/**
     * 簡單二分查找
     * @param arr
     * @param value
     * @return
     */
    public static int bSeaarch(int[] arr,int value){
        int low=0;
        int high=arr.length-1;
        while (low<=high){
            int mid=low+((high-low)>>1);
            if (value==arr[mid]){
                return mid;
            }else if (value>arr[mid]){
                low=mid+1;
            }else {
                high=mid-1;
            }
        }
        return -1;
    }

 /**
     * 查找第一個值等于給定值的元素
     * @param arr
     * @param value
     * @return
     */
    public static int bSeaarch2(int[] arr,int value){
        int low=0;
        int high=arr.length-1;
        while (low<=high){
            int mid=low+((high-low)>>1);
            //如果給定的值大于區(qū)間中間元素
            if (value>arr[mid]){
                low=mid+1;
            }else if (value<arr[mid]){  //如果給定的值大于區(qū)間中間元素
                high=mid-1;
            }else{  //如果給定的值等于區(qū)間中間元素
                //當前中間元素為第一個或者中間元素的前一個不等于給定值，則當前元素就是要查找第一個值
                if (mid==0||arr[mid-1]!=value){
                    return mid;
                }else {
                    high=mid-1;
                }
            }
        }
        return -1;
    }

/**
     * 查找最后一個值等于給定元素
     * @param arr
     * @param value
     * @return
     */
    public static int bseaarch3(int[] arr,int value){
        int low=0;
        int high=arr.length-1;
        while (low<=high){
            int mid=low+((high-low)>>1);
            //如果跟定的值大于區(qū)間數組中間值，則 low=mid+1
            if (value>arr[mid]){
                low=mid+1;
            }else if (value<arr[mid]){  //如果跟定的值小于區(qū)間數組中間值，則 high=mid-1
                high=mid-1;
            }else {
                //如果區(qū)間數組中間值是數組最后一個元素或者中間值的下一個元素不等于給定值，返回當前mid索引
                if ((mid==arr.length-1)||(arr[mid+1]!=value)) {
                    return mid;
                }else { //繼續(xù)在下一區(qū)間查找
                    low=mid+1;
                }
            }
        }
        return -1;
    }

   /**
     * 查找第一個大于等于給定值的元素
      * @param arr
     * @param value
     * @return
     */
    public static int bsearch4(int[] arr,int value){
        int low=0;
        int high=arr.length-1;
        while (low<=high){
            int mid=low+((high-low)>>1);
            //如區(qū)間元素中間值大于等于給定元素
            if (arr[mid]>=value){
                // 如區(qū)間元素是數組第一個元素或者下一個元素小于給定值，則當前索引滿足條件
                if (mid==0||arr[mid-1]<value){
                    return mid;
                }else { //不滿足上面條件，繼續(xù)循環(huán)
                    high=mid-1;
                }
            }else {
                low=mid+1;
            }
        }
         return -1;
    }

/**
     * 查找最后一個小于于等于給定值的元素  `int[] a={9,10,12,13,14,15,16}
     * @param arr
     * @param value
     * @return
     */
    public static int bsearch6(int[] arr,int value){
        int low=0;
        int high=arr.length-1;
        while (low<=high){
            int mid=low+((high-low)>>1);
            if (arr[mid]>value){
               high=mid-1;
            }else {
                if ((mid==arr.length-1)||(arr[mid+1]>value)) {
                    return mid;
                }else {
                    low=mid+1;
                }
            }
        }
        return -1;
    }