 7 4 5 10 2 8 1 7 4trunc(runif(25, min=1, max=11)) # another 25 random whole numbers between 1 and 10 [1] 1 5 5 10 8 7 1 2 6 3 8 4 9 7 1 7 5 5 6 9 9 7 1 3 4#-----------------------------
# set.seed(SOME_WHOLE_NUMBER)
#-----------------------------
set.seed(1)
trunc(runif(3, min=1, max=10)) # 5 random whole numbers between 1 and 9[1] 3 4 6trunc(runif(3, min=1, max=10)) # another 5 random whole numbers between 1 and 9[1] 9 2 9trunc(runif(3, min=1, max=10)) # another 5 random whole numbers between 1 and 9[1] 9 6 6set.seed(1)
trunc(runif(3, min=1, max=10)) # start again with same numbers[1] 3 4 6set.seed(1)
trunc(runif(3, min=1, max=10)) # start again with same numbers[1] 3 4 6trunc(runif(3, min=1, max=10)) # continue in with the same numbers as when seed was 1[1] 9 2 9trunc(runif(3, min=1, max=10)) # continue in with the same numbers as when seed was 1[1] 9 6 6set.seed(99) # different seed starts again with different numbers
trunc(runif(3, min=1, max=10)) #[1] 6 2 7trunc(runif(3, min=1, max=10)) #[1] 9 5 9set.seed(99) # start again with same seed
trunc(runif(3, min=1, max=10)) #[1] 6 2 7trunc(runif(3, min=1, max=10)) #[1] 9 5 9set.seed(1) # back to first sequence of numbers
trunc(runif(3, min=1, max=10)) # start again with same numbers[1] 3 4 6trunc(runif(3, min=1, max=10)) # continue in with the same numbers as when seed was 1[1] 9 2 935.15 Random numbers : sample()
#-----------------------------------------------------------------------------
# sample
#
# NOTE: This is review. We already covered the sample function in an earlier class.
#-----------------------------------------------------------------------------
# View the help page by typing:
#
# ?sample
sample(c(10,20,30,40,50,60,70,80,90,100), 3) # sample 3 items from the set[1] 70 20 30sample(c(10,20,30,40,50,60,70,80,90,100), 7) # sample 7 items from the set[1] 30 10 50 80 20 60 100sample(c(10,20,30,40,50,60,70,80,90,100), 10) # sample 10 items from the set [1] 90 50 100 10 70 80 60 20 30 40sample(c(10,20,30,40,50,60,70,80,90,100)) # sample 10 items from the set [1] 90 10 40 30 60 20 50 80 100 70# with replacement
sample(c(10,20,30,40,50,60,70,80,90,100), 7, replace=TRUE) # allow same item more than once[1] 40 100 90 70 60 90 80sample(c(10,20,30,40,50,60,70,80,90,100), 25, replace=TRUE) # allow same item more than once [1] 90 70 80 60 100 70 30 100 60 80 20 20 60 60 10 30 30 80 60
[20] 70 60 80 70 10 40sample(c(10,20,30,40,50,60,70,80,90,100), 25, replace=FALSE) # ERRORError in sample.int(length(x), size, replace, prob): cannot take a sample larger than the population when 'replace = FALSE'sample(c(10,20,30,40,50,60,70,80,90,100), 25) # ERRORError in sample.int(length(x), size, replace, prob): cannot take a sample larger than the population when 'replace = FALSE'sample(1:10) # sample all items without replacement [1] 8 9 10 1 6 4 3 7 5 2sample(1:10, replace=TRUE) # sample 10 times with replacement [1] 6 1 5 6 1 9 7 7 3 6# set probabilities on specific values
sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 1 1 2 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 3 1 1 1 3sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 1 1 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2# set.seed works for sample too
set.seed(9876)
sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 1 1 2 1 1 1 1 3 1 1 3 3 1 1 2 2 1 2 1 1 2 1 1 1 1set.seed(9876)
sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1sample(c(1,2,3), 25, replace=TRUE, prob=c(.7,.2,.1)) # 70% prob 1, 20% prob 2, 10% prob 3 [1] 1 1 2 1 1 1 1 3 1 1 3 3 1 1 2 2 1 2 1 1 2 1 1 1 135.16 Another exmaple - guessingGame()
