# 14  Iterations: While Loop

In the previous chapter you got introduced to your first iterative construct: `for` loops. You use this type of loop when you know how many times a given computation needs to be repeated. But what about those situations in which you have to repeat a process without necessarily knowing how many times this repetition will take place? This is where we need a more general type of loop, namely, the while loop.

## 14.1 Motivation

Let’s begin with the same toy example discussed in the previous chapter. Say you have a vector `vec <- c(3, 1, 4)`, and suppose you want to obtain a new vector `vec2` that adds 1 to every element in `vec`. You know that this can easily be achieved using vectorized code:

``````vec <- c(3, 1, 4)

vec2 <- vec + 1
vec2``````
``[1] 4 2 5``

Again, in order to explain the concept of a `while` loop, I am going to ask you to pretend that R does not have vectorized code.

What would you need to do in order to add 1 to the elements in `vec`? As we mentioned in the preceding chapter, you would need to do something like this:

``````# new vector to be updated
vec2 <- rep(0, 3)

# repetitive steps
vec2[1] <- vec[1] + 1
vec2[2] <- vec[2] + 1
vec2[3] <- vec[3] + 1``````

That is, take the first element in `vec` and add 1, then take the second element in `vec` and add 1, and finally the third element in `vec` and add 1. Basically, you are performing the same type of operation several times: selecting an element in `vec` and adding 1 to it. But there’s a lot of (unnecessary) repetition.

We’ve seen how to write a `for` loop to take care of the addition computation. Alternatively, we can also approach this problem from a slightly different perspective by considering a stopping condition to decide when to terminate the repetitive process of adding 1 to the elements in `vec`.

What stopping condition can we use? Well, one example may involve: “let’s keep selecting a single element in `vec` and adding 1 to it, until we exhaust all elements in `vec`”. In other words, let’s keep iterating until we reach the last element in `vec`.

As usual, the first step involves identifying the common structure of the repetitive steps. We can make the repetitive code a bit more general by referring to each position as `pos`:

``vec2[pos] <- vec[pos] + 1``

Once we have the correct abstraction for the code that needs to be repetead, then we can encapsulate it with a `while` loop. Let me first show you an example and then we’ll examine it in detail:

``````# input vector
vec <- c(3, 1, 4)

# initialize output vector
vec2 <- rep(0, 3)

# declare auxiliary iterator
pos <- 1

# while loop
while (pos <= length(vec)) {
vec2[pos] <- vec[pos] + 1
pos <- pos + 1  # update iterator
}``````

The first thing that I should mention is that writing an R `while` loop is a bit more complex than writing a `for` loop. The complexity has to do with some of the things that R does not automatically take care of in a `while` loop.

One main difference between a `for` loop and a `while` loop is that in the latter we must explicit declare the auxiliary iterator and give it an initial value: `pos <- 1`.

Next we have the `while` statement. This statement is technically a function, but I prefer to think of it, and call it, a statement (like the `if` and the `for` statements). What you pass inside parenthesis of the `while` declaration is a condition. This is basically any piece of code that R will evaluate and coerce it into a logical condition that is `TRUE` or `FALSE`. The `while` loop iterates as long as the condition is `TRUE`. If the condition becomes `FALSE` then the loop is terminated.

The code of the repetitive steps consists of an R expression `{ ... }`. This is where we indicate what to do at each step. Often, an important piece of code that we need to include here involves increasing the value of the auxiliary iterator: `pos <- pos + 1`. In this particular example, if we don’t increase the iterator `pos`, the loop would iterate forever.

Note that the condition is the stopping condition, which in turn depends on the auxiliary iterator: `pos <= length(vec)`. You can think of this condition as: “let’s keep iterating until we reach the last element in `vec`”.

## 14.2 Anatomy of a While Loop

Now that you’ve seen a first example of a `while` loop, I can give you a generic template for this kind of iterative construct:

``````iterator <- initial

while (condition) {
do_something
iterator <- iterator + 1
}``````

What’s going on?

• you need to declare the auxiliary iterator with some initial value

• you declare the `while` statement by giving a condition inside parenthesis

• the condition must be a piece of code that gets evaluated into a single logical value: `TRUE` or `FALSE`

• the condition is used as the stopping condition: if the condition is `TRUE` the loop keeps iterating; when the condition becomes `FALSE` the loop is terminated

• we use an R compound expression `{ ... }` to embrace the code that will be repeated at each iteration

• inside the loop, you typically need to increase the value of the `iterator`; even if the `condition` does not depend on the `iterator`, it’s a good idea to keep track of the number of iterations in the loop

## 14.3 Another Example

Let’s see a more interesting example.

Say we generate a vector with 10 different integer numbers between 1 and 100, arranged in increasing order. To make things more interesting, we are going to generate these numbers in a random way using the `sample.int()` function that allows us to get a random sample of `size = 10` integers, sampling without replacement (`replace = FALSE`):

``````set.seed(234)  # for replication purposes

# vector of 10 random integers between 1 and 100
random_numbers = sample.int(n = 100, size = 10, replace = FALSE)
random_numbers = sort(random_numbers)
random_numbers``````
`` [1]  1 18 31 34 46 56 68 92 97 98``

What are we going to do with these `random_numbers`? We are going to compute a cumulative sum until its value becomes greater than 100. And we are going to consider these two questions:

• What is the value of the cumulative sum?

• How many numbers were added to reach the sum’s value?

My recommendation is to always start with baby steps. Simply put, start writing code for a couple of concrete steps so that you understand what kind of computations will be repeated, and what things they have in common:

``````# initialize output sum
total_sum = 0

# accumulate numbers
total_sum = total_sum + random_numbers[1]
total_sum = total_sum + random_numbers[2]
total_sum = total_sum + random_numbers[3]
# ... keep adding numbers as long as total_sum <= 100``````

There are three important aspects to keep in mind:

• we need an object to store the cumulative sum: `total_sum`

• we need an iterator to move through the elements of `random_numebrs`

• and of course we need to determine a stopping-condition: `total_sum <= 100`

Here’s the code:

``````# initialize object of cumulative sum
total_sum = 0

# declare iterator
pos = 0

# repetitive steps
while (total_sum <= 100) {
pos = pos + 1
total_sum = total_sum + random_numbers[pos]
}

# what is the value of the cumulative sum?
total_sum``````
``[1] 130``
``````# how many iterations were necessary?
pos``````
``[1] 5``

Observe that in this example, we declared `pos = 0`. Then, at each iteration, we increase its value `pos = pos + 1`, and then we added `random_numbers[pos]` to the previous `total_sum` value, effectively updating the cumulative sum.

For comparison purposes, consider this other `while` loop. It looks extremely similar to the preceding loop but there is an important difference.

``````# initialize object of cumulative sum
total_sum = 0

# declare iterator
pos = 1

# repetitive steps
while (total_sum <= 100) {
total_sum = total_sum + random_numbers[pos]
pos = pos + 1
}

# what is the value of the cumulative sum?
total_sum``````
``[1] 130``
``````# how many iterations were necessary?
pos``````
``[1] 6``

Can you see the difference between these two `while` loops?

In this second loop, the iterator is declared as `pos = 1`, and its value is increased after updating the cumulative sum. While `total_sum` has the correct value, `pos` does not indicate anymore the right number of iterations.

I wanted to show you this second example to make a point: in a `while` loop you not only need to declare the iterator before entering the loop, but you also need to carefully think what initial value you’ll use, as well as when to increase its value inside the loop. Some times the very first thing to do in each iteration is to increase the value of the iterator; some times that’s the last thing to do. It all depends on the specific way you are approaching a given iterative task.

### 14.3.1 While Loops and Next statement

Sometimes we need to skip a certain iteration if a given condition is met, this can be done with the `next` statement. The following code chunk contains an abstract template that uses `next`:

``````iterator <- initial

while (condition) {
do_something
if (skip_condition) {
next
}
iterator <- iterator + 1
}``````

As a less abstract example, let’s bring back the while loop of the cumulative sum of random numbers, but this time say we want to skip any numbers between 30 and 39. This means we need an `if-else` statement to check whether a given element of `random_numbers` is between 30 and 39. If yes, we should skip that element and go to the `next` iteration. Here is how to do it:

``````total_sum = 0
pos = 0

while (total_sum <= 100) {
pos = pos + 1
if (random_numbers[pos] %in% 30:39) {
next
}
total_sum = total_sum + random_numbers[pos]
}

total_sum``````
``[1] 121``
``pos``
``[1] 6``

### 14.3.2 While Loops and Break statement

In addition to skipping certain iterations, sometimes we need to stop a loop from iterating if a given condition is met. This can be done with the `break` statement, which is shown below in an abstract code template:

``````while (condition) {
expr1
expr2
if (stop_condition) {
break
}
expr3
expr4
}``````

Let’s go back to the cumulative sum example. Say we want to stop iterating if numbers are greater than or equal to 40. Like we did previously, we need again an `if-else` statement to check whether a given element of `random_numbers` is greater than or equal to 40. If yes, we stop the loop from iterating by using the `break` statement as follows:

``````total_sum = 0
pos = 0

while (total_sum <= 100) {
pos = pos + 1
if (random_numbers[pos] >= 40) {
break
}
total_sum = total_sum + random_numbers[pos]
}

total_sum``````
``[1] 84``
``pos``
``[1] 5``