二分搜索（Binary Search）

当我们在字典中查找某个单的时候，一般我们会翻到一个大致的位置（假设吧，翻到中间位置），开始查找。如果翻到的正好有我们要的词，那运气好，查找结束。如果我们要找的词还在这个位置的前面，那我们对前面的这一半词典继续搜索，翻到某个位置（假设是四分之一的位置）等等。这个二分搜索的工作原理一样。相应的算法就叫做二进制搜索算法。

迭代版本算法：

//iterative binary search which returns index of element
int binarySearchIterative(int arr[], int size, int data)
{
    int low = 0;
    int high = size-1;
    int mid;

    while(low<=high)
    {
        mid = low + (high-low)/2; //To avoid overflow by (low + high)

        if(arr[mid] == data)
            return mid;
        else
        {
            if(arr[mid] < data)
                low = mid + 1; // search in right half
            else
                high = mid - 1; // search in left half
        }
    }

    return -1;
}

递归版本算法：

//recursive binary search which returns index of element
int binarySearchRecursive(int arr[], int low, int high, int data)
{
    if(low<=high)
    {
        int mid = low + (high-low)/2; // To avoid overflow

        if(arr[mid] == data)
            return mid;
        else
        {
            if(arr[mid] < data)
                //search in right half.
                return binarySearchRecursive(arr, mid+1, high, data);
            else
                //search in left half.
                return binarySearchRecursive(arr, low, mid-1, data);
        }
    }
    return -1;
}