/**
     * 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(dāng)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(dāng)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(shù)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(shù)組中間值，則 high=mid-1
                high=mid-1;
            }else {
                //如果區(qū)間數(shù)組中間值是數(shù)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(dāng)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(shù)組第一個元素或者下一個元素小于給定值，則當(dāng)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;
    }