lapply and sapply in R Programming - Time & Space Complexity

Time Complexity: lapply and sapply

O(n)

Understanding Time Complexity

We want to understand how the time taken by lapply and sapply grows as the input list gets bigger.

How does the number of operations change when we apply a function to many items?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

my_list <- list(1, 2, 3, 4, 5)
result_lapply <- lapply(my_list, function(x) x * 2)
result_sapply <- sapply(my_list, function(x) x * 2)

This code applies a simple function to each item in a list using lapply and sapply.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Applying the function to each element in the list.
• How many times: Once for each element in the list (n times).

How Execution Grows With Input

As the list gets bigger, the function runs more times, one for each item.

Input Size (n)	Approx. Operations
10	10 function calls
100	100 function calls
1000	1000 function calls

Pattern observation: The number of operations grows directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

This means the time grows in a straight line as the list gets bigger.

Common Mistake

[X] Wrong: "lapply and sapply run faster because they are special functions."

[OK] Correct: They still apply the function to each item one by one, so time grows with the number of items.

Interview Connect

Understanding how these functions scale helps you write efficient code and explain your choices clearly in real projects.

Self-Check

"What if the function inside lapply took longer for bigger numbers? How would the time complexity change?"

Practice

1. What is the main difference between lapply and sapply in R?

easy

A. lapply modifies the original list, sapply does not.

B. lapply works only on vectors, sapply works only on lists.

C. lapply always returns a list, while sapply tries to simplify the result.

D. lapply is faster than sapply in all cases.

Solution

1. Step 1: Understand return types of lapply and sapply

   lapply always returns a list regardless of the function applied.

2. Step 2: Understand simplification behavior of sapply

   sapply tries to simplify the output to a vector or matrix if possible, otherwise returns a list.

3. Final Answer:

   lapply always returns a list, while sapply tries to simplify the result. -> Option C

4. Quick Check:

   Return type difference = lapply always returns a list, while sapply tries to simplify the result. [OK]

Hint: Remember: lapply = list output, sapply = simpler output if possible [OK]

Common Mistakes:

• Thinking lapply works only on vectors
• Believing sapply always returns a list
• Assuming lapply modifies original data

2. Which of the following is the correct syntax to apply the function sqrt to each element of a list my_list using lapply?

easy

A. lapply(my_list, sqrt)

B. lapply(my_list, sqrt())

C. lapply(sqrt, my_list)

D. lapply(my_list sqrt)

Solution

1. Step 1: Identify correct function call syntax

   The function name should be passed without parentheses to lapply, so sqrt not sqrt().

2. Step 2: Confirm argument order

   The first argument is the list, second is the function to apply: lapply(my_list, sqrt).

3. Final Answer:

   lapply(my_list, sqrt) -> Option A

4. Quick Check:

   Function without () and correct order = lapply(my_list, sqrt) [OK]

Hint: Pass function name without () as second argument in lapply [OK]

Common Mistakes:

• Using parentheses after function name inside lapply
• Swapping argument order
• Missing comma between arguments

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

nums <- list(a = 1:3, b = 4:6)
lapply(nums, sum)
sapply(nums, sum)

medium

A. Both return a list with sums: list(a=6, b=15)

B. lapply returns list(a=6, b=15), sapply returns numeric vector c(a=6, b=15)

C. lapply returns numeric vector, sapply returns list

D. Both return numeric vector c(6, 15)

Solution

1. Step 1: Calculate sums for each list element

   Sum of 1:3 is 6, sum of 4:6 is 15.

2. Step 2: Understand output types of lapply and sapply

   lapply returns a list with sums named by list elements; sapply simplifies to a numeric vector with names.

3. Final Answer:

   lapply returns list(a=6, b=15), sapply returns numeric vector c(a=6, b=15) -> Option B

4. Quick Check:

   lapply = list, sapply = vector if possible [OK]

Hint: lapply always list; sapply tries vector or matrix [OK]

Common Mistakes:

• Confusing output types of lapply and sapply
• Assuming both return same structure
• Ignoring named elements in output

4. Consider this code snippet:

my_list <- list(1, 2, 3)
lapply(my_list, function(x) x^2)

What is wrong with this code if the goal is to get a numeric vector of squared values?

medium

A. Nothing is wrong; it returns a numeric vector.

B. The anonymous function is incorrect; it should use x*x instead of x^2.

C. The list elements should be named for lapply to work.

D. Using lapply returns a list, not a numeric vector.

Solution

1. Step 1: Understand output type of lapply

   lapply always returns a list, even if function returns single values.

2. Step 2: Identify how to get numeric vector output

   To get a numeric vector, sapply should be used instead of lapply.

3. Final Answer:

   Using lapply returns a list, not a numeric vector. -> Option D

4. Quick Check:

   lapply output is list, not vector [OK]

Hint: Use sapply for vector output, lapply always returns list [OK]

Common Mistakes:

• Thinking lapply returns vector
• Believing function syntax is wrong
• Assuming names are required for lapply

5. You have a list of numeric vectors: data_list <- list(c(1,2), c(3,4,5), c(6)). You want to create a numeric vector of the means of each vector, but if a vector is empty, return NA for that element. Which code correctly does this using lapply or sapply?

hard

A. sapply(data_list, function(x) if(length(x) == 0) NA else mean(x))

B. lapply(data_list, function(x) if(length(x) == 0) NA else mean(x))

C. sapply(data_list, mean, na.rm=TRUE)

D. lapply(data_list, mean, na.rm=TRUE)

Solution

1. Step 1: Handle empty vectors with conditional inside function

   The function checks if length is zero, returns NA; else returns mean.

2. Step 2: Use sapply to get numeric vector output

   Using sapply simplifies the result to a numeric vector, which is desired.

3. Final Answer:

   sapply(data_list, function(x) if(length(x) == 0) NA else mean(x)) -> Option A

4. Quick Check:

   Conditional function + sapply for vector output [OK]

Hint: Use sapply with if-else inside function for conditional output [OK]

Common Mistakes:

• Using lapply and expecting vector output
• Not handling empty vectors explicitly
• Passing na.rm=TRUE without checking empty vectors