find-gcd()

Step 1: Understanding the Problem

First, we need to understand what the Greatest Common Divisor (GCD) is. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

Now, our task is to create a swift function that calculates the GCD of two input numbers.

Step 2: Choose an Algorithm for GCD

The Euclidean algorithm, an efficient method for computing the GCD, is the most common method to solve this problem. The key principle of the Euclidean algorithm is that the greatest common divisor of two numbers also divides their difference. We find the GCD of two input numbers a and b as follow:

• If b = 0, then the GCD is a
• Else: GCD is the GCD of (b , a mod b)

Let's implement this in Swift.

func gcd(_ a: Int, _ b: Int) -> Int {
    if b == 0 {
        return a
    }
    return gcd(b, a % b)
}

Step 3: Test the Function

After defining our function, let's test it with some numbers to ensure it's working correctly.

print(gcd(48, 18)) // should print: 6
print(gcd(101, 103)) // should print: 1

Step 4: Optimizing the Function

The current implementation is a recursive function, which could cause a stack overflow if the initial b is very large. To prevent this, we can rewrite the implementation in an iterative manner.

func gcdIterative(_ a: Int, _ b: Int) -> Int {
var a = a
var b = b

while b != 0 {
    let temp = b
    b = a % b
    a = temp
}
 return a
}

Conclusion

Computing the GCD of two numbers is a common mathematical task in programming, and Swift code can implement it effectively. Our function 'gcdIterative' efficiently computes the GCD with the help of the Euclidean algorithm and can handle large inputs without risk of stack overflow.

Here is the final code:

func gcdIterative(_ a: Int, _ b: Int) -> Int {
  var a = a
  var b = b

  while b != 0 {
    let temp = b
    b = a % b
    a = temp
  }
  return a
}
print(gcdIterative(48, 18)) // prints: 6
print(gcdIterative(101, 103)) // prints: 1