Recursive functions in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple factorial recursion

What is the output of this R code when calling factorial(4)?

R Programming

factorial <- function(n) {
  if (n == 0) {
    return(1)
  } else {
    return(n * factorial(n - 1))
  }
}
factorial(4)

A 120

B Error: object 'factorial' not found

C 10

D 24

💡 Hint

Remember factorial of 4 is 4 * 3 * 2 * 1.

The function calls itself multiplying n by factorial of n-1 until n is 0, where it returns 1. So factorial(4) = 4*3*2*1 = 24.

❓ Predict Output

intermediate

Output of Fibonacci recursive function

What is the output of fib(5) given this R function?

R Programming

fib <- function(n) {
  if (n <= 1) {
    return(n)
  } else {
    return(fib(n - 1) + fib(n - 2))
  }
}
fib(5)

A 5

B 8

C 3

D Error: recursive call limit reached

💡 Hint

Fibonacci sequence starts 0,1,1,2,3,5...

fib(5) = fib(4) + fib(3) = 3 + 2 = 5. The function returns the 5th Fibonacci number starting from 0.

🔧 Debug

advanced

Identify the error in this recursive sum function

What error will this R code produce when calling sum_recursive(3)?

R Programming

sum_recursive <- function(n) {
  if (n == 0) {
    return(0)
  } else {
    return(n + sum_recursive)
  }
}
sum_recursive(3)

A 6

B Error: argument is missing, with no default

C Error: object 'sum_recursive' not found

D Error: recursive call limit reached

💡 Hint

Check how the recursive call is made inside the function.

The recursive call is missing the argument n-1, so R tries to call sum_recursive() without arguments causing an error about missing argument.

❓ Predict Output

advanced

Output of recursive string reversal

What is the output of reverse_str('abc') with this R function?

R Programming

reverse_str <- function(s) {
  if (nchar(s) == 0) {
    return("")
  } else {
    return(paste0(substr(s, nchar(s), nchar(s)), reverse_str(substr(s, 1, nchar(s) - 1))))
  }
}
reverse_str('abc')

A "cba"

B "abc"

C Error: non-numeric argument to binary operator

D "bac"

💡 Hint

The function takes last character and appends reversed rest.

The function takes last character 'c' and appends reverse of 'ab' which is 'ba', so output is 'cba'.

🧠 Conceptual

expert

Maximum recursion depth error cause

Which option best explains why this recursive R function causes a 'maximum recursion depth exceeded' error?

R Programming

infinite_recursion <- function(n) {
  if (n == 0) {
    return(0)
  } else {
    return(infinite_recursion(n + 1))
  }
}
infinite_recursion(1)

A The base case is missing so recursion never stops.

B The function has a syntax error causing infinite calls.

C The function never reaches the base case because n increases instead of decreasing.

D The function calls itself with the same argument causing infinite loop.

💡 Hint

Check how the argument changes in recursive calls.

The function increases n each call, so it never reaches n == 0 base case, causing infinite recursion until limit is reached.

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