Factorial Using Recursion in DSA Typescript - Execution Trace

Concept Flow - Factorial Using Recursion

Call factorial(n)

↓

Is n <= 1?

Yes→Return 1

No↓

Call factorial(n-1)

↓

Multiply n * factorial(n-1)

↓

Return result

The function calls itself with n-1 until it reaches 1, then returns 1 and multiplies back up.

Execution Sample

DSA Typescript

function factorial(n: number): number {
  if (n <= 1) return 1;
  return n * factorial(n - 1);
}

Calculates factorial of n by calling itself with n-1 until base case.

Execution Table

Step	Call	n	Condition n<=1?	Action	Return Value	Stack Depth
1	factorial(4)	4	No	Call factorial(3)		1
2	factorial(3)	3	No	Call factorial(2)		2
3	factorial(2)	2	No	Call factorial(1)		3
4	factorial(1)	1	Yes	Return 1	1	4
5	factorial(2)	2	No	Return 2 * 1	2	3
6	factorial(3)	3	No	Return 3 * 2	6	2
7	factorial(4)	4	No	Return 4 * 6	24	1
8	End			All calls returned		0

💡 Recursion ends when n <= 1, then results multiply back up the call stack.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	Final
n	4	4	3	2	1	2	3	4	4
Return Value					1	2	6	24	24
Stack Depth	0	1	2	3	4	3	2	1	0

Key Moments - 3 Insights

Why does factorial(1) return 1 instead of calling factorial(0)?

Because the base case is n <= 1 (see Step 4 in execution_table), it stops recursion to avoid infinite calls.

How does the multiplication happen after the base case returns?

After factorial(1) returns 1 (Step 4), each previous call multiplies n by the returned value (Steps 5-7).

What does stack depth represent in recursion?

Stack depth shows how many calls are waiting to complete; it increases with each call and decreases as calls return (see variable_tracker).

Visual Quiz - 3 Questions

Look at the execution_table, what is the return value of factorial(2) at Step 5?

A 2

B 1

C 6

D 24

💡 Hint

Check the 'Return Value' column at Step 5 in execution_table.

At which step does the recursion reach its base case?

A Step 3

B Step 4

C Step 5

D Step 7

💡 Hint

Look for the step where 'Condition n<=1?' is Yes in execution_table.

If the input n was 3 instead of 4, what would be the final return value?

A 3

B 24

C 6

D 1

💡 Hint

Check the pattern of multiplication in execution_table and variable_tracker for n=4 and adjust for n=3.

Concept Snapshot

Factorial Using Recursion:
- Base case: if n <= 1, return 1
- Recursive case: return n * factorial(n-1)
- Calls stack up until base case, then multiply back
- Stack depth shows call layers
- Stops when base case reached

Full Transcript

This visualization shows how factorial is calculated using recursion. The function calls itself with n-1 until it reaches the base case where n is 1 or less. At that point, it returns 1. Then each previous call multiplies its n by the returned value from the deeper call. The execution table tracks each call, the condition check, and the return values as the recursion unwinds. The variable tracker shows how n, return values, and stack depth change step by step. Key moments clarify why the base case stops recursion and how multiplication happens after. The quiz tests understanding of return values, base case step, and effect of changing input.