Logical indexing in R Programming - Time & Space Complexity

Time Complexity: Logical indexing

O(n)

Understanding Time Complexity

Logical indexing lets us pick elements from a list or vector using true or false values.

We want to see how the time to do this grows as the list gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

x <- 1:1000
idx <- x %% 2 == 0
result <- x[idx]

This code creates a vector from 1 to 1000, makes a logical vector marking even numbers, and selects those even numbers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each element to see if it meets the condition (even number).
• How many times: Once for every element in the vector (n times).

How Execution Grows With Input

As the vector gets bigger, the program checks more elements one by one.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to select elements grows in a straight line as the list gets longer.

Common Mistake

[X] Wrong: "Logical indexing is instant no matter how big the vector is."

[OK] Correct: The program must check each element to decide if it matches, so bigger vectors take more time.

Interview Connect

Understanding how logical indexing scales helps you write efficient data filters and shows you can think about code speed clearly.

Self-Check

"What if we used multiple conditions combined with & or | for logical indexing? How would the time complexity change?"

Practice

1. What does logical indexing in R do when applied to a vector like v[c(TRUE, FALSE, TRUE)]?

easy

A. Selects elements of v where the index is TRUE

B. Selects elements of v where the index is FALSE

C. Returns the length of v

D. Returns an error because logical vectors cannot index

Solution

1. Step 1: Understand logical indexing

   Logical indexing uses a TRUE/FALSE vector to pick elements from the original vector where TRUE is present.

2. Step 2: Apply logical vector to v

   Elements at positions with TRUE in the logical vector are selected; others are skipped.

3. Final Answer:

   Selects elements of v where the index is TRUE -> Option A

4. Quick Check:

   TRUE picks elements [OK]

Hint: TRUE means pick element, FALSE means skip [OK]

Common Mistakes:

• Thinking FALSE picks elements
• Confusing logical indexing with numeric indexing
• Assuming logical vector length doesn't matter

2. Which of the following is the correct syntax to select elements of vector x where values are greater than 5 using logical indexing?

easy

A. x[> 5]

B. x > 5[x]

C. x[x > 5]

D. x[5 > x]

Solution

1. Step 1: Understand logical condition syntax

   The condition x > 5 creates a logical vector TRUE where elements are greater than 5.

2. Step 2: Use logical vector to index x

   Using x[x > 5] selects elements of x where the condition is TRUE.

3. Final Answer:

   x[x > 5] -> Option C

4. Quick Check:

   Correct logical indexing syntax [OK]

Hint: Put condition inside square brackets after vector [OK]

Common Mistakes:

• Placing condition outside brackets
• Using invalid syntax like x[> 5]
• Swapping operands in condition

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

v <- c(10, 3, 7, 2, 9)
v[v >= 7]

medium

A. [1] 10 3 7 2 9

B. [1] 3 2

C. Error: invalid logical indexing

D. [1] 10 7 9

Solution

1. Step 1: Evaluate the logical condition v >= 7

   This creates a logical vector: TRUE, FALSE, TRUE, FALSE, TRUE for elements 10, 3, 7, 2, 9 respectively.

2. Step 2: Select elements where condition is TRUE

   Elements at TRUE positions are 10, 7, and 9.

3. Final Answer:

   [1] 10 7 9 -> Option D

4. Quick Check:

   Only values >= 7 selected [OK]

Hint: Check which elements satisfy condition, pick those [OK]

Common Mistakes:

• Including elements less than 7
• Confusing >= with >
• Expecting an error due to indexing

4. Identify the error in this R code snippet:

nums <- c(4, 8, 15, 16, 23, 42)
nums[nums > 10 & TRUE]

medium

A. No error, code runs correctly

B. Logical vector length mismatch

C. Incorrect use of & with TRUE

D. Syntax error due to missing parentheses

Solution

1. Step 1: Analyze logical condition nums > 10 & TRUE

   The expression nums > 10 returns a logical vector; AND with TRUE keeps it unchanged.

2. Step 2: Check for errors

   The logical vector length matches nums, and syntax is correct, so no error occurs.

3. Final Answer:

   No error, code runs correctly -> Option A

4. Quick Check:

   Logical AND with TRUE keeps vector same [OK]

Hint: AND with TRUE keeps condition unchanged [OK]

Common Mistakes:

• Thinking & TRUE causes error
• Expecting length mismatch error
• Missing that & works element-wise

5. Given a vector temps <- c(23, NA, 19, 25, NA, 21), how can you use logical indexing to select only the non-missing values?

hard

A. temps[is.na(temps)]

B. temps[!is.na(temps)]

C. temps[temps != NA]

D. temps[temps > NA]

Solution

1. Step 1: Understand how to detect missing values

   The function is.na(temps) returns TRUE for missing values (NA) and FALSE otherwise.

2. Step 2: Use logical NOT to select non-missing

   Using !is.na(temps) creates a logical vector TRUE where values are not missing.

3. Step 3: Index temps with this logical vector

   This selects only the non-NA values from temps.

4. Final Answer:

   temps[!is.na(temps)] -> Option B

5. Quick Check:

   Use !is.na() to filter out NA [OK]

Hint: Use !is.na() to pick non-missing values [OK]

Common Mistakes:

• Using temps != NA which is invalid
• Selecting is.na(temps) to get missing values
• Trying to compare with NA using > or <