pivot_wider (long to wide) in R Programming - Time & Space Complexity

Time Complexity: pivot_wider (long to wide)

O(n)

Understanding Time Complexity

When we use pivot_wider in R, we change data from a long format to a wide format.

We want to understand how the time it takes grows as the data gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

library(tidyr)
data_long <- data.frame(
  id = rep(1:1000, each = 3),
  key = rep(c('A', 'B', 'C'), times = 1000),
  value = rnorm(3000)
)
data_wide <- pivot_wider(data_long, names_from = key, values_from = value)
    

This code takes a long table with repeated ids and keys, and makes it wide by spreading keys into columns.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Scanning all rows to group by id and spread key values.
• How many times: Each of the n rows is processed once to place values in the wide format.

How Execution Grows With Input

As the number of rows grows, the work grows roughly in direct proportion.

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

Pattern observation: Doubling the input roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to pivot grows linearly with the number of rows in the data.

Common Mistake

[X] Wrong: "Pivoting data is always slow because it rearranges everything multiple times."

[OK] Correct: Actually, pivot_wider processes each row once, so the time grows steadily, not wildly.

Interview Connect

Understanding how data reshaping scales helps you work efficiently with real datasets and shows you can reason about performance.

Self-Check

"What if the number of unique keys grows with the input size? How would the time complexity change?"

Practice

1. What does the pivot_wider function do in R's tidyverse?

easy

A. It filters rows based on a condition.

B. It transforms data from long format to wide format by spreading key-value pairs into columns.

C. It sorts data in ascending order.

D. It merges two data frames by a common column.

Solution

1. Step 1: Understand the purpose of pivot_wider

   The function is designed to reshape data by turning unique values from one column into multiple columns.

2. Step 2: Compare with other data operations

   Filtering, sorting, and merging are different operations; pivot_wider specifically changes data shape from long to wide.

3. Final Answer:

   It transforms data from long format to wide format by spreading key-value pairs into columns. -> Option B

4. Quick Check:

   pivot_wider = long to wide reshape [OK]

Hint: pivot_wider spreads rows into columns for easier comparison [OK]

Common Mistakes:

• Confusing pivot_wider with filtering or sorting functions
• Thinking pivot_wider merges data frames
• Assuming pivot_wider removes rows instead of reshaping

2. Which of the following is the correct syntax to use pivot_wider to spread the column key into multiple columns with values from value?

easy

A. pivot_wider(data, values_from = key, names_from = value)

B. pivot_wider(data, spread = key, gather = value)

C. pivot_wider(data, key = names_from, value = values_from)

D. pivot_wider(data, names_from = key, values_from = value)

Solution

1. Step 1: Recall pivot_wider argument names

   The correct arguments are names_from for the column to spread and values_from for the values to fill.

2. Step 2: Match arguments to columns

   pivot_wider(data, names_from = key, values_from = value) correctly uses names_from = key and values_from = value, matching the expected syntax.

3. Final Answer:

   pivot_wider(data, names_from = key, values_from = value) -> Option D

4. Quick Check:

   names_from = key, values_from = value [OK]

Hint: Use names_from for columns, values_from for data [OK]

Common Mistakes:

• Swapping names_from and values_from arguments
• Using incorrect argument names like spread or gather
• Passing arguments in wrong order or with wrong names

3. Given this data frame in R:

library(tidyr)
data <- data.frame(
  id = c(1,1,2,2),
  variable = c('A', 'B', 'A', 'B'),
  value = c(10, 20, 30, 40)
)
result <- pivot_wider(data, names_from = variable, values_from = value)
print(result)

What will be the output?

medium

A. id A B
1 1 10 20
2 2 30 40

B. id variable value
1 1 A 10
2 1 B 20
3 2 A 30
4 2 B 40

C. id A
1 1 10
2 2 30

D. Error: object 'pivot_wider' not found

Solution

1. Step 1: Understand pivot_wider effect on data

   It converts the 'variable' column values ('A', 'B') into separate columns, filling them with corresponding 'value' entries.

2. Step 2: Check the resulting data frame structure

   Each 'id' has columns 'A' and 'B' with values 10, 20 for id=1 and 30, 40 for id=2.

3. Final Answer:

   id A B 1 1 10 20 2 2 30 40 -> Option A

4. Quick Check:

   pivot_wider spreads variable into columns with values [OK]

Hint: pivot_wider creates columns from variable, fills with value [OK]

Common Mistakes:

• Expecting original long format output
• Confusing column names after pivot
• Not loading tidyr library causing error

4. You run this code but get an error:

library(tidyr)
data <- data.frame(
  id = c(1,1,2,2),
  variable = c('A', 'B', 'A', 'B'),
  value = c(10, 20, 30, 40)
)
result <- pivot_wider(data, names_from = variable)
print(result)

What is the likely cause of the error?

medium

A. The library tidyr is not loaded.

B. The data frame has duplicate rows causing conflict.

C. Missing the values_from argument to specify which column fills new columns.

D. The variable column contains invalid characters.

Solution

1. Step 1: Check pivot_wider required arguments

   pivot_wider needs both names_from and values_from to know which columns to spread and fill.

2. Step 2: Identify missing argument

   The code only provides names_from = variable but misses values_from, causing an error.

3. Final Answer:

   Missing the values_from argument to specify which column fills new columns. -> Option C

4. Quick Check:

   values_from argument is required [OK]

Hint: Always include values_from with names_from in pivot_wider [OK]

Common Mistakes:

• Forgetting values_from argument
• Assuming names_from alone is enough
• Not reading error messages carefully

5. You have this long data frame with sales data:

sales <- data.frame(
  store = c('X', 'X', 'Y', 'Y'),
  product = c('apple', 'banana', 'apple', 'banana'),
  sales_amount = c(100, 150, 200, 250)
)

You want to create a wide table where each product is a column showing sales per store. Which code correctly does this and handles missing values by filling with 0?

hard

A. pivot_wider(sales, names_from = product, values_from = sales_amount, values_fill = 0)

B. pivot_wider(sales, names_from = sales_amount, values_from = product, values_fill = 0)

C. pivot_wider(sales, names_from = product, values_from = sales_amount)

D. pivot_wider(sales, names_from = store, values_from = sales_amount, values_fill = NA)

Solution

1. Step 1: Identify columns to spread and fill

   The products ('apple', 'banana') become new columns, so names_from = product. The sales amounts fill these columns, so values_from = sales_amount.

2. Step 2: Handle missing values

   Use values_fill = 0 to replace any missing sales with zero for completeness.

3. Final Answer:

   pivot_wider(sales, names_from = product, values_from = sales_amount, values_fill = 0) -> Option A

4. Quick Check:

   Use values_fill to replace missing with 0 [OK]

Hint: Add values_fill = 0 to fill missing cells with zero [OK]

Common Mistakes:

• Swapping names_from and values_from
• Not using values_fill causing NA in output
• Using wrong columns for names_from or values_from