#-------------------------------------------------------------------------
# Write a guessing game function
#-------------------------------------------------------------------------
# Function should
# 1. pick a random number between 1 and 100
# 2. allow the user to guess the number
# 3. keep looping until the user guesses correctly
# 4. return the number of times it took the user to guess correctly
#-------------------------------------------------------------------------
# NOTE: The following line of code that appears in the function is important
# but easy to forget to include. This line of code converts the guess
# from character to numeric. Without this line you would wind up with a
# very hard to catch bug.
#
# guess <- as.numeric(guess)
#
# Remember that readline always returns a character value.
# Without the code shown above, guess would be character and num would be numeric.
# This would have caused the following problem:
#
# 1. The code "if(guess < num)", which appears in the code below will
# be comparing a character value with a numeric value.
#
# 2. Remember that character values sort and compare differently than
# numeric values. For the purpose of this dicussions, remember
# that "29" and "3" are both character values, while
# 29 and 3 (without the quotes) are numeric values.
#
# 29 < 3 is obviously FALSE, however ..
#
# "29" < "3" is TRUE!!!
#
# This is because character values have different rules for
# comparison than numeric values do. (Remember - because the first
# character, in "29" i.e. the "2" is less than the first charcter
# in "3", i.e. "3", "29" is less than "3".
#
# 3. Because the code "guess < num" compares a character value (i.e. guess)
# and a numeric value (i.e. guess) the rules of "implicit conversions"
# determines that both values will be implicitly converted
# to character values. That means that if guess was "29" and num was 3
# "29" < 3 would be implicitly converted to "29" < "3" which would
# be TRUE! That would cause the block of code following
# if(guess < num) be executed and the user would be told
# "higher, guess again:" instead of the correct answer of
# "lower, guess again".
#
# 4. By converting the guess to numeric, the code if(guess < num) will
# now correctly compare two numeric values and will correctly
# figure out that 29 < 3 is FALSE and will correctly tell the user
# "lower, guess again".
#-------------------------------------------------------------------------
guessingGame <- function(low=1, high=100){
if (!is.numeric(low) || length(low) != 1 || trunc(low) != low ||
!is.numeric(high) || length(high) != 1 || trunc(high) != high ) {
stop("min and max must each be single whole numbers")
}
if (low >= high){
stop("low must be less than high")
}
num <- sample(low:high, 1)
numGuesses <- 1
guess <- readline("guess: ")
guess <- as.numeric(guess) # IMPORTANT LINE - see the NOTE in comments above
while(guess != num) {
if (guess < num){
guess <- readline("higher, guess again: ")
} else if (guess > num) {
guess <- readline("lower, guess again: ")
}
guess <- as.numeric(guess) # IMPORTANT LINE - see comment above for more info
numGuesses <- numGuesses + 1
}
return(numGuesses)
}
#guessingGame()
#guessingGame()
#guessingGame()35.17 Another example - Fibonacci sequence
#-------------------------------------
# Another example - Fibonacci sequence
#-------------------------------------
# The numbers 0 1 1 2 3 5 8 13 21 34 55 89 144 ...
# are the first few number in the infinite sequence
# of "Fibonacci numbers". The first two numbers are 0 and 1
# Every other number in the sequence is the sum of the
# two numbers that precede it.
#
# Write a function fib(n) that returns the first
# n numbers from the fibonacci sequence.
#
# n is expected to be a single non-negative whole number.
# The function should stop with an appropriate
# error message if it is not.
#
# EXAMPLE:
# > fib(1)
# 0
#
# > fib(4)
# 0 1 1 2
#
# > fib(8)
# 0 1 1 2 3 5 8 13
fib <- function(n){
if (!is.numeric(n) || length(n) != 1 || n <= 0){
stop("n must be a single whole non-negative number")
}
if (n == 1){
return(0)
} else if (n == 2) {
return(c(0,1))
}
# set up the variables for the condition in the while
# (n already has a value since it is an argument to the function)
answer <- c(0,1)
while(length(answer) < n){ # a condition that will eventually become FALSE
twoPrevious <- answer[length(answer)-1]
onePrevious <- answer[length(answer)]
# change a variable that's in the condition
answer<-c(answer,onePrevious+twoPrevious)
}
return(answer)
}
fib(0)Error in fib(0): n must be a single whole non-negative numberfib(1)[1] 0fib(4)[1] 0 1 1 2fib(8)[1] 0 1 1 2 3 5 8 13fib(20) [1] 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377
[16] 610 987 1597 2584 4181lapply(1:10, fib)[[1]]
[1] 0
[[2]]
[1] 0 1
[[3]]
[1] 0 1 1
[[4]]
[1] 0 1 1 2
[[5]]
[1] 0 1 1 2 3
[[6]]
[1] 0 1 1 2 3 5
[[7]]
[1] 0 1 1 2 3 5 8
[[8]]
[1] 0 1 1 2 3 5 8 13
[[9]]
[1] 0 1 1 2 3 5 8 13 21
[[10]]
[1] 0 1 1 2 3 5 8 13 21 3435.18 another example - primesUpTo(maxNum)
rm(list=ls()) # start over ...
