二分法

二分查找（折半查找）(递归实现二分查找)

       二分查找又称折半查找，优点是比较次数少，查找速度快，平均性能好；其缺点是要求待查表为有序表，且插入删除困难。因此，折半查找方法适用于不经常变动而查找频繁的有序列表。首先，假设表中元素是按升序排列，将表中间位置记录的关键字与查找关键字比较，如果两者相等，则查找成功；否则利用中间位置记录将表分成前、后两个子表，如果中间位置记录的关键字大于查找关键字，则进一步查找前一子表，否则进一步查找后一子表。重复以上过程，直到找到满足条件的记录，使查找成功，或直到子表不存在为止，此时查找不成功。

算法要求

必须采用顺序存储结构

必须按关键字大小有序排列。

算法时间复杂度：O(h)=O(log2n)

二分查找分两种情况

（1）[  ]

left = 0; right = pseq->size-1;

left<=right;

mid = left+(right-left)>>1;

left = mid+1;

right = mid-1;

(其他情况最后会出现死循环)

void SeqListBinarySearch(SeqList *Seq,DaTatype data)
{
     int left = 0;;
     int right = Seq->size - 1;
     int mid = 0;
     while (left <= right)
     {
           mid = left + ((right - left) >> 1);
           if (Seq->array[mid] > data)

                right = mid - 1;

           else if (Seq->array[mid] < data)

               left = mid + 1;
           else
           {
                printf("%d\n",mid);
                return;
           }
     }
     printf("-1\n");
     return ;

}

（2）[  )

left = 0; right = pseq->size;

left<right;

mid = left+(right-left)>>1;

left = mid+1;

right = mid;

(其他情况最后会出现死循环)
 

void SeqListBinarySearch(SeqList *Seq, DaTatype data)
{
     int left = 0;;
     int right = Seq->size;
     int mid = 0;
     while (left < right)
     {
           mid = left + ((right - left) >> 1);
           if (Seq->array[mid] > data)
                right = mid;
           else if (Seq->array[mid] < data)
                left = mid + 1;
           else
           {
                printf("%d\n", mid);
                return;
           }
     }
     printf("-1\n");
     return;
}

递归实现

int Bin_Search(SeqList *Seq, int left, int right, DaTatype data)

{

     int mid = left + ((right - left) >> 1);

     if (left <= right)

     {

           if (Seq->array[mid] < data)

           {

                return Bin_Search(Seq, mid + 1, right, data);

           }

           else if (Seq->array[mid]>data)

           {

                return Bin_Search(Seq, left, right - 1, data);

           }

           else

                return mid;

     }

     else

           return -1;

}