Question

I am solving "Programming Pearls" exercises. 4.11 say:

Write and prove the correctness of a recursive binary search function in C or C++ with this declaration:

int binarysearch(DataType x[], int n);

Use this function alone; do not call any other recursive function.

I came up with:

int bsearch_rec_array_only(int key, int* arr, int n)
{
    int mid;

    if (n < 0)
        return -1;

    mid = n / 2;

    if (arr[mid] == key)
        return (int) ((size_t) arr + mid * sizeof(*arr));
    else if (arr[mid] < key)
        return bsearch_rec_array_only(key, arr + mid + 1, n - mid - 1);
    else
        return bsearch_rec_array_only(key, arr, mid - 1);
}

However - there is problem. I return the offset including array address because otherwise how to know the relative offset of the element to original array?

So I need this wrapper:

int bsearch_array_only_wrap(int key, int* arr, int n)
{
    int offset;
    if (n == 0)
        return -1;

    offset = bsearch_rec_array_only(key, arr, n);

    if (offset == -1)
        return -1;
    else       
        return (offset - (int) arr) / sizeof(*arr);
}

It s not recursive - it just calls bsearch_rec_array_only and computes offset.

But this seems complicated. Can you find a better solution?

Answer 1

Your problem is that the code doesn t return the offset of the element from the array s beginning, but a pointer cast into an int. The fact that you used a cast should show you that there something s wrong in the code.

Try returning an offset. Something like this:

if (arr[mid] == key)
        return mid;
else if (arr[mid] < key) {
        int i = bsearch_rec_array_only(key, arr + mid + 1, n - mid - 1);
        return (i != -1) ? i + mid + 1 : -1;
} else
        return bsearch_rec_array_only(key, arr, mid - 1);

Answer 2

Here is the correct answer:

// Recursive binary search
int bsearch(int key, int * arr, int n)
{
    if (n == 0)
    {
        return -1;
    }

    int m = n / 2;
    int found;

    if (arr[m] == key)
    {
        found = m;
    }
    else if (arr[m] < key)
    {
        // Upper half. We ll search in upper half of the current array with new length 
        // of the upper half.
        found = bsearch(key, arr + m + 1, n - m - 1);

        if (found != -1)
        {
            // Since we ve found a key, need to offset it to make valid in the 
            // current search scope
            found += m + 1;
        }
    }
    else
    {
        // Lower half, there is no need to offset the array. 
        // New array length is equal to the current middle point.
        found = bsearch(key, arr, m);
    }

    assert(found == -1 || (found >= 0 && found < n && arr[found] == key));

    return found;
}

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