# The following code was already created above. This is the exact same
# code. It is copied here for reference, since the next function,
# primesUpTo, calls this code.
is.prime <- function( num ) {
if (num < 2){
return(FALSE)
}
divisor <- 2
while ( divisor <= sqrt(num) ) {
if (num %% divisor == 0){
return(FALSE)
}
divisor <- divisor + 1
}
return(TRUE)
}
#-----------------------------------------
# Get all primes up to a certain number
#-----------------------------------------
# Things to think about in the next function.
#
# 1. What would happen if the line: numToCheck = numToCheck + 1
# were placed inside of the block of code for the if?
# All primes up to n
primesUpTo = function( maxNum ){
primes = numeric(0)
# Set up the variables that are used in the condition
# maxNum already has a value since it is an argument to the function
numToCheck = 2
while (numToCheck <= maxNum){ # a condition that will eventually become FALSE
if(is.prime(numToCheck)){
primes = c(primes, numToCheck)
}
# change a variable that is in the condition in a way that will eventually
# make the condition become FALSE
numToCheck = numToCheck + 1
}
primes
}
primesUpTo(10)[1] 2 3 5 7primesUpTo(100) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97primesUpTo(1000) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
[19] 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151
[37] 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
[55] 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359
[73] 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463
[91] 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593
[109] 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701
[127] 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827
[145] 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953
[163] 967 971 977 983 991 99735.19 another example - firstNPrimes ( N )
#---------------------------------
# Get first n primes
#---------------------------------
# Things to think about in the following function.
#
# 1. What would happen if the line: numberToCheck = numberToCheck + 1
# was not typed at all?
firstNPrimes = function( numPrimes ){
# This is the variable that will be returned.
# It is also a variable that is used in the condition.
# We MUST give it a value for both of these reasons.
primes = numeric(0)
# Setup any other values that the while loop will need.
numberToCheck = 2
while(length(primes)<numPrimes){ # condition that will evenutually become FALSE
if (is.prime(numberToCheck)){
primes = c(primes, numberToCheck)
}
# change a variable that is used the the condition in a way that
# eventually the condition will become FALSE
numberToCheck = numberToCheck + 1
}
primes
}
firstNPrimes(10) [1] 2 3 5 7 11 13 17 19 23 29firstNPrimes(20) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71firstNPrimes(100) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
[19] 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151
[37] 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
[55] 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359
[73] 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463
[91] 467 479 487 491 499 503 509 521 523 541primes3000 = firstNPrimes(3000)
length(primes3000) # 3000[1] 3000tail(primes3000, 10) [1] 27337 27361 27367 27397 27407 27409 27427 27431 27437 2744935.20 Another example - flightsBeforeReturning() , itineraray()
#############################################################.
# The following example is interesting but doesn't add any new
# concepts.
#
# 2022 - We skipped going over this example in class for both
# Wilf and Beren classes but I told students to look at this example
# on their own.
#
# -Prof. Rosenthal
#############################################################.
#---------------------------------------------------------------------
# How many flights are needed before you get back to the city you
# started?
#---------------------------------------------------------------------
# Given the following data:
# The vector cities has names and values that are the same set of cities
# just arranged in a different order. Interpret the names of the vector
# positions as the cities where an airline has flights. The management of
# the company schedules the flights based on the data in the vector.
# (see below for more info)
cities = c("new york", "london", "tokyo", "l.a.", "tel aviv", "brussels", "moscow")
names(cities) = sort(cities)
cities brussels l.a. london moscow new york tel aviv tokyo
"new york" "london" "tokyo" "l.a." "tel aviv" "brussels" "moscow" # The airline has a complex scheduling system for each of their planes.
# Each plane flies from city to city to city based on the data shown above.
# Eventually a plane will return to its original city.
#
# For example, a plane that
# starts in Brussels will fly to New York
# From New york, that same plane will fly to Tel Aviv.
# From Tel Aviv, that same plane will fly back to Brussels
# for a total of 3 flights before it returns to where it started.
#
# Similarly, a plane that
# starts in L.A. office will fly to London.
# From London, that same plane will fly to Tokyo.
# From Tokyo, that same plane will fly to Moscow.
# From Moscow that same plane will fly back to L.A.
# for a total of 4 flights before it returns to where it started.
#
# Write a function
# flightsBeforeReturning = function(staringCity, schedulingVector)
#
# that figures out how many flights it will take for a plane that
# starts in startingCity will have to fly before it returns to the same
# startingCity based on the data in the schedulingVector.
flightsBeforeReturning = function(startingCity, schedulingVector){
currentCity = startingCity
numberOfFlights = 0
while( schedulingVector[ currentCity ] != startingCity ){
currentCity = schedulingVector[ currentCity ]
numberOfFlights = numberOfFlights + 1
}
if (schedulingVector[startingCity] != startingCity)
numberOfFlights = numberOfFlights + 1
numberOfFlights
}
cities brussels l.a. london moscow new york tel aviv tokyo
"new york" "london" "tokyo" "l.a." "tel aviv" "brussels" "moscow" flightsBeforeReturning("brussels", cities) # 3[1] 3flightsBeforeReturning("l.a.", cities) # 4[1] 4flightsBeforeReturning("london", cities) # 4[1] 4flightsBeforeReturning("moscow", cities) # 4[1] 4flightsBeforeReturning("new york", cities) # 3[1] 3flightsBeforeReturning("tel aviv", cities) # 3[1] 3flightsBeforeReturning("tokyo", cities) # 4[1] 4# Similar function to above, but this time return the actual sequence of
# cities that are visited
itinerary = function(startingCity, schedulingVector){
currentCity = startingCity
visitedCities = startingCity
while( schedulingVector[ currentCity ] != startingCity ){
visitedCities = c(visitedCities, schedulingVector[currentCity])
currentCity = schedulingVector[ currentCity ]
}
# Add the last leg of the itinerary but only if we flew SOMEWHERE first
if (schedulingVector[startingCity] != startingCity){
visitedCities = c(visitedCities, startingCity)
}
names(visitedCities) = NULL # remove the names
visitedCities
}
cities brussels l.a. london moscow new york tel aviv tokyo
"new york" "london" "tokyo" "l.a." "tel aviv" "brussels" "moscow" itinerary("brussels", cities) # "brussels" "new york" "tel aviv" "brussels"[1] "brussels" "new york" "tel aviv" "brussels"itinerary("l.a.", cities) # "l.a." "london" "tokyo" "moscow" "l.a." [1] "l.a." "london" "tokyo" "moscow" "l.a." itinerary("london", cities) # "london" "tokyo" "moscow" "l.a." "london"[1] "london" "tokyo" "moscow" "l.a." "london"itinerary("moscow", cities) # "moscow" "l.a." "london" "tokyo" "moscow"[1] "moscow" "l.a." "london" "tokyo" "moscow"itinerary("new york", cities) # "new york" "tel aviv" "brussels" "new york"[1] "new york" "tel aviv" "brussels" "new york"itinerary("tel aviv", cities) # "tel aviv" "brussels" "new york" "tel aviv"[1] "tel aviv" "brussels" "new york" "tel aviv"itinerary("tokyo", cities) # "tokyo" "moscow" "l.a." "london" "tokyo" [1] "tokyo" "moscow" "l.a." "london" "tokyo" 35.21 Using lapply and sapply to call a function multiple times
Suppose we wanted to get multiple factorials and put them in a vector. We could do so by putting the code for a while loop inside the body of another while loop (i.e. this is called a nested loop). We will explore how to do that in the next section. However, nested loops can be confusing, especially for new programmers.
For now, a simpler way to get the factorials of each value in a numeric vector is to use the lapply function. (For a review of lapply see this section.
#----------------------------------------------------------------
# The myFactorial function above only works with a single number.
# You can get the factorials of many numbers by using lapply
# to get a list of the answers for several numbers
#----------------------------------------------------------------
lapply(c(1,3,5,10), myFactorial) # find the myFactorials of 1,2,3 and 4Error: object 'myFactorial' not found35.21.1 sapply is similar to lapply
#---------------------------------------------------------------------
# sapply
#---------------------------------------------------------------------
# The sapply function is similar to the lapply function.
#
# The "l" in lapply stands for "list" since the return value of
# lapply is always a list.
#
# The "s" in sapply stands for "simplify". The idea of sapply is that
# sapply can sometimes return the data in a "simpler" structure
# than lapply does. In this regard, vectors and matrices are
# considered "simpler" than lists.
#
# sapply processes the data in a similar way to lapply. Each value
# in the vector is passed to the specified function. The return values
# from the function calls are then gathered into a single object
# (a list, a matrix or a vector) in the following way:
#
# - If every "answer" (i.e. the return value from the function call)
#is a single vector of length 1, then sapply will return
# all of the answers in a single vector instead of returning a list of answers.
#
# - If every "answer" is a vector that has more than one value but all answers
# are the same length (e.g. all answers have 2 values or all answers have 3 values, etc)
# then sapply returns a matrix. Each column in the matrix will contain one of the answers.
#
# - If different "answers" are of different lengths or different classes
# of data, then sapply returns a list of answers. In this case, sapply
# and lapply return the same value.
#
# The "s" in "sapply" stands for "simplify". In other words, sapply
# might return a vector or a matrix, instead of a list. Vectors and matrices
# can be thought of as "simpler" data structures than lists, hence the name "sapply".
#
# The "l" in "lapply" stands for "list". This is because the result
# of calling lapply is ALWAY a list of answers.
#---------------------------------------------------------------------
# compare the following call to sapply with the next call to lapply
# sapply returns a vector in this case since myFactorial always returns a single number
sapply(c(1,3,5,10), myFactorial) Error: object 'myFactorial' not found# lapply always returns a list of answers (remember "l" stands for "list")
lapply(c(1,3,5,10), myFactorial) Error: object 'myFactorial' not found35.21.2 sapply - returns vector, matrix or list
As mentioned above, depending on the return values from the function calls, sapply might return a vector, a matrix or a list.
As shown above with the myFactorial function, when all function calls return a single value, sapply returns a vector.
