Question

Let’s say I have a large collection of elements.
Each element has a “position” field, which is a positive integer.
No two elements have the same value for the field “position”.

The only supported operation of the collection is: addElement(newElement, positionAfterElement), where:
– newElement is the new element to be added (its position is unknown for now)
– positionAfterElement is an existing element of the collection.

The function will guarantee that:
– position(positionAfterElement) < position(newElement)
– no other element in the collection has a position between position(positionAfterElement) and position(newElement)

I can change the value of all the element positions as I wish but I want to minimize the number of changes (on average).

How should I implement the addElement function?

I could just push all the elements with higher positions by 1 but I am pretty sure there must be a better way to do this.

Thanks all for your help.

Answer 1

OK, so here is what I implemented, in pseudo-code:

addElement(newElement, positionAfterElement):
    p0 <- positionOf(positionAfterElement)
    c <- 5
    finished <- false
    while (not finished):
        search for all elements which positions are in the range [p0 + 1, p0 + c]
        if there are less than c elements in that range:  // the range is not full
            adjust position of elements in the range, and position of newElement,
            so that
              - elements are correctly ordered
              - element positions are "evenly spread out" within the range
            finished <- true
        else:                                             // the range is full
            c <- c * 2
    end while
end addElement