排序

    //插入排序
    public static void insertionSort(int[] arr) {
        for (int j = 1; j < arr.length; j++) {
            int key = arr[j];
            int i = j - 1;
            while (i >= 0 && arr[i] > key) {
                arr[i + 1] = arr[i];
                i = i - 1;
            }
            arr[i + 1] = key;
        }
    }

    //选择排序
    public static void selectionSort(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++) {
            int minIdx = i;
            for (int j = i + 1; j < arr.length; j++) {
                if (arr[minIdx] > arr[j]) {
                    minIdx = j;
                }
            }
            int temp = arr[i];
            arr[i] = arr[minIdx];
            arr[minIdx] = temp;
        }
    }

    //归并排序
    public static void mergeSort(int[] arr, int low, int high) {
        if ((low + 1) > high) {
            return;
        }
        int mid = (low + high) >> 1;
        mergeSort(arr, low, mid);
        mergeSort(arr, mid + 1, high);
        merge(arr, low, mid, high);
    }

    private static void merge(int[] arr, int low, int mid, int high) {
        int n1 = mid - low + 1;
        int n2 = high - mid;

        int[] left = new int[n1 + 1];
        int[] right = new int[n2 + 1];

        for(int i = 0; i < n1; i++) {
            left[i] = arr[low + i];
        }
        for (int i = 0; i < n2; i++) {
            right[i] = arr[mid + 1 + i];
        }
        left[n1] = Integer.MAX_VALUE;
        right[n2] = Integer.MAX_VALUE;

        int i = 0;
        int j = 0;
        int k = low;
        while (k <= high) {
            if (left[i] <= right[j]) {
                arr[k++] = left[i++];
            } else {
                arr[k++] = right[j++];
            }
        }
    }

    //快速排序
    public static void quickSort(int arr[], int low, int high) {
        if (low >= high) {
            return;
        }
        int temp = arr[low];
        int i = low;
        int j = high;
        while (i < j) {
            while (j > i && arr[j] >= temp) {
                j--;
            }
            arr[i] = arr[j];
            while (i < j && arr[i] <= temp) {
                i++;
            }
            arr[j] = arr[i];
        }
        arr[i] = temp;

        quickSort(arr, low, i - 1);
        quickSort(arr, i + 1, high);
    }

    //堆排序
    public static void heapSort(int[] arr) {
        buildMaxHeap(arr);
        for (int i = arr.length - 1; i > 0; i--) {
            swap(arr, i, 0);
            maxHeapify(arr, i, 0);
        }
    }


    //建堆
    public static void buildMaxHeap(int[] arr) {
        for (int i = arr.length / 2 - 1; i >= 0; i--) {
            maxHeapify(arr, arr.length, i);
        }
    }

    //维护堆的性质
    public static void maxHeapify(int[] arr, int len, int i) {
        int l = 2 * i + 1;
        int r = 2 * i + 2;
        int largest = i;
        if (l < len && arr[l] > arr[largest]) {
            largest = l;
        }
        if (r < len && arr[r] > arr[largest]) {
            largest = r;
        }
        if (largest != i) {
            swap(arr, i, largest);
            maxHeapify(arr, len, largest);
        }
    }

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

　　

    //计数排序
    public static int[] countSort(int[] arr) {

        int min = arr[0];
        int max = arr[0];
        for (int i = 0; i < arr.length; i++) {
            if (arr[i] < min) {
                min = arr[i];
            }
            if (arr[i] > max) {
                max = arr[i];
            }
        }

        int[] countArr = new int[max - min + 1];
        for(int i = 0; i < arr.length; i++) {
            countArr[arr[i] - min]++;
        }

        for(int i = 1; i < countArr.length; i++) {
            countArr[i] = countArr[i] + countArr[i - 1];
        }

        int[] sortedArr = new int[arr.length];
        for (int i = arr.length - 1; i >= 0; i--) {
            sortedArr[countArr[arr[i] - min] - 1] = arr[i];
            countArr[arr[i] - min]--;
        }

        return sortedArr;
    }