Author: root

1. Problem Definition

Write a function to sort a given integer array in ascending order.
You must implement it using the bubble sort algorithm, which is the most basic sorting method,
and include the process of optimizing the code considering time complexity and space complexity.

Problem: Given an arbitrary integer array, write a Swift function that uses
the bubble sort algorithm to sort this array in ascending order.

2. Overview of Bubble Sort Algorithm

Bubble sort is a simple sorting algorithm that works by comparing two adjacent elements and
swapping them if they are not in the correct order. This process is repeated for all indices of the array,
and in the worst case, it has a time complexity of O(n²) when the size of the array is n.
The main characteristics of bubble sort are as follows:

• Simple and easy to understand algorithm
• Usually easy to implement and useful for small datasets
• Worst case O(n²), average O(n²), best case O(n) (when already sorted)

3. Algorithm Steps

The basic method of using bubble sort is as follows:

1. Start by comparing adjacent elements from the first element of the array.
2. If the first element is greater than the second element, swap the two elements.
3. Repeat this process until the end of the array.
4. When you reach the end of the array, the largest element will move to the end of the array.
5. Repeat the above steps n-1 times.

This process ensures that the largest element moves towards the end at each step.

Bubble Sort Implementation (Swift Code)

func bubbleSort(_ array: inout [Int]) {
    let n = array.count
    for i in 0.. array[j+1] {
                // Swap
                let temp = array[j]
                array[j] = array[j+1]
                array[j+1] = temp
                swapped = true
            }
        }
        // If no two elements were swapped by inner loop, then break
        if !swapped {
            break
        }
    }
}
    

4. Code Explanation

The above bubbleSort function takes an array as an argument and sorts it in ascending order.
Key Points:

• inout keyword allows the function to modify the array directly.
• The reason for using n-i-1 in the second for loop is that with each iteration the largest element moves to the end of the array.
  Therefore, the last element is already sorted and does not need to be checked.
• The swapped variable checks if the sorting is already completed to reduce unnecessary iterations.

5. Testing and Example

Below is an example that tests the bubbleSort function.

var myArray = [64, 34, 25, 12, 22, 11, 90]
print("Before sorting: \(myArray)")

bubbleSort(&myArray)

print("After sorting: \(myArray)")
    

Running the above code will display the array before and after sorting.
This will confirm that the bubble sort algorithm has been implemented successfully.

6. Time Complexity and Optimization

The time complexity of bubble sort is O(n²) in the worst case.
Even when the array is already sorted, it can perform at O(n) in the best case.
To optimize this, the swapped variable can be introduced to avoid unnecessary iterations.

In Swift, using bubble sort for large arrays is inefficient.
In this case, it is recommended to use advanced sorting algorithms (e.g., Quick Sort, Merge Sort).

7. Conclusion

In this tutorial, we explored how to implement the bubble sort algorithm in Swift and its process.
Bubble sort is easy to understand and simple to implement, but its performance may degrade in real usage.
Therefore, when dealing with complex datasets, other algorithms should be considered.
In the next tutorial, we will cover the more efficient sorting algorithm called Quick Sort.

8. References

For a deeper understanding of the algorithm, please refer to the materials below:

• Wikipedia – Bubble Sort
• GeeksforGeeks – Bubble Sort
• Swift.org – Swift Official Documentation

Hello! In this course, we will delve deeper into algorithms for preparing coding tests using Swift, specifically focusing on Bubble Sort. The problem we will solve is sorting an array, and we will implement this using the Bubble Sort algorithm. This course will include the following topics:

• Explanation of the principles and workings of Bubble Sort
• Implementation of the code in Swift
• Examples of code execution
• Suggestions for optimization and improvement
• Analysis of the time complexity of Bubble Sort

1. What is Bubble Sort?

Bubble Sort is a very simple and intuitive sorting algorithm. It works by comparing two adjacent elements in an array and sorting them in order. This process can be visualized as the largest value “bubbling” up to the end of the array.

The Working Principle of Bubble Sort

1. Start from the beginning of the array and compare two adjacent elements.
2. If the first element is greater than the second, swap the two elements.
3. Repeat this process until the end of the array.
4. After completing one pass, the largest value moves to the end of the array.
5. Repeat this process until the last element remains sorted.

2. Problem Definition

Given an integer array, sort this array in ascending order using Bubble Sort.

Input: [64, 34, 25, 12, 22, 11, 90]
Output: [11, 12, 22, 25, 34, 64, 90]

3. Implementation of Swift Code

Now, let’s write the code to solve this problem using Swift.

func bubbleSort(arr: [Int]) -> [Int] {
    var sortedArray = arr
    let n = sortedArray.count
    
    for i in 0.. sortedArray[j+1] {
                // Swap
                let temp = sortedArray[j]
                sortedArray[j] = sortedArray[j+1]
                sortedArray[j+1] = temp
            }
        }
    }
    return sortedArray
}

// Example execution
let array = [64, 34, 25, 12, 22, 11, 90]
let sortedArray = bubbleSort(arr: array)
print(sortedArray)  // Output: [11, 12, 22, 25, 34, 64, 90]

4. Code Execution Example

When we execute the above Swift code, the given array is successfully sorted. In this code, we use two nested for loops to compare all the elements of the array. This can be time-consuming, but the true advantage of Bubble Sort is its intuitive nature.

5. Optimization and Improvement Methods

Bubble Sort has a time complexity of O(n^2), which is inefficient. However, a few simple optimization techniques can be applied:

• Early termination: If no swaps occur during a pass, the array is already sorted, so no further comparisons are necessary.
• Reducing the range of comparisons: Elements at both ends that have already been passed don’t need to be compared in subsequent passes.

The code with these optimizations can be modified as follows:

func optimizedBubbleSort(arr: [Int]) -> [Int] {
    var sortedArray = arr
    let n = sortedArray.count
    var swapped: Bool
    
    for i in 0.. sortedArray[j+1] {
                // Swap
                let temp = sortedArray[j]
                sortedArray[j] = sortedArray[j+1]
                sortedArray[j+1] = temp
                swapped = true
            }
        }
        // If no swaps occurred, sorting is complete, so exit
        if !swapped {
            break
        }
    }
    return sortedArray
}

6. Time Complexity of Bubble Sort

The time complexity of Bubble Sort is O(n^2) in both average and worst-case scenarios. The best case (when the array is already sorted) can be O(n), making it more efficient. For this reason, Bubble Sort may be effective on small data sets, but in real applications, it is common to use more efficient sorting algorithms.

Conclusion

In this course, we had the opportunity to implement Bubble Sort using Swift and learn the basics of algorithm sorting. By solving basic problems like sorting an array, we were able to understand the workings and time complexity of algorithms. In the next course, we will cover a more efficient sorting algorithm called Quick Sort. Thank you for being with us!