Kotlin coding test course, Euclidean algorithm

Hello! In this article, we will explore algorithm problem-solving methods using Kotlin. Specifically, I will explain the Euclidean algorithm in detail and describe the process of solving a specific problem using it. The Euclidean algorithm is an efficient way to find the greatest common divisor (GCD) of two numbers and is utilized in many algorithm problems.

1. What is the Euclidean Algorithm?

The Euclidean algorithm is a method proposed by the ancient Greek mathematician Euclid for finding the greatest common divisor of two integers. For two integers a and b, the GCD is defined as follows:

GCD(a, b) = GCD(b, a % b), and GCD(a, 0) = a.

In other words, we repeat the process of swapping a with b and b with a % b until the remainder when dividing a by b becomes 0. Ultimately, the value of b will be the GCD.

2. Algorithm Problem

3. Problem-Solving Process

3.1 Problem Analysis

To solve the problem, we need to understand how to find the greatest common divisor of the two input values A and B. Since we can easily find the GCD using the Euclidean algorithm, we will use this method.

3.2 Algorithm Design

We will utilize the Euclidean algorithm for this problem. The algorithm proceeds as follows:

1. Receive the input values.
2. Repeat until A is not 0.
3. While possible, rearrange A and B and calculate the remainder.
4. When the value of B becomes 0, print the value of A.

3.3 Kotlin Code

fun gcd(a: Int, b: Int): Int {
        var x = a
        var y = b
        while (y != 0) {
            val temp = y
            y = x % y
            x = temp
        }
        return x
    }

    fun main() {
        val input = readLine()!!
        val parts = input.split(" ")
        val A = parts[0].toInt()
        val B = parts[1].toInt()
        println(gcd(A, B))
    }

3.4 Code Execution

Example input:
48 18

When the code is executed, the following output appears:

6

4. Complexity Analysis

The time complexity of the Euclidean algorithm is O(log(min(A, B))), making it a very efficient algorithm. Therefore, it maintains a sufficiently fast processing speed even as input values increase.

5. Conclusion

In this post, we discussed the problem of finding the greatest common divisor using the Euclidean algorithm. It can be implemented simply in Kotlin, and this algorithm can be applied to various problems. Understanding and applying such techniques is very important when solving algorithm problems. In the next post, we will cover more complex algorithm problems.