Java five sorting algorithm summary tool class

This tool class simply and clearly summarizes the five sorting algorithms of Java: Quick Sort, Hill Sort, Insertion Sort, Heap Sort, and Merge Sort. There is no explanation of these sorting algorithms in the code. I hope to explain the ideas in Check the relevant instructions yourself. Here is just a summary of these algorithms for your use.

public class Sort {
  public static <AnyType extends Comparable<? super AnyType>> void insertionSort(AnyType[] a) {
    insertionSort(a, 0, a.length - 1);
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void insertionSort(AnyType[] a, int left, int right) {
    int j;  // 记录第一个比tmp小的元素的后边一位的位置
 
    for (int p = left; p <= right; p++) {
      AnyType tmp = a[p];
      for (j = p; j > left && tmp.compareTo(a[j - 1]) < 0; j--) {
        a[j] = a[j - 1];
      }
      a[j] = tmp;
    }
  }
 
  public static <AnyType extends Comparable<? super AnyType>> void shellSort(AnyType[] arr) {
    int j;
 
    for (int gap = arr.length / 2; gap > 0; gap /= 2) {
      for (int i = gap; i < arr.length; i++) {
        AnyType tmp = arr[i];
        for (j = i; j >= gap && tmp.compareTo(arr[j - gap]) < 0; j -= gap) {
          arr[j] = arr[j - gap];
        }
        arr[j] = tmp;
      }
    }
  }
 
  private static int leftChild(int i) {
    return i * 2 + 1;
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void perculateDown(AnyType[] arr, int i, int size) {
    AnyType tmp = arr[i];
 
    for (int child; (child = leftChild(i)) < size; i = child) {
      if (child != size - 1 && arr[child].compareTo(arr[child + 1]) < 0) {
        child++;
      }
      if (tmp.compareTo(arr[child]) < 0) {
        arr[i] = arr[child];
      } else {
        break;
      }
    }
    arr[i] = tmp;
  }
 
  public static <AnyType extends Comparable<? super AnyType>> void heapSort(AnyType[] arr) {
    for (int i = arr.length / 2; i >= 0; i--) {
      perculateDown(arr, i, arr.length);
    }
    for (int i = arr.length - 1; i >= 0; i--) {
      swapReferences(arr, 0, i);
      perculateDown(arr, 0, i);
    }
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void swapReferences(AnyType[] arr, int i, int j) {
    AnyType tmp = arr[i];
    arr[i] = arr[j];
    arr[j] = tmp;
  }
 
  public static <AnyType extends Comparable<? super AnyType>> void mergeSort(AnyType[] arr) {
    AnyType[] tmp = ((AnyType[]) new Comparable[arr.length]);
    mergeSort(arr, 0, arr.length - 1, tmp);
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void mergeSort(AnyType[] arr, int start, int end, AnyType[] tmp) {
    if (start < end) {
      int mid = (start + end) >> 1;
      mergeSort(arr, start, mid, tmp);
      mergeSort(arr, mid + 1, end, tmp);
      merge(arr, start, mid, end, tmp);
    }
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void merge(AnyType[] arr, int start, int mid, int end, AnyType[] tmp) {
    int i = start, j = mid + 1, k = start;
    while (i <= mid && j <= end) {
      if (arr[i].compareTo(arr[j]) < 0) {
        tmp[k++] = arr[i++];
      } else {
        tmp[k++] = arr[j++];
      }
    }
 
    while (i <= mid) {
      tmp[k++] = arr[i++];
    }
 
    while (j <= end) {
      tmp[k++] = arr[j++];
    }
 
    for (int m = start; m <= end; m++) {
      arr[m] = tmp[m];
    }
  }
 
  public static <AnyType extends Comparable<? super AnyType>> void quickSort(AnyType[] arr) {
    quickSort(arr, 0, arr.length - 1);
  }
 
  private static <AnyType extends Comparable<? super AnyType>> void quickSort(AnyType[] arr, int left, int right) {
    if (left + LENGTH_DIFF <= right) {
 
      AnyType pivot = medium(arr, left, right);
 
      int i = left, j = right;
      while (true) {
        while (arr[++i].compareTo(pivot) < 0);
        while (arr[--j].compareTo(pivot) > 0);
 
        if (i < j) {
          swapReferences(arr, i, j);
        } else {
          break;
        }
      }
 
      swapReferences(arr, i, right);
      quickSort(arr, left, i - 1);
      quickSort(arr, i + 1, right);
    } else {
      insertionSort(arr, left, right);
    }
  }
 
  private static <AnyType extends Comparable<? super AnyType>> AnyType medium(AnyType[] arr, int left,
      int right) {
    int center = (left + right) / 2;
    if (arr[center].compareTo(arr[left]) < 0) {
      swapReferences(arr, center, left);
    }
    if (arr[left].compareTo(arr[right]) > 0) {
      swapReferences(arr, left, right);
    }
    if (arr[center].compareTo(arr[right]) < 0) {
      swapReferences(arr, center, right);
    }
     
    return arr[right];
  }
 
  private final static int LENGTH_DIFF = 20;
}