10 steps from each end! so, if you start searching from both ends at once, they must meet at some middle place m in between.
the left side of this search has only a thousand forks. if this is also true of the side on the right, then the search will be several hundred times smaller. and then, if you also have some way to guess where that middle place m might be, then you might further reduce that search by dividing each side into two 5-step searches.
if all this works, then your total search will have become several thousand times smaller! however, none of this is certain to work because 