The examples below show that when all function calls return vectors of more than one value, but all of the same length, then sapply returns a matrix.
The examples below also show that when the function calls return vectors of different lengths, or different classes of data (e.g. dataframes, lists, etc), then sapply returns a list.
#..................................................................
# These values and functions will be used below to demonstrate the
# differences between the lapply and sapply functions.
#..................................................................
# the following function always returns a vector of 3 numbers
# regardless of the value of num. See examples below.
getThreeNumbers = function(num){
if(length(num) > 1 || !is.numeric(num)){
stop("num is expected to be a single number")
}
c(num, num+10, num+100)
}
getThreeNumbers(2)[1] 2 12 102getThreeNumbers(3)[1] 3 13 103getThreeNumbers(5)[1] 5 15 105# the following function returns different length vectors
# for different values of num. See examples below.
repNumTimes = function(num){
if(length(num) > 1 || !is.numeric(num)){
stop("num is expected to be a single number")
}
rep(num, num)
}
repNumTimes(2)[1] 2 2repNumTimes(3)[1] 3 3 3repNumTimes(5)[1] 5 5 5 5 5# These are some numbers we will use with the following examples
nums = c(1,3,5,10)
# Function f always returns 3 numbers so sapply returns a matrix of 3 rows.
# There will be as many columns in the matrix as there are numbers in nums.
lapply(nums, getThreeNumbers) # a list[[1]]
[1] 1 11 101
[[2]]
[1] 3 13 103
[[3]]
[1] 5 15 105
[[4]]
[1] 10 20 110sapply(nums, getThreeNumbers) # a matrix [,1] [,2] [,3] [,4]
[1,] 1 3 5 10
[2,] 11 13 15 20
[3,] 101 103 105 110# Function g returns different length vectors for different numbers
# so sapply returns a list, just as lapply does.
lapply(nums, repNumTimes) # a list[[1]]
[1] 1
[[2]]
[1] 3 3 3
[[3]]
[1] 5 5 5 5 5
[[4]]
[1] 10 10 10 10 10 10 10 10 10 10sapply(nums, repNumTimes) # also a list[[1]]
[1] 1
[[2]]
[1] 3 3 3
[[3]]
[1] 5 5 5 5 5
[[4]]
[1] 10 10 10 10 10 10 10 10 10 1035.22 Example: Combining techniques - loops, lapply/sapply, named lists
The following examples show how to use lapply and sapply with the is.prime function.
The following gets the first 20 numbers and checks if they are prime. It’s relatively easy to see which number is prime and which is not as the results are in order - 1st answer is TRUE or FALSE for 1, 2nd answer is TRUE or FALSE for 2, etc.
lapply(1:20, is.prime) [[1]]
[1] FALSE
[[2]]
[1] TRUE
[[3]]
[1] TRUE
[[4]]
[1] FALSE
[[5]]
[1] TRUE
[[6]]
[1] FALSE
[[7]]
[1] TRUE
[[8]]
[1] FALSE
[[9]]
[1] FALSE
[[10]]
[1] FALSE
[[11]]
[1] TRUE
[[12]]
[1] FALSE
[[13]]
[1] TRUE
[[14]]
[1] FALSE
[[15]]
[1] FALSE
[[16]]
[1] FALSE
[[17]]
[1] TRUE
[[18]]
[1] FALSE
[[19]]
[1] TRUE
[[20]]
[1] FALSEThe following gets the prime status of the first few odd numbers. It’s harder to see which number is prime and which is not as the first TRUE/FALSE is for 1, the second TRUE/FALSE is for 3, the third TRUE/FALSE is for 5, etc.
lapply(seq(1,19,by=2), is.prime) # harder to read ... 2nd answer is for 3 not 2[[1]]
[1] FALSE
[[2]]
[1] TRUE
[[3]]
[1] TRUE
[[4]]
[1] TRUE
[[5]]
[1] FALSE
[[6]]
[1] TRUE
[[7]]
[1] TRUE
[[8]]
[1] FALSE
[[9]]
[1] TRUE
[[10]]
[1] TRUEWe can make it easier to see which number is prime and which is not by creating a named vector where the name of each element in the vector is the number that was checked.
# add names
x = lapply(seq(1,19,by=2), is.prime)
names(x) = seq(1,19,by=2)
x # names must start with a letter. If they don't you can include the name in `backticks`$`1`
[1] FALSE
$`3`
[1] TRUE
$`5`
[1] TRUE
$`7`
[1] TRUE
$`9`
[1] FALSE
$`11`
[1] TRUE
$`13`
[1] TRUE
$`15`
[1] FALSE
$`17`
[1] TRUE
$`19`
[1] TRUEx$`9` # FALSE[1] FALSEx$`17` # TRUE[1] TRUE#------------------------------------------.
