Question

I have two sorted NSMutableArrays (or I can use any other collection, not critical), I need to insert objects from the first array to the second and preserve sort order in the second array. What is the optimal (fastest) method to do that? I can implement all the known good algorithms, but my question is, if there is already some built-in method? If not, what is the best algorithm in my case?

Answer 1

The real answer would be: it depends, since you are asking: what is the fastest way of inserting objects from one array into another while preserving sort order.

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There is no built in way of inserting in the right place of a sorted array. You can achieve the same effect by just adding the two arrays together but it won’t be "the fastest way".

What is actually faster depends on many things like: how much data does the arrays contain, what is the ratio of data in array₁ vs array₂ (does one array contain much more data than the other)?, etc.

NOTE: You should probably begin with the simple solution and only optimize once you experience performance problems. Do measurements with a large data set though, to see that your solution works with whatever data your users may have.

Inserting items from one sorted array into another sorted array

If you want to merge the two arrays by inserting objects in the right place then normal algorithms apply. You should insert the smaller array into the bigger array and try to insert entire sorted sequences where possible instead of every item one by one.

For best performance you should try to make a batch insert using insertObjects:atIndexes: instead of inserting the object one by one.

You can use indexOfObject:inSortedRange:options:usingComparator: to find the index that each item should be inserted in the other array if you specify NSBinarySearchingInsertionIndex for the options. Also, the comparator you are using must be the same as the comparator that sorted the array, otherwise the result is "undefined".

With this in mind you would do something like this

Create mutable index
For every ITEