Vector indexing (1-based) in R Programming - Time & Space Complexity

Time Complexity: Vector indexing (1-based)

O(k)

Understanding Time Complexity

We want to understand how long it takes to get elements from a vector in R.

How does the time change when we ask for one or many elements?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

# Create a vector of numbers
vec <- 1:1000

# Access a single element
x <- vec[500]

# Access multiple elements
y <- vec[c(10, 20, 30)]

This code gets elements from a vector by their position using 1-based indexing.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing elements by index in the vector.
• How many times: Once for each element requested (single or multiple).

How Execution Grows With Input

Getting one element takes about the same time no matter the vector size.

Input Size (n)	Approx. Operations
10	1 for single element, 3 for three elements
100	1 for single element, 3 for three elements
1000	1 for single element, 3 for three elements

Pattern observation: Time grows with how many elements you ask for, not the total vector size.

Final Time Complexity

Time Complexity: O(k)

This means the time depends on how many elements you access, not the whole vector size.

Common Mistake

[X] Wrong: "Accessing an element takes longer if the vector is bigger."

[OK] Correct: Vector indexing in R directly jumps to the element, so size does not slow it down.

Interview Connect

Knowing how vector access time works helps you write faster code and explain your choices clearly.

Self-Check

"What if we accessed elements using a loop instead of all at once? How would the time complexity change?"

Practice

1. In R, what is the position of the first element in a vector v when using indexing like v[1]?

easy

A. The first element (position 1)

B. The zeroth element (position 0)

C. The last element

D. An error because indexing starts at 0

Solution

1. Step 1: Understand R vector indexing

   R vectors start indexing at 1, not 0 like some other languages.

2. Step 2: Apply indexing to vector v

   Using v[1] selects the first element of the vector.

3. Final Answer:

   The first element (position 1) -> Option A

4. Quick Check:

   R indexing starts at 1 = first element [OK]

Hint: Remember: R indexing always starts at 1, never 0 [OK]

Common Mistakes:

• Thinking indexing starts at 0 like in Python or C
• Confusing position 1 with last element
• Assuming indexing causes an error if 0 is used

2. Which of the following is the correct syntax to get the third element from a vector vec in R?

easy

A. vec[3]

B. vec<3>

C. vec{3}

D. vec(3)

Solution

1. Step 1: Recall R vector indexing syntax

   In R, square brackets [] are used to access elements by position.

2. Step 2: Identify correct syntax for third element

   Using vec[3] correctly accesses the third element.

3. Final Answer:

   vec[3] -> Option A

4. Quick Check:

   Use square brackets for indexing in R [OK]

Hint: Use square brackets [] to index vectors in R [OK]

Common Mistakes:

• Using parentheses () instead of square brackets
• Using curly braces {} which are invalid for indexing
• Using angle brackets <> which are not valid syntax

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

nums <- c(10, 20, 30, 40, 50)
nums[2:4]

medium

A. [10 20 30]

B. [20 30 40]

C. [20 30 40 50]

D. [30 40 50]

Solution

1. Step 1: Understand the vector and indexing range

   The vector nums has elements 10, 20, 30, 40, 50 at positions 1 to 5.

2. Step 2: Extract elements from position 2 to 4

   Using nums[2:4] selects elements at positions 2, 3, and 4 which are 20, 30, and 40.

3. Final Answer:

   [20 30 40] -> Option B

4. Quick Check:

   Positions 2 to 4 = 20, 30, 40 [OK]

Hint: Use colon : to select a range of positions [OK]

Common Mistakes:

• Including position 5 by mistake
• Starting range at 1 instead of 2
• Confusing vector values with positions

4. Consider the R code below. What is the error and how to fix it?

vals <- c(5, 10, 15, 20)
print(vals[0])

medium

A. Error: Use parentheses instead of brackets

B. No error; prints 5

C. Error: Index 0 is invalid; use index starting at 1

D. Error: Vector must be numeric

Solution

1. Step 1: Identify the indexing error

   In R, vector indexing starts at 1; index 0 is invalid and returns an empty vector.

2. Step 2: Correct the index to start at 1

   Replace vals[0] with vals[1] to access the first element.

3. Final Answer:

   Error: Index 0 is invalid; use index starting at 1 -> Option C

4. Quick Check:

   R indexing starts at 1, not 0 [OK]

Hint: Never use 0 as index in R vectors [OK]

Common Mistakes:

• Assuming 0 is a valid index like in other languages
• Trying to use parentheses for indexing
• Thinking vector type causes the error

5. You have a vector data <- c(3, 6, 9, 12, 15). How do you create a new vector containing only the 1st, 3rd, and 5th elements using vector indexing in R?

hard

A. data[1, 3, 5]

B. data[1:3:5]

C. data[c(0, 2, 4)]

D. data[c(1, 3, 5)]

Solution

1. Step 1: Understand how to select multiple elements

   In R, use c() inside square brackets to select multiple positions.

2. Step 2: Apply correct indexing for positions 1, 3, and 5

   Using data[c(1, 3, 5)] selects elements at these positions: 3, 9, and 15.

3. Final Answer:

   data[c(1, 3, 5)] -> Option D

4. Quick Check:

   Use c() inside [] to pick multiple positions [OK]

Hint: Use c() inside [] to select multiple indices [OK]

Common Mistakes:

• Using colon with multiple steps incorrectly
• Using commas inside [] without c()
• Using zero-based indices like 0, 2, 4