# Use sapply to get multiple results
#------------------------------------------.
sapply(1:20, is.prime) # result is below [1] FALSE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE
[13] TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE# FALSE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE FALSE
sapply(seq(1,19,by=2), is.prime) # # check just the odd numbers [1] FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE# [1] FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
# add names
x = sapply(seq(1,19,by=2), is.prime)
names(x) = seq(1,19,by=2)
x # result is below 1 3 5 7 9 11 13 15 17 19
FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE # 1 3 5 7 9 11 13 15 17 19
# FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
x[9] # result is below - we only checked odd numbers so the 9th number checked is 17 17
TRUE # 17
# TRUE
x["9"] # result is below - the value whose "name" is "9" 9
FALSE # 9
# FALSE 35.23 NESTED LOOPS
#####################################################################
#####################################################################
##
## NESTED LOOPS
##
## A "nested loop" is a loop inside of another loop (similar
## to "nested ifs")
##
## We often refer to the "outer loop" and the "inner loop".
##
#####################################################################
#####################################################################
rm(list=ls()) # start over
example = function( maxOuter, maxInner){
outer = 1
while(outer <= maxOuter){
cat("OUTER LOOP (before inner loop): outer=", outer, "\n\n")
inner = 1
while(inner <= maxInner){
cat(" INNER LOOP: outer=",outer,"inner=",inner,"\n")
inner = inner + 1
}
outer = outer + 1
}
}
example(maxOuter = 2, maxInner = 3)OUTER LOOP (before inner loop): outer= 1
INNER LOOP: outer= 1 inner= 1
INNER LOOP: outer= 1 inner= 2
INNER LOOP: outer= 1 inner= 3
OUTER LOOP (before inner loop): outer= 2
INNER LOOP: outer= 2 inner= 1
INNER LOOP: outer= 2 inner= 2
INNER LOOP: outer= 2 inner= 3 example(maxOuter = 3, maxInner = 5)OUTER LOOP (before inner loop): outer= 1
INNER LOOP: outer= 1 inner= 1
INNER LOOP: outer= 1 inner= 2
INNER LOOP: outer= 1 inner= 3
INNER LOOP: outer= 1 inner= 4
INNER LOOP: outer= 1 inner= 5
OUTER LOOP (before inner loop): outer= 2
INNER LOOP: outer= 2 inner= 1
INNER LOOP: outer= 2 inner= 2
INNER LOOP: outer= 2 inner= 3
INNER LOOP: outer= 2 inner= 4
INNER LOOP: outer= 2 inner= 5
OUTER LOOP (before inner loop): outer= 3
INNER LOOP: outer= 3 inner= 1
INNER LOOP: outer= 3 inner= 2
INNER LOOP: outer= 3 inner= 3
INNER LOOP: outer= 3 inner= 4
INNER LOOP: outer= 3 inner= 5 35.24 example - primesUpTo() with nested loops
###############################################################################
#
# Examples of nested loops
#
###############################################################################
rm(list=ls()) # start over ...
#-----------------------------------------------------------------------------
# Above we defined a
#
# primesUpTo = function( n )
#
# That returns a vector of all the primes up to n. For example:
#
# > primesUpTo(15)
# [1] 2 3 5 7 11 13
#
# In that version of the function, we used a single loop. We also
# called the function is.prime that we had defined earlier inside of the loop.
# Both the funciton is.prime and the function primesUpTo, used a single
# loop for each function.
#
#
# ***********************************************************************
# *** THE FOLLOWING IS ANOTHER WAY OF WRITING THE SAME FUNCTION. ***
# *** THIS VERSION DOES NOT CALL is.prime AT ALL. RATHER THIS SINGLE ***
# *** FUNCTION DOES ALL OF THE WORK USING TWO DIFFERENT LOOPS - ***
# *** ONE INSIDE THE OTHER (i.e. a "nested loop") ***
# ***********************************************************************
#
# The following function, primesUpTo_nestedLoops, returns the exact same values
# as the primesUpTo function above. However, this version of the function
# does NOT call is.prime. Rather, this version calculates whether a number
# is prime directly in the same function by using a nested loop (i.e.
# one loop inside of another loop)
#-----------------------------------------------------------------------------
rm(list=ls())
primesUpTo_nestedLoops = function( maxNum ){
primes = numeric(0)
