//冒泡排序
    public static int[] Sort(int [] arr) {
        if(arr ==null||arr.length==0) return null;
        for(int i = 0 ; i <arr.length;i++) {
            for(int j = 0;j<arr.length-i-1;j++) {
                if(arr[j+1]<arr[j]) {
                    int tmp = arr[j+1];
                    arr[j+1] = arr[j];
                    arr[j] = tmp;
                }
            }
        }
        return arr;
    }

//插入排序
    public static int[] insertSort(int[] arr) {
        if(arr==null||arr.length==0) return null;
        for(int i = 0 ;i<arr.length;i++) {
            int cur = arr[i];
            int preIndex = i-1;
            while(preIndex>=0&&cur<arr[preIndex]) {
                arr[preIndex+1] = arr[preIndex];
                preIndex--;
            }
            arr[preIndex+1]=cur;
        }
        return arr;
    }

// 希尔排序
    public static int[] shellSort(int[] arr) {
        if (arr == null || arr.length == 0) return null;
        int gap = arr.length / 2;
        while(gap!=0) {
            for(int i = 0 ; i <arr.length;i++) {
                int cur = arr[i];
                int preIndex = i-gap;
                while(preIndex>=0&&cur<arr[preIndex]) {
                    arr[preIndex+gap] =arr[preIndex];
                    preIndex-=gap;
                }
                arr[preIndex+gap] = cur;
            }
            gap/=2;
        }
        return arr;
    }

//快速排序
    public static int[] quickSort(int[] arr, int start, int end) {
        if (arr == null || arr.length == 0 || start < 0 || end > arr.length || start > end) return null;
        int i = start;
        int j = end;
        int pivot = arr[start];
        while (i != j) {
            while (i < j && pivot <= arr[j]) {
                j--;
            }
            while (i < j && pivot >= arr[i]) {
                i++;
            }
            // 交换ij
            int tmp = arr[i];
            arr[i] = arr[j];
            arr[j] = tmp;
        }
        // 相遇交换
        arr[start]=arr[i];
        arr[i] = pivot;
        quickSort(arr, start, j-1);
        quickSort(arr, j+1, end);
        return arr;
    }

//归并排序
      private static void mergeSort(int[] arr, int start, int end) {
        if(start>=end) return;
        int mid = (start + end )/2;
        mergeSort(arr, start, mid);
        mergeSort(arr, mid+1, end);
        merge(arr,start,mid,end);
    }

    private static void merge(int[] arr, int start, int mid, int end ) {
        int i = start;
        int j = mid+1;
        int[] tmp = new int[arr.length];
        int t =0;
        while(i<=mid&&j<=end) {
            if(arr[i]>=arr[j]) {
                tmp[t++]=arr[j++];
            }else {
                tmp[t++] = arr[i++];
            }
        }
        while(i<=mid) {
            tmp[t++] = arr[i++];
        }
        while(j<=end) {
            tmp[t++] = arr[j++];
        }
        t= 0 ; 
        int tmpL =  start;
        while(tmpL<=end) {
            arr[tmpL++] = tmp[t++];
        }
    }

//选择排序
    public static int[] selectSort(int [] arr) {
        if(arr==null||arr.length==0) return null;
        for(int i =0;i<arr.length;i++) {
            int minIndex = i;
            for(int j= i+1;j<arr.length;j++) {
                if(arr[minIndex]>arr[j]) {
                    minIndex = j ;
                }
            }
            int tmp = arr[i];
            arr[i] = arr[minIndex];
            arr[minIndex] = tmp;
        }
        return arr;
    }

//堆排序
public static int[] heapSort(int[] arr) {
        if (arr == null || arr.length == 0)
            return arr;
        //从倒数第二排开始
        for (int i = arr.length / 2 - 1; i >= 0; i--) {
            heapify(arr, arr.length, i);
        }
        //从后往前排
        for (int i = arr.length - 1; i >= 0; i--) {
            swap(arr, i, 0);
            heapify(arr, i, 0);//i=arr.length-1
        }
        return arr;
    }

    public static void heapify(int[] arr, int size, int i) {
        int maxIndex = i;
        int left = 2 * i + 1;
        int right = 2 * i + 2;
 
        if (left < size && arr[left] > arr[maxIndex]) {
            maxIndex = left;
        }
        if (right < size && arr[right] > arr[maxIndex]) {
            maxIndex = right;
        }
        if (maxIndex != i) {
            swap(arr, i, maxIndex);
            heapify(arr, size, maxIndex);
        }
    }

    public static void swap(int[] arr, int i, int j) {
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

都是自学的有错误还请大家指出，谢谢