Negative indexing for exclusion in R Programming - Time & Space Complexity

Time Complexity: Negative indexing for exclusion

O(n)

Understanding Time Complexity

We want to understand how the time it takes to exclude elements using negative indexing changes as the size of the data grows.

How does the program's work increase when we remove items by negative indexing?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

# Exclude elements at positions 2 and 5
result <- vec[-c(2, 5)]

This code creates a vector and then removes elements at specific positions using negative indexing.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Copying all elements except those excluded into a new vector.
• How many times: Each element is checked once to decide if it should be included.

How Execution Grows With Input

As the vector size grows, the program must look at each element to decide if it should be kept or removed.

Input Size (n)	Approx. Operations
10	About 10 checks
100	About 100 checks
1000	About 1000 checks

Pattern observation: The work grows roughly in direct proportion to the size of the vector.

Final Time Complexity

Time Complexity: O(n)

This means the time to exclude elements grows linearly with the number of elements in the vector.

Common Mistake

[X] Wrong: "Removing a few elements with negative indexing is instant and does not depend on vector size."

[OK] Correct: Even if only a few elements are removed, the program still checks every element to build the new vector, so time grows with vector size.

Interview Connect

Understanding how data exclusion scales helps you write efficient code and explain your choices clearly in real projects or interviews.

Self-Check

What if we excluded elements using a logical vector instead of negative indexing? How would the time complexity change?

Practice

1. In R, what does negative indexing like x[-2] do to the vector x?

easy

A. It returns the vector x with the second element doubled.

B. It returns only the second element of x.

C. It returns the vector x without the second element.

D. It causes an error because negative indexes are not allowed.

Solution

1. Step 1: Understand negative indexing in R

   Negative indexing excludes elements at the specified positions from the result.

2. Step 2: Apply negative index to x[-2]

   This means the second element is removed from the vector x, returning all others.

3. Final Answer:

   It returns the vector x without the second element. -> Option C

4. Quick Check:

   Negative index excludes elements [OK]

Hint: Negative index removes elements by position [OK]

Common Mistakes:

• Thinking negative index selects elements
• Confusing negative index with subtraction
• Assuming negative index causes error

2. Which of the following is the correct syntax to exclude the 1st and 3rd elements from a vector v in R?

easy

A. v[-c(1, 3)]

B. v[c(-1, 3)]

C. v[c(1, -3)]

D. v[-1, -3]

Solution

1. Step 1: Recall syntax for excluding multiple elements

   Use negative indexing with a vector of positions inside c(), like -c(1, 3).

2. Step 2: Check each option

   v[-c(1, 3)] correctly uses v[-c(1, 3)] to exclude 1st and 3rd elements. Others misuse negative signs or commas.

3. Final Answer:

   v[-c(1, 3)] -> Option A

4. Quick Check:

   Negative vector inside c() excludes multiple elements [OK]

Hint: Use negative vector inside c() to exclude multiple elements [OK]

Common Mistakes:

• Placing negative signs inside c() incorrectly
• Using commas instead of c() for multiple indexes
• Mixing positive and negative indexes in one vector

3. What is the output of the following R code?

vec <- c(10, 20, 30, 40, 50)
result <- vec[-c(2, 4)]
print(result)

medium

A. [1] 20 40

B. [1] 10 30 50

C. [1] 10 20 30 40 50

D. [1] 30 50

Solution

1. Step 1: Identify elements to exclude

   Negative indexing -c(2, 4) removes elements at positions 2 and 4, which are 20 and 40.

2. Step 2: List remaining elements

   Remaining elements are at positions 1, 3, and 5: 10, 30, and 50.

3. Final Answer:

   [1] 10 30 50 -> Option B

4. Quick Check:

   Exclude 2nd and 4th elements [OK]

Hint: Remove elements at given positions with negative c() [OK]

Common Mistakes:

• Including excluded elements by mistake
• Confusing element values with positions
• Expecting only excluded elements as output

4. Consider this R code snippet:

nums <- c(5, 10, 15, 20)
new_nums <- nums[-2, 3]
print(new_nums)

What is the error in this code?

medium

A. Incorrect use of comma in negative indexing causing subscript error.

B. Negative indexing cannot be used with numeric vectors.

C. The vector nums is empty, so indexing fails.

D. The code runs without error and prints the vector.

Solution

1. Step 1: Analyze the indexing syntax

   Negative indexing uses a single vector inside brackets. Using a comma like nums[-2, 3] implies matrix indexing, which is invalid for a vector.

2. Step 2: Identify the error type

   This causes a subscript error because nums is a vector, not a matrix or data frame.

3. Final Answer:

   Incorrect use of comma in negative indexing causing subscript error. -> Option A

4. Quick Check:

   Comma in vector indexing causes error [OK]

Hint: No commas in vector negative indexing [OK]

Common Mistakes:

• Using commas like in matrices for vectors
• Assuming negative indexing works with multiple arguments
• Ignoring error messages about subscripts

5. You have a vector data <- c(3, 6, 9, 12, 15, 18). You want to create a new vector excluding all elements at even positions using negative indexing. Which code correctly achieves this?

hard

A. new_data <- data[-seq(1, length(data), by=2)]

B. new_data <- data[-c(2, 4, 6, 8)]

C. new_data <- data[-c(1, 3, 5)]

D. new_data <- data[-seq(2, length(data), by=2)]

Solution

1. Step 1: Identify even positions in the vector

   Even positions are 2, 4, 6. Using seq(2, length(data), by=2) generates these positions dynamically.

2. Step 2: Use negative indexing to exclude these positions

   Applying negative indexing with -seq(2, length(data), by=2) removes elements at even positions.

3. Final Answer:

   new_data <- data[-seq(2, length(data), by=2)] -> Option D

4. Quick Check:

   Negative seq() excludes even positions [OK]

Hint: Use seq() with negative index to exclude positions [OK]

Common Mistakes:

• Hardcoding indexes without checking vector length
• Excluding odd positions instead of even
• Using indexes outside vector length