Efficient algorithm to find first available name

Question

I have an array containing names of items. I want to give the user the option to create items without specifying their name, so my program will have to supply a unique defau

Answer 1

A logarithmic-time approach, assuming that you never leave "holes" by deleting items:

// Inverse binary search for the last one.
int upperBound = 1;
while(isInUse(upperBound)) upperBound *= 2;

// Standard binary search for the end once we have a ballpark.
int lowerBound = upperBound / 2;
while(lowerBound < upperBound - 1)
{
    int midpoint = (lowerBound + upperBound) / 2;
    if (isInUse(midpoint))
        lowerBound = midpoint;
    else
        upperBound = midpoint;
}
return upperBound;

If item numbers can be freed by deleting, nothing short of linear search will work unless you also keep a "free list" and pick from that.