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

You could try to do the following:

first:

• loop through the list, and get all numbered items, this is complexity N
• for every numbered item, put the item in a tree (in C++: std::map), this is complexity log(N)

So now you have built up a map with the used numbers, with complexity "N x log(N)"

Next, iterate to the tree and as soon you see a 'hole', use the number. Worst case is complexity N.

So in total, the complexity is N x log(N) + N, or simplified: N log(N).