Recursive functions in R Programming - Step-by-Step Execution

Concept Flow - Recursive functions

Call function with n

↓

Check base case: n == 1?

Yes→Return 1

No↓

Call function with n-1

↓

Wait for result

↓

Multiply n by result

↓

Return result

↓

Previous call resumes

↓

Final result returned

The function calls itself with a smaller input until it reaches the base case, then returns and combines results back up.

Execution Sample

R Programming

factorial <- function(n) {
  if (n == 1) {
    return(1)
  } else {
    return(n * factorial(n - 1))
  }
}
factorial(3)

Calculates factorial of 3 by calling itself with smaller numbers until 1.

Execution Table

Step	Call	n	Condition (n==1?)	Action	Return Value
1	factorial(3)	3	No	Call factorial(2)
2	factorial(2)	2	No	Call factorial(1)
3	factorial(1)	1	Yes	Return 1	1
4	factorial(2)	2	No	Calculate 2 * 1	2
5	factorial(3)	3	No	Calculate 3 * 2	6

💡 Reached base case at n=1, then returned results back up the call stack.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
n	3	3	2	1	2	3
Return Value				1	2	6

Key Moments - 3 Insights

Why does the function call itself with n-1 instead of just looping?

The execution_table shows at Step 1 and 2 that the function calls itself with smaller n to break the problem into simpler parts until the base case is reached.

What stops the recursion from going forever?

Step 3 in the execution_table shows the base case condition n==1 returns 1, stopping further recursive calls.

How does the function combine results from recursive calls?

Steps 4 and 5 show the function multiplies n by the returned value from the smaller call, building the final result back up.

Visual Quiz - 3 Questions

Look at the execution_table, what is the return value at Step 3?

A 3

B 2

C 1

D 6

💡 Hint

Check the 'Return Value' column at Step 3 where n=1 and base case returns 1.

At which step does the function first check the base case condition?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Condition (n==1?)' column to find when it is 'Yes'.

If we call factorial(4), how many total calls will appear in the execution_table?

A 3

B 4

C 5

D 6

💡 Hint

Each call reduces n by 1 until 1, so count calls from 4 down to 1.

Concept Snapshot

Recursive functions call themselves with smaller inputs.
They must have a base case to stop.
Each call waits for the smaller call's result.
Results combine as calls return.
Example: factorial(n) = n * factorial(n-1) with base case factorial(1)=1.

Full Transcript

This example shows how a recursive function works by calling itself with smaller inputs until it reaches a base case. The function factorial calls itself with n-1 until n equals 1. At that point, it returns 1. Then each previous call multiplies n by the returned value, building the final result. The execution table tracks each call, the condition check, and the return values step-by-step. The variable tracker shows how n and return values change during execution. Key moments clarify why recursion calls itself, how it stops, and how results combine. The quiz tests understanding of these steps.