# Set up the variables that are used in the condition
# maxNum already has a value since it is an argument to the function
numToCheck = 2
while (numToCheck <= maxNum){ # a condition that will eventually become FALSE
isPrime = TRUE
# Check if numToCheck is prime. If it isn't prime set the variable
# isPrime to FALSE.
divisor = 2
while(divisor < numToCheck){
if ( numToCheck %% divisor == 0){
isPrime = FALSE
}
divisor = divisor + 1
}
if(isPrime == TRUE){
primes = c(primes, numToCheck)
}
# change a variable that is in the condition in a way that will eventually
# make the condition become FALSE
numToCheck = numToCheck + 1
}
primes
}
primesUpTo_nestedLoops(10)[1] 2 3 5 7primesUpTo_nestedLoops(100) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97# VERSION WITH "nested loops"
primesUpTo_nestedLoops = function( maxNum ){
primes = numeric(0)
numToCheck = 2
while (numToCheck <= maxNum){
# Use an inner loop to figure out if numToCheck is in fact prime
# and if it is add numToCheck to the vector primes
isPrime = TRUE
divisor = 2
while(divisor < numToCheck){
if( numToCheck %% divisor == 0){
isPrime = FALSE
}
divisor = divisor+1
}
# Add the numToCheck to the primes if it in fact is prime
if(isPrime) {
primes = c(primes, numToCheck)
}
numToCheck = numToCheck + 1
}
primes
}
primesUpTo_nestedLoops(10)[1] 2 3 5 7primesUpTo_nestedLoops(100) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97primesUpTo_nestedLoops(1000) [1] 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
[19] 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151
[37] 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
[55] 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359
[73] 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463
[91] 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593
[109] 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701
[127] 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827
[145] 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953
[163] 967 971 977 983 991 99735.25 example - firstNPrimes() with nested loops
#---------------------------------------------------------------------------
# QUESTION
#
# Rewrite the function myt to use a single loop (not a nested loop).
#
# HINTS
#
# - Use a single loop.
#
# The loop should keep updating a variable, eg. inRow, that contains
# the number of a row from the input matrix. For example
#
# If the input matrix has 3 rows then the loop should go around 3 times.
# The 1st time through the loop, the variable inRowNumber, should contain 1,
# The 2nd time through the loop, the variable inRowNumber, should contain 2,
# The 3rd time through the loop, the variable inRowNumber, should contain 3
#
# - Inside the loop use matrix notation to assign the values from
# a row in the input matrix to the corresponding column
# in the output matrix
#
#---------------------------------------------------------------------------
#############.
# ANSWER
#############.
myt=function( m ){
returnValue = matrix(1 ,nrow=ncol(m) ,ncol=nrow(m))
inRow = 1
while(inRow <= nrow(m)) {
returnValue[ , inRow] = m[inRow , ]
inRow = inRow + 1
}
returnValue
}
mat = matrix(seq(10,180,10), nrow=3, ncol=6)
mat [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 10 40 70 100 130 160
[2,] 20 50 80 110 140 170
[3,] 30 60 90 120 150 180myt(mat) [,1] [,2] [,3]
[1,] 10 20 30
[2,] 40 50 60
[3,] 70 80 90
[4,] 100 110 120
[5,] 130 140 150
[6,] 160 170 18035.26 More practice - drawing shapes with numbers
#####################################################################.
# SOME "TOY" FUNCTIONS
#
# Below are a few "toy" examples of using nested loops. Exercises
# like these help you to become more familiar with the concepts
# of nested loops. This is similar to playing "scales" when learning
# to play the piano - no one will play scales in real life - but
# it is important to get the hang of things when you're first
# starting out.
#####################################################################.
#---------------------------------------------------------------------
# The following are some simple functions that do NOT use nested loops.
# These are provided for comparison with the equivalent versions that use
# nested loops which we will show you below.
#---------------------------------------------------------------------
rm(list=ls()) # start over
# draw a line of x's of the specified width
# Do not use the rep function. Use the cat function and a loop.
drawLine_WithXs = function( width ) {
while(width > 0){
cat("x")
width = width - 1
}
}
drawLine_WithXs(4) # xxxxxxxxdrawLine_WithXs(5) # xxxxxxxxxx# draw a box of x's
drawBox_WithXs = function(h, w){
while(h > 0){
drawLine_WithXs(w)
cat("\n")
h = h - 1
}
}
drawBox_WithXs(3,4) # box of 3 rows and 4 columns of x'sxxxx
xxxx
xxxx# Draw a horizontal line with calls to cat that displays the numbers as shown below
drawLine_WithNums = function(width){
num1 = 1
while(num1 <= width){
cat(num1)
num1 = num1 + 1
}
}
drawLine_WithNums(4) # 12341234drawLine_WithNums(5) # 1234512345#-----------------------------------------------------------------------
# drawBox using nested loops
#-----------------------------------------------------------------------
# QUESTION:
# Write a function
# drawBox1 = function(height, width)
#
# height and width are expected to be whole numbers between 1 and 9.
# The function should draw a box that has dimensions height rows and width columns.
# The box should be drawn with numbers such that each number represent the
# number of the column it is in. For example:
#
# > drawBox1(3, 5)
# 12345
# 12345
# 12345
drawBox1 = function(height, width){
rowNumber = 1
while(rowNumber <= height){
colNumber = 1
while(colNumber <= width){
cat(colNumber)
colNumber = colNumber + 1
}
cat("\n")
rowNumber = rowNumber + 1
}
}
#debugonce(drawBox1)
drawBox1(3, 4)1234
1234
1234# 1234
# 1234
# 1234
drawBox1(4,9)123456789
123456789
123456789
123456789#-----------------------------------------------------------------------------
