求数字在非降序数组中出现的次数

题目描述：

在一个非降序排列的数组中，找出数字target出现的次数。非降序数组，比如{1，1，1，2，3，4，5，5，6}

思路一：

先通过二分查找，找到arr[index]等于target的index，在分别向前后遍历，直到arr[index] != target为止。算法实现简单，但是当数组形如{x,x,...,x}，此时查找x的时间复杂度就退化为线性的O(n).

思路二：

1. 首先通过二分查找，找到arr[mid] == target的mid；2. 然后分别对arr[0~mid]和arr[mid~(arr.length-1)]用二分查找，找到最左边的target的index：left，找到最右边的target的index：right；3. return right-left+1;

Java代码实现如下：

/** * @author Mengjun Li * @create 2017/9/29 * @since 1.0.0 */public class Test {    public static void main(String[] args) {        int[] arr = new int[]{3, 4, 4, 6, 7, 8, 9, 9, 9, 9, 9, 9, 10, 11, 12, 13, 14};        int target = 9;        System.out.println("输入数组中 "+target+" 的个数为 "+findNum(arr,target));    }    public static int findNum(int[] arr, int target) {        if (arr == null)            return 0;        int len = arr.length;        if (len < 1)            return 0;        if (arr[0] > target || target > arr[len - 1])            return 0;        int mid = findIndex(arr, 0, len - 1, target);        if (mid == -1)            return 0;        int left = findLeft(arr, 0, mid, target);        System.out.println("left=" + left);        int right = findRight(arr, mid, len - 1, target);        System.out.println("right= " + right);        return right - left + 1;    }    private static int findLeft(int[] arr, int left, int right, int target) {        while (left < right) {            int mid = (left + right) >> 1;            if (arr[mid] == target)                right = mid;            else                left = mid + 1;        }        return right;    }    private static int findRight(int[] arr, int left, int right, int target) {        while (left < right) {            int mid = (left + right + 1) >> 1;            if (arr[mid] == target)                left = mid;            else                right = mid - 1;        }        return left;    }    private static int findIndex(int[] arr, int left, int right, int target) {        int mid;        while (left <= right) {            mid = (left + right) >> 1;            if (arr[mid] == target)                return mid;            else if (arr[mid] < target)                left = mid + 1;            else                right = mid - 1;        }        return -1;    }}

输出如下：

left=6right= 11输入数组中 9 的个数为 6