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Control Structures and Logic

a. Suppose I create a vector x <- 1:120. Then I decide to set all values in 'x' greater than 78 to 0. I write the following code, but get a warning message and it doesn't do anything to 'x'. What is wrong with the code?

if(x > 78) {
        x <- 0
}

The syntax of this R expression is incorrect.
The expression uses curly braces.
There are no elements in 'x' that are greater than 78
'x' is a vector of length 120 and 'if' can only test a single logical statement.
'x' cannot be set to 0 because 'x' is a vector and 0 is a scalar.

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b. Suppose I want to calculate the value of 1 + 1/2 + 1/3 + ··· + 1/100. I write the following code, but it doesn't seem to work. What's wrong with the code? (try to figure out the answer without running the code first)

x <- 0
i <- 1
while(i <= 100) {
        x <- x + 1/i
}

The command 'x <- x + 1/i' is illegal.
The sum is too big for R to handle, resulting in the 'floating point overflow' error.
There is a syntax error in 'while(i <= 100)'. It should be 'while(i<100 | i==100)'.
The computer appears to hang, but that's just because R is slow in dealing with a while-loop. It takes a few seconds (or tens of seconds depending on your computer speed) for R to finish the computation.
It's an infinite loop: the condition i <= 100 will always be true.

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c. In the following code, what will be returned by the last command?

x <- c(1,5,10,10,5,1)
y <- c(10,5,1)
x == y

A logical vector of length 6 with values FALSE, TRUE, FALSE, FALSE, FALSE, FALSE
A logical vector of length 1 with the value FALSE
A logical vector of length 6 with values FALSE, TRUE, FALSE, TRUE, TRUE, TRUE
An error message
A logical vector of length 3 with values FALSE, TRUE, FALSE

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d. Suppose x is an integer vector of length 366. Each element in x is an integer between 1 and 365. Consider the following code:

for (n in 2:366) {
   if (any(x[1:(n-1)]==x[n])) {
      break
   }
}
print(n)

What does this code do?
It counts the total number of elements in 'x', i.e. n is the same as length(x).
It counts the number of repeated numbers in 'x'.
It searches for the first occurance of a repeated number in 'x'.
It generates a random number and stores it in 'n'.
None of the above.

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Hint: If you find it hard to figure out, try assigning x to some specific values and run the code. For example, try x <- c(1:365,34) and x <- c(rep(1:7,52),105,218) and see what you'll get. Which of the answers above seem to match the outputs? Once you identify a possible correct answer, try running the code with x <- sample.int(365, 366, replace=TRUE), which draws 366 integers randomly between 1 and 365 with replacement and assigns them to x. Is the result consistent with the possible correct answer?