# QUESTION:
# Write a function
# drawBox2 = function(height, width)
#
# height and width are expected to be whole numbers between 1 and 9.
# The function should draw a box that has dimensions height rows and width columns.
# The box should be drawn with numbers such that each number represent the
# number of the row it is in. For example:
#
# > drawBox1(3, 5)
# 11111
# 22222
# 33333
drawBox2 = function(height, width){
rowNumber = 1
while(rowNumber <= height){
colNumber = 1
while(colNumber <= width){
cat(rowNumber)
colNumber = colNumber + 1
}
cat("\n")
rowNumber = rowNumber + 1
}
}
drawBox2(3,4)1111
2222
3333# 1111
# 2222
# 3333
#-----------------------------------------------------------------------------
# Write the function drawBox3 to produce the results according to the pattern
# demonstrated in the following example:
#
# EXAMPLE:
# > drawBox3(3,4)
# 3333
# 2222
# 1111
#-----------------------------------------------------------------------------
drawBox3 = function(height, width){
rowNumber = height
while(rowNumber > 0){
colNumber = 1
while(colNumber <= width){
cat(rowNumber)
colNumber = colNumber + 1
}
cat("\n")
rowNumber = rowNumber - 1
}
}
drawBox3(3,4)3333
2222
1111# 3333
# 2222
# 1111
#-----------------------------------------------------------------------------
# Write the function drawBox4 to produce the results according to the pattern
# demonstrated in the following example:
#
# EXAMPLE:
# > drawBox3(3,4)
# 1234
# 1234
# 1234
#-----------------------------------------------------------------------------
drawBox4 = function(height, width){
rowNumber = 1
while (rowNumber <= height){
colNumber = 1
while(colNumber <= width) {
cat( colNumber )
colNumber = colNumber + 1
}
cat("\n")
rowNumber = rowNumber+1
}
}
drawBox4(3,4)1234
1234
1234# 1234
# 1234
# 1234
#-----------------------------------------------------------------------------
# Write the function drawBox4 to produce the results according to the pattern
# demonstrated in the following example:
#
# EXAMPLE:
# > drawBox5(3,4)
# 4321
# 4321
# 4321
#-----------------------------------------------------------------------------
#############.
# ANSWER
#############.
drawBox5 = function(height, width){
row = 1
while(row <= height){
col = width
while( col >= 1){
cat(col)
col = col - 1
}
cat("\n")
row = row + 1
}
}
drawBox5(3,4)4321
4321
4321# 4321
# 4321
# 4321
#-----------------------------------------------------------------------------
# Write the function drawTriangle1 to produce the results according to the pattern
# demonstrated in the following example:
#
# EXAMPLE:
# > drawTriangle1(3)
# 1
# 12
# 123
#
# > drawTriangle(5)
# 1
# 12
# 123
# 1234
# 12345
#-----------------------------------------------------------------------------
#############.
# ANSWER
#############.
drawTriangle1 = function(size){
row = 1
while(row <= size){
col = 1
while(col <= row){
cat(col)
col = col + 1
}
cat("\n")
row = row + 1
}
}
drawTriangle1(3)1
12
123drawTriangle1(9)1
12
123
1234
12345
123456
1234567
12345678
123456789# 1
# 12
# 123
#-----------------------------------------------------------------------------
# Write the function drawTriangle1 to produce the results according to the pattern
# demonstrated in the following example:
#
# EXAMPLE:
# > drawTriangle2(3)
# 111
# 22
# 3
#-----------------------------------------------------------------------------
#############.
# ANSWER
#############.
drawTriangle2 = function(size){
outer = 1
while( outer <= size ){
inner = 1
while( inner <= size - outer + 1){
cat ( outer )
inner = inner + 1
}
cat("\n")
outer = outer + 1
}
}
drawTriangle2(3)111
22
3# 111
# 22
# 3
drawTriangle2(5)11111
2222
333
44
535.27 Other ways to do something over and over …
In R there are a few ways to do something over and over again … Often it is possible to recreate the same effect as a while loop by using one of these other approaches.
- Vector arithmetic automaticlly performs the same operation over and over to each item in the vector. For example:
# the folloiwng adds 1 to each number
nums = c(10,20,30)
nums + 1[1] 11 21 31- R has many “vectorized functions” that do something over and over. For exmaple, the prod function takes the product of all the values in a vector. This can be used to very quickly calculate the factorial of a number without actually using the factorial (or myFactorial) function.
prod(1:5) # product of the values in the vector, i.e. 120 - same as myFactorial(5)[1] 120The apply family of R functions, e.g. lapply and sapply (we’ll cover this later) perform a function for each value in a vector (or a list). See example below.
R has other types of loops - e.g. for loop (covered in another chapter) and repeat loop (not covered in this book)