关于二分查找

1、首先二分查找判断元素是否存在，存在返回其位置，不存在返回-1.代码如下：

int bsearchWithoutRecursion(int array[], int low, int high, int target)
{
while(low <= high)
{
int mid = (low + high)/2;
if (array[mid] > target)
high = mid - 1;
else if (array[mid] < target)
low = mid + 1;
else //find the target
return mid;
}
//the array does not contain the target
return -1;
<pre name="code" class="cpp">

2、

1）二分法寻上界：

//Find the fisrt element, whose value is larger than target, in a sorted array
int BSearchUpperBound(int array[], int low, int high, int target)
{
//Array is empty or target is larger than any every element in array
if(low > high || target >= array[high]) return -1;

int mid = (low + high) / 2;
while (high > low)
{
if (array[mid] > target)
high = mid;
else
low = mid + 1;

mid = (low + high) / 2;
}

return mid;
}

2）二分法寻下界：

//Find the last element, whose value is less than target, in a sorted array
int BSearchLowerBound(int array[], int low, int high, int target)
{
//Array is empty or target is less than any every element in array
if(high < low  || target <= array[low]) return -1;

int mid = (low + high + 1) / 2; //make mid lean to large side
while (low < high)
{
if (array[mid] < target)
low = mid;
else
high = mid - 1;

mid = (low + high + 1) / 2;
}

return mid;
}

2、若要寻找严格的上下界，则把上面的大小判断修改即可：换成大于等于和小于等于。

去掉判断数组边界的等号：
target >= array[high]改为 target > array[high]
在与中间值的比较中加上等号：
array[mid] > target改为array[mid] >= target