Time Complexity of Sorting Algorithms

The time complexity of sorting algorithms is an important factor to consider when choosing the right algorithm for your data. It determines how the algorithm's runtime increases with the size of the input.

Let's take a look at the time complexities of some common sorting algorithms:

• Bubble Sort: Bubble sort has a worst-case time complexity of O(n^2), where n is the number of elements in the array. This makes it inefficient for large datasets.

• Insertion Sort: Insertion sort also has a worst-case time complexity of O(n^2). However, it performs well on small or partially sorted arrays.

• Merge Sort: Merge sort has a worst-case time complexity of O(n log n), which makes it more efficient than bubble sort and insertion sort for larger datasets.

• Quick Sort: Quick sort has an average-case time complexity of O(n log n). It also has a worst-case time complexity of O(n^2) in rare cases, but this can be mitigated by using randomized pivot selection.

• Radix Sort: Radix sort has a time complexity of O(d * (n + b)), where d is the number of digits in the maximum element, n is the number of elements, and b is the base of the number system. It can be more efficient than comparison-based sorting algorithms for large datasets with a limited range of values.

When choosing a sorting algorithm, consider the size of the dataset, the degree of sorting required, and the characteristics of the data. Additionally, consider other factors such as space complexity and stability of the algorithm.

Now, let's take a look at an example of bubble sort in action:

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public class Main {

    public static void main(String[] args) {

        int[] arr = {5, 2, 7, 1, 3};

        bubbleSort(arr);

    }

​

    public static void bubbleSort(int[] arr) {

        int n = arr.length;

        for (int i = 0; i < n-1; i++) {

            for (int j = 0; j < n-i-1; j++) {

                if (arr[j] > arr[j+1]) {

                    int temp = arr[j];

                    arr[j] = arr[j+1];

                    arr[j+1] = temp;

                }

            }

        }

    }

}