Understanding the QuickSort Algorithm: Divide and Conquer

In the world of computer science, QuickSort stands out as one of the most efficient and widely used sorting algorithms. Its remarkable speed in sorting large data sets is due to its “Divide and Conquer” strategy. Let's discover how QuickSort works!

What is QuickSort?

QuickSort is a sorting algorithm that employs the "Divide and Conquer" technique. It selects an element, called a pivot, and partitions the list into two subarrays: one containing elements smaller than the pivot and another with elements larger. The process repeats recursively over these subarrays until the list is completely sorted.

The choice of pivot may vary. A simple approach is to select the first element in the list. However, other strategies may be more effective depending on the scenario.

QuickSort Steps

1. Recursion Stopping Criterion

When the list has 0 or 1 element, it is already sorted, and the algorithm finishes.

// Verifica se a lista tem 0 ou 1 elemento (já ordenada)
if (integerList.isEmpty() || integerList.size() == 1) {
    return integerList;
}

2. List Partitioning:

The next step involves selecting a pivot and dividing the list into two subarrays: one with smaller elements and the other with elements larger than the pivot. See an example of how this can be done:

int pivo = integerList.get(0); // Escolhendo o primeiro elemento como pivô
List<Integer> menores = new ArrayList<>();
List<Integer> maiores = new ArrayList<>();
for (int i = 1; i < integerList.size(); i++) {
   if (integerList.get(i) < pivo) {
      menores.add(integerList.get(i));
   } else {
      maiores.add(integerList.get(i));
   }
}

Note: Note that the comparison starts at i=1, preventing the pivot from being included in the subarray of minors.

3. Recursion:

Recursion comes into play! The algorithm calls itself the smallest and largest subarrays, repeating the process until complete sorting. The combination of results is demonstrated below:

List<Integer> sorted = new ArrayList<>(quickSort(menores));
sorted.add(pivo);
sorted.addAll(quickSort(maiores));
return sorted;

Complexity of the Algorithm

QuickSort has an asymptotic time complexity of O(n log n), demonstrating high efficiency, especially compared to algorithms such as Bubble Sort, which has O(n²) complexity.

Note: This explanation is an adaptation based on Chapter 4 of the book "Understanding Algorithms" by Aditya Bhargava. It should be noted that there may be nuances not addressed here, and it is recommended that you consult additional sources for a more in-depth study.

Conclusion

QuickSort is a robust algorithm that uses recursion to sort lists efficiently. Its main attribute is execution speed, particularly on long lists, compared to other sorting algorithms. For a more complete understanding, reading the book "Understanding Algorithms" is suggested.

Have you ever used QuickSort in any project? Share your experience in the comments!

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