Function arguments in R Programming - Time & Space Complexity

Time Complexity: Function arguments

O(n)

Understanding Time Complexity

When we use functions with arguments, it is important to see how the time to run the function changes as the input changes.

We want to know: how does the work inside the function grow when the input size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

my_sum <- function(x) {
  total <- 0
  for (i in seq_along(x)) {
    total <- total + x[i]
  }
  return(total)
}

values <- 1:100
my_sum(values)
    

This function adds up all numbers in a vector given as an argument.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that goes through each element of the input vector.
• How many times: Once for each item in the input vector.

How Execution Grows With Input

As the input vector gets bigger, the function does more additions, one for each item.

Input Size (n)	Approx. Operations
10	10 additions
100	100 additions
1000	1000 additions

Pattern observation: The work grows directly with the size of the input vector.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the input vector gets bigger.

Common Mistake

[X] Wrong: "The function runs in the same time no matter how big the input is."

[OK] Correct: Because the function adds each number one by one, more numbers mean more work and more time.

Interview Connect

Understanding how function arguments affect time helps you explain how your code handles different input sizes clearly and confidently.

Self-Check

"What if the function used two loops, each going through the input vector? How would the time complexity change?"

Practice

1. What is the purpose of function arguments in R?
my_function <- function(x, y) { x + y }

easy

A. To create variables outside the function

B. To print output from the function

C. To send information into the function for processing

D. To stop the function from running

Solution

1. Step 1: Understand what arguments do

   Arguments are values you give to a function so it can use them inside its code.

2. Step 2: Look at the example function

   The function takes x and y as inputs and adds them, showing arguments are inputs.

3. Final Answer:

   To send information into the function for processing -> Option C

4. Quick Check:

   Function arguments = inputs [OK]

Hint: Arguments are inputs you give to functions [OK]

Common Mistakes:

• Thinking arguments print output
• Confusing arguments with variables outside
• Believing arguments stop function execution

2. Which of the following is the correct way to define a function with two arguments a and b in R?

easy

A. my_func <- function {a, b} return(a + b)

B. my_func <- function(a, b) { return(a + b) }

C. my_func <- function[a, b] { return(a + b) }

D. my_func <- function(a; b) { return(a + b) }

Solution

1. Step 1: Recall R function syntax

   Functions use parentheses () to list arguments separated by commas.

2. Step 2: Check each option

   Only my_func <- function(a, b) { return(a + b) } uses parentheses and commas correctly; others use wrong brackets or separators.

3. Final Answer:

   my_func <- function(a, b) { return(a + b) } -> Option B

4. Quick Check:

   Function args use (a, b) [OK]

Hint: Use parentheses and commas for arguments [OK]

Common Mistakes:

• Using square brackets instead of parentheses
• Separating arguments with semicolons
• Omitting parentheses around arguments

3. What will be the output of this R code?

add <- function(x, y = 5) {
  x + y
}
add(3)

medium

A. 8

B. 3

C. 5

D. Error: missing argument y

Solution

1. Step 1: Understand default argument values

   The function add has y defaulting to 5 if not provided.

2. Step 2: Call the function with one argument

   Calling add(3) uses x=3 and default y=5, so result is 3 + 5 = 8.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   3 + default 5 = 8 [OK]

Hint: Default arguments fill in missing values [OK]

Common Mistakes:

• Expecting error when argument is missing
• Ignoring default argument values
• Confusing which argument has default

4. Identify the error in this R function definition:

multiply <- function(x, y) {
  result <- x * z
  return(result)
}

medium

A. Function should not use return statement

B. Function name cannot be multiply

C. Arguments must have default values

D. Variable z is not defined inside the function

Solution

1. Step 1: Check variables used inside function

   The function uses z but only x and y are arguments; z is undefined.

2. Step 2: Understand variable scope

   Variables inside functions must be defined or passed as arguments; z is missing.

3. Final Answer:

   Variable z is not defined inside the function -> Option D

4. Quick Check:

   Undefined variable = error [OK]

Hint: Use only defined arguments or variables inside functions [OK]

Common Mistakes:

• Using variables not passed as arguments
• Thinking return is optional error
• Believing arguments must have defaults

5. You want to create a function greet that takes a name and an optional greeting message (default "Hello"). Which function definition is correct to achieve this?

hard

A. greet <- function(name, message = "Hello") { paste(message, name) }

B. greet <- function(name = "Hello", message) { paste(message, name) }

C. greet <- function(name, message) { paste(message, name) }

D. greet <- function(message = "Hello", name) { paste(name, message) }

Solution

1. Step 1: Identify default argument placement

   In R, arguments with defaults must come after those without defaults.

2. Step 2: Check each option

   greet <- function(name, message = "Hello") { paste(message, name) } correctly places message with default after name without default and uses paste correctly.

3. Final Answer:

   greet <- function(name, message = "Hello") { paste(message, name) } -> Option A

4. Quick Check:

   Default args last = correct [OK]

Hint: Put default arguments after required ones [OK]

Common Mistakes:

• Placing default arguments before required ones
• Forgetting default values
• Mixing argument order in paste function