Binary search in C with recursive function accepting only length
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20-09-2019 - |
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?
Solution
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);
OTHER TIPS
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;
}