Kotlin Coding Test Course, Merge Sort

Hello, and welcome to the Kotlin coding test course. In this course, we will delve into the ‘Merge Sort’ algorithm and use it to solve real-world problems. Merge Sort is one of the efficient sorting algorithms with non-zero complexity, which is very useful when sorting large datasets.

1. Introduction to Merge Sort

Merge Sort is an algorithm that employs a Divide and Conquer approach. It splits the array in half, recursively sorts each half, and then merges the two sorted arrays to create a final sorted array. This process can be divided into three major steps:

  1. Divide the array in half based on the midpoint
  2. Recursively sort each sub-array
  3. Merge the two sorted sub-arrays to create the final sorted array

2. Time Complexity of Merge Sort

The time complexity of Merge Sort is O(n log n) in the worst, average, and best cases. This means that the sorting process increases logarithmically based on the number of elements. The space complexity is O(n), requiring additional memory due to the creation of another array to store the sorted results.

3. Understanding the Merge Sort Algorithm

To understand the Merge Sort algorithm, let’s consider the following steps:

3.1. Steps of the Algorithm

1. If the array has one or no elements, it is already sorted, so return it.
2. Split the array into two sub-arrays based on the midpoint index.
3. Recursively call the merge sort function for each sub-array.
4. Merge the two sorted sub-arrays to create one sorted array.

3.2. Implementing Merge Sort

Now, let’s implement the above procedure in Kotlin. Here is a simple code example that implements Merge Sort:


fun mergeSort(arr: IntArray): IntArray {
    if (arr.size < 2) {
        return arr
    }

    val mid = arr.size / 2
    val left = mergeSort(arr.sliceArray(0 until mid))
    val right = mergeSort(arr.sliceArray(mid until arr.size))
    return merge(left, right)
}

fun merge(left: IntArray, right: IntArray): IntArray {
    val merged = IntArray(left.size + right.size)
    var i = 0
    var j = 0
    var k = 0

    while (i < left.size && j < right.size) {
        if (left[i] <= right[j]) {
            merged[k++] = left[i++]
        } else {
            merged[k++] = right[j++]
        }
    }
    
    while (i < left.size) {
        merged[k++] = left[i++]
    }
    
    while (j < right.size) {
        merged[k++] = right[j++]
    }

    return merged
}

4. Algorithm Problem: Sorting the Given Array

The task is to sort the given array using Merge Sort. The input consists of an array of integers, and the goal is to sort this array and output it. The problem is as follows:

Problem Description

Sort the given array in ascending order using the Merge Sort algorithm.

Input
- The first line contains the size of the array N (1 ≤ N ≤ 1000).
- The second line consists of N integers that form the array.

Output
- Output the N integers sorted in ascending order.

Problem Solving Process

To solve this problem, follow these steps:

  1. Call the merge sort function to sort the input array.
  2. Output the sorted array.

4.1. Code to Solve the Problem


fun main() {
    val n = readLine()!!.toInt()
    val arr = readLine()!!.split(" ").map { it.toInt() }.toIntArray()

    val sortedArr = mergeSort(arr)

    println(sortedArr.joinToString(" "))
}

5. Example

For example, let’s assume the following input is provided:

Input:
5
4 2 3 1 5

The output for this input should be:

Output:
1 2 3 4 5

6. Conclusion

Understanding the Merge Sort algorithm is crucial for coding tests. This algorithm is used to solve various problems, so sufficient practice is necessary. In this course, we covered the basic concepts of Merge Sort, its implementation, and how to solve actual coding test problems. We will explore even more diverse algorithms and problem-solving methods in the future, so stay tuned!