I need to find run time analysis and description of the algorithm complexity (i.e., BigO) Thank you! /////////////////////////////////////////////////////////////////////////////////////////////// import java.io.File; import java.io.FileNotFoundException; import java.util.Arrays; import java.util.Scanner; public class Sorting { private static int n; public static void main(String[] args) { int[] arr = readFile("Data.txt"); // Bubble sort long startTime = System.nanoTime(); bubbleSort(arr); long endTime = System.nanoTime(); System.out.println("Bubble sort time: " + (endTime - startTime) + " nanoseconds"); // Selection sort startTime = System.nanoTime(); selectionSort(arr); endTime = System.nanoTime(); System.out.println("Selection sort time: " + (endTime - startTime) + " nanoseconds"); // Insertion sort startTime = System.nanoTime(); insertionSort(arr); endTime = System.nanoTime(); System.out.println("Insertion sort time: " + (endTime - startTime) + " nanoseconds"); // Merge sort startTime = System.nanoTime(); mergeSort(arr); endTime = System.nanoTime(); System.out.println("Merge sort time: " + (endTime - startTime) + " nanoseconds"); // Quick sort startTime = System.nanoTime(); quickSortTime = quickSort(arr, 0, arr.length-1); endTime = System.nanoTime(); System.out.println("Quick sort time: " + (endTime - startTime) + " nanoseconds"); } private static int[] readFile(String filename) { int[] arr = null; try { File file = new File(filename); Scanner scanner = new Scanner(file); n = scanner.nextInt(); arr = new int[n]; for (int i = 0; i < n; i++) { arr[i] = scanner.nextInt(); } scanner.close(); } catch (FileNotFoundException e) { System.out.println("File not found: " + filename); System.exit(0); } return arr; } private static void bubbleSort(int[] arr) { 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; } } } } private static void selectionSort(int[] arr) { for (int i = 0; i < n - 1; i++) { int minIndex = i; for (int j = i + 1; j < n; j++) { if (arr[j] < arr[minIndex]) { minIndex = j; } } int temp = arr[i]; arr[i] = arr[minIndex]; arr[minIndex] = temp; } } private static void insertionSort(int[] arr) { for (int i = 1; i < n; i++) { int key = arr[i]; int j = i - 1; while (j >= 0 && arr[j] > key) { arr[j + 1] = arr[j]; j--; } arr[j + 1] = key; } } private static void mergeSortHelper(int[] arr, int left, int right) { if (left < right) { int mid = (left + right) / 2; mergeSortHelper(arr, left, mid); mergeSortHelper(arr, mid+1, right); merge(arr, left, mid, right); } } private static void merge(int[] arr, int left, int mid, int right) { int[] temp = new int[right-left+1]; int i = left, j = mid+1, k = 0; while (i <= mid && j <= right) { if (arr[i] <= arr[j]) { temp[k++] = arr[i++]; } else { temp[k++] = arr[j++]; } } while (i <= mid) { temp[k++] = arr[i++]; } while (j <= right) { temp[k++] = arr[j++]; } for (i = left, k = 0; i <= right; i++, k++).

1. I need to find run time analysis and description of the algorithm complexity (i.e., BigO)
Thank you!
///////////////////////////////////////////////////////////////////////////////////////////////
import java.io.File;
import java.io.FileNotFoundException;
import java.util.Arrays;
import java.util.Scanner;
public class Sorting {
private static int n;
public static void main(String[] args) {
int[] arr = readFile("Data.txt");
// Bubble sort
long startTime = System.nanoTime();
bubbleSort(arr);
long endTime = System.nanoTime();
System.out.println("Bubble sort time: " + (endTime - startTime) + " nanoseconds");
// Selection sort
startTime = System.nanoTime();
selectionSort(arr);
endTime = System.nanoTime();
System.out.println("Selection sort time: " + (endTime - startTime) + " nanoseconds");
// Insertion sort
startTime = System.nanoTime();
insertionSort(arr);
endTime = System.nanoTime();
System.out.println("Insertion sort time: " + (endTime - startTime) + " nanoseconds");
// Merge sort
startTime = System.nanoTime();
mergeSort(arr);
endTime = System.nanoTime();
System.out.println("Merge sort time: " + (endTime - startTime) + " nanoseconds");
// Quick sort
startTime = System.nanoTime();
quickSortTime = quickSort(arr, 0, arr.length-1);
endTime = System.nanoTime();
System.out.println("Quick sort time: " + (endTime - startTime) + " nanoseconds");
}
private static int[] readFile(String filename) {
int[] arr = null;
try {
File file = new File(filename);
Scanner scanner = new Scanner(file);

2. n = scanner.nextInt();
arr = new int[n];
for (int i = 0; i < n; i++) {
arr[i] = scanner.nextInt();
}
scanner.close();
} catch (FileNotFoundException e) {
System.out.println("File not found: " + filename);
System.exit(0);
}
return arr;
}
private static void bubbleSort(int[] arr) {
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;
}
}
}
}
private static void selectionSort(int[] arr) {
for (int i = 0; i < n - 1; i++) {
int minIndex = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < arr[minIndex]) {
minIndex = j;
}
}
int temp = arr[i];
arr[i] = arr[minIndex];
arr[minIndex] = temp;
}
}
private static void insertionSort(int[] arr) {
for (int i = 1; i < n; i++) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];

3. j--;
}
arr[j + 1] = key;
}
}
private static void mergeSortHelper(int[] arr, int left, int right) {
if (left < right) {
int mid = (left + right) / 2;
mergeSortHelper(arr, left, mid);
mergeSortHelper(arr, mid+1, right);
merge(arr, left, mid, right);
}
}
private static void merge(int[] arr, int left, int mid, int right) {
int[] temp = new int[right-left+1];
int i = left, j = mid+1, k = 0;
while (i <= mid && j <= right) {
if (arr[i] <= arr[j]) {
temp[k++] = arr[i++];
} else {
temp[k++] = arr[j++];
}
}
while (i <= mid) {
temp[k++] = arr[i++];
}
while (j <= right) {
temp[k++] = arr[j++];
}
for (i = left, k = 0; i <= right; i++, k++) {
arr[i] = temp[k];
}
}
public static long mergeSort(int[] arr) {
long startTime = System.nanoTime();
mergeSortHelper(arr, 0, arr.length-1);
long endTime = System.nanoTime();
return endTime - startTime;
}
private static long quickSort(int[] arr, int low, int high) {
long startTime = System.nanoTime();
if (low < high) {

4. int pivotIndex = partition(arr, low, high);
quickSort(arr, low, pivotIndex - 1);
quickSort(arr, pivotIndex + 1, high);
}
long endTime = System.nanoTime();
return endTime - startTime;
}
private static int partition(int[] arr, int low, int high) {
int pivot = arr[high];
int i = low - 1;
for (int j = low; j < high; j++) {
if (arr[j] < pivot) {
i++;
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
int temp = arr[i+1];
arr[i+1] = arr[high];
arr[high] = temp;
return i+1;
}
}