Recursive functions in R Programming - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a recursive function that calculates the factorial of a number.

R Programming

factorial <- function(n) {
  if (n == 0) {
    return(1)
  } else {
    return(n * factorial([1]))
  }
}

Drag options to blanks, or click blank then click option'

An * 1

Bn + 1

Cn - 1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 1 does not reduce the problem size.

The recursive call must reduce the number by 1 each time to reach the base case.

2fill in blank

medium

Complete the code to define a recursive function that computes the nth Fibonacci number.

R Programming

fibonacci <- function(n) {
  if (n <= 1) {
    return(n)
  } else {
    return(fibonacci([1]) + fibonacci(n - 2))
  }
}

Drag options to blanks, or click blank then click option'

A1

Bn + 1

Cn - 2

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using n - 2 for both calls is incorrect.

The Fibonacci sequence is defined as fib(n) = fib(n-1) + fib(n-2).

3fill in blank

hard

Fix the error in the recursive function that sums numbers from 1 to n.

R Programming

sum_to_n <- function(n) {
  if (n == 1) {
    return(1)
  } else {
    return(n + sum_to_n([1]))
  }
}

Drag options to blanks, or click blank then click option'

An + 1

Bn - 1

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using 1 does not reduce the problem size.

The recursive call must reduce n by 1 to reach the base case.

4fill in blank

hard

Fill both blanks to create a recursive function that counts down from n to 1 and prints each number.

R Programming

countdown <- function(n) {
  if (n == 0) {
    return()
  }
  print([1])
  countdown([2])
}

Drag options to blanks, or click blank then click option'

An

Bn - 1

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Printing n - 1 before the call changes the order.

Calling countdown with n + 1 causes infinite recursion.

The function prints the current number n, then calls itself with n - 1.

5fill in blank

hard

Fill all three blanks to define a recursive function that reverses a string.

R Programming

reverse_string <- function(s) {
  if (nchar(s) == 0) {
    return("")
  } else {
    return(paste0(substring(s, [1]), reverse_string(substring(s, [2], [3]))) )
  }
}

Drag options to blanks, or click blank then click option'

Anchar(s)

B1

C2

Dnchar(s) - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using fixed numbers instead of nchar(s) causes errors.

Incorrect substring indices cause wrong output.

The function takes the last character (substring from nchar(s) to nchar(s)) and appends the reverse of the rest (substring from 1 to nchar(s)-1).

Here, the blanks represent the last character and the rest of the string.

Practice

1. What is the main purpose of a base case in a recursive function?

easy

A. To stop the recursion and prevent infinite calls

B. To call the function again with the same input

C. To increase the input size for the next call

D. To print the result of the recursion

Solution

1. Step 1: Understand recursion basics

   A recursive function calls itself repeatedly with smaller inputs.

2. Step 2: Identify the role of base case

   The base case stops the recursion to avoid infinite loops and eventual crash.

3. Final Answer:

   To stop the recursion and prevent infinite calls -> Option A

4. Quick Check:

   Base case = stop recursion [OK]

Hint: Base case always stops recursion to avoid infinite loops [OK]

Common Mistakes:

• Forgetting the base case causes infinite recursion
• Thinking base case calls function again
• Confusing base case with recursive step

2. Which of the following is the correct syntax to define a recursive function fact in R that calculates factorial?

easy

A. fact <- function(n) { repeat n * fact(n - 1) }

B. fact <- function(n) { while(n > 0) n * fact(n - 1) }

C. fact <- function(n) { if(n == 1) n + fact(n - 1) }

D. fact <- function(n) { if(n == 0) 1 else n * fact(n - 1) }

Solution

1. Step 1: Check base case and recursive call

   fact <- function(n) { if(n == 0) 1 else n * fact(n - 1) } correctly uses if condition for base case (n == 0) and recursive call with n-1.

2. Step 2: Identify syntax errors in other options

   Options B, C, and D misuse loops or have wrong base case or missing else.

3. Final Answer:

   fact <- function(n) { if(n == 0) 1 else n * fact(n - 1) } -> Option D

4. Quick Check:

   Correct base case and recursive call syntax [OK]

Hint: Base case uses if, recursive call uses else with smaller input [OK]

Common Mistakes:

• Using loops instead of recursion
• Missing else leads to errors
• Wrong base case condition

3. What is the output of this R code?

fib <- function(n) {
  if (n <= 1) return(n)
  else return(fib(n-1) + fib(n-2))
}
fib(4)

medium

A. 5

B. 4

C. 3

D. 7

Solution

1. Step 1: Trace fib(4) calls

   fib(4) = fib(3) + fib(2); fib(3) = fib(2) + fib(1); fib(2) = fib(1) + fib(0)

2. Step 2: Calculate values bottom-up

   fib(1)=1, fib(0)=0; fib(2)=1+0=1; fib(3)=1+1=2; fib(4)=2+1=3

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Fibonacci(4) = 3 [OK]

Hint: Fibonacci(4) = 3 by adding previous two values [OK]

Common Mistakes:

• Confusing index starting at 0 or 1
• Adding wrong recursive calls
• Forgetting base cases

4. Identify the error in this recursive R function to sum numbers from 1 to n:

sum_to_n <- function(n) {
  if (n == 1) return(1)
  else return(n + sum_to_n(n))
}
sum_to_n(3)

medium

A. The recursive call uses the same n, causing infinite recursion

B. The function should use a loop instead

C. The base case is missing

D. The return statement is outside the function

Solution

1. Step 1: Check recursive call argument

   The function calls sum_to_n(n) instead of sum_to_n(n-1), so input never decreases.

2. Step 2: Understand effect of error

   This causes infinite recursion because n stays the same and base case is never reached.

3. Final Answer:

   The recursive call uses the same n, causing infinite recursion -> Option A

4. Quick Check:

   Recursive call must reduce input [OK]

Hint: Recursive call must use smaller input to reach base case [OK]

Common Mistakes:

• Calling function with same argument
• Missing base case
• Confusing recursion with loops

5. Write a recursive R function flatten_list that takes a nested list of numbers and returns a flat vector of all numbers.
What is the correct approach?

hard

A. Use recursion but forget to combine results from recursive calls

B. Check if input is a list; if yes, recursively flatten each element and combine; else return the element as vector

C. Return the input directly without any processing

D. Use a for loop to iterate and append elements without recursion

Solution

1. Step 1: Identify recursive structure

   Nested lists require checking each element; if it's a list, call flatten_list recursively.

2. Step 2: Combine results properly

   Combine all flattened elements into one vector to get a flat list of numbers.

3. Final Answer:

   Check if input is a list; if yes, recursively flatten each element and combine; else return the element as vector -> Option B

4. Quick Check:

   Recursion + combine results = flatten list [OK]

Hint: Recursively flatten each list element and combine results [OK]

Common Mistakes:

• Not combining recursive results
• Forgetting to check if element is a list
• Using loops only without recursion