# 1. Introduction

Recursion is a technique in programming where a function calls itself to solve smaller instances of a problem. Tail recursion is a specialized form of recursion where the recursive call is the last operation in the function. Scala, with its functional programming paradigm, provides first-class support for tail recursion, which is optimized by the compiler to avoid stack overflow errors, making it more efficient. In this blog post, we will implement a tail-recursive function to calculate the factorial of a number in Scala.

# 2. Program Steps

1. Initialize the Scala environment.

2. Define a method to calculate the factorial of a number using tail recursion.

3. Implement an inner helper function to assist with the tail recursion.

4. Test the tail-recursive factorial method by calling it with a sample number.

5. Execute the program.

# 3. Code Program

``````object TailRecursiveFactorial {
def main(args: Array[String]): Unit = {
// Test the tail recursive factorial method
val number = 5
println(s"Factorial of \$number is: \${factorial(number)}")
}

// Tail recursive factorial method
def factorial(n: Int): BigInt = {
@scala.annotation.tailrec
def factorialHelper(n: Int, accumulator: BigInt): BigInt = {
if (n <= 1) accumulator
else factorialHelper(n - 1, n * accumulator)
}

factorialHelper(n, 1)
}
}

``````

### Output:

```Factorial of 5 is: 120
```

### Explanation:

1. The TailRecursiveFactorial object contains our main method and the tail-recursive factorial function.

2. The factorial function computes the factorial of a number using tail recursion. It takes in an integer n and returns its factorial as a BigInt.

3. Inside the factorial function, we define a helper function called factorialHelper. This helper function takes in an integer n and an accumulator to hold the result of the factorial.

4. The @scala.annotation.tailrec annotation ensures that our function is truly tail-recursive. If it's not, the compiler will raise an error.

5. If n is less than or equal to 1, we return the accumulator since the factorial of numbers less than or equal to 1 is 1. Otherwise, we make a recursive call to factorialHelper with n-1 and n * accumulator.

6. Finally, in the main method, we test our tail-recursive factorial method with the number 5 and print out the result.