Let's say we want to write a function in C that finds a specified target value in an unsorted array of ints. In general, this is simple and runs in O(n) time:
int search(int *data, int len, int target)
{
int i;
for(i = 0; i < len; i++)
if(data[i]==target) return i;
return -1;
}
Let's say we're being masochistic and want to approach this with a divide and conquer algorithm instead. We'll run into trouble on the recursive part because we can't exclude half the array each time, like we can with binary search:
int search(int *data, int start, int stop, int target)
{
// Base case: we've divided the array into two size subarray
if(stop==start+1)
{
if(data[start]==target) return start;
if(data[stop]==target) return stop;
return -1;
}
/* The recursion part is tricky.
We *need* to parse both halves of the array, because we can't safely
exclude any part of the array; it's not sorted, so we can't predict
which half it's going to be in.*/
else
{
/** This obviously doesn't work. */
int mid = (stop-start)/2;
return search(data, start, mid, target);
return search(data, mid+1, stop, target);
}
}
Is there any way to make this work?
NOTE: This is not asking people to do my homework for me, as some of you may think when reading this question. It is, however, inspired by curiosity after I encountered this problem when trying to solve a question in an assignment that I've submitted earlier this week.
How about changing the recursive call to:
else
{
int mid = (stop-start)/2;
int x = search(data, start, mid, target);
if (x == -1)
return search(data, mid+1, stop, target);
else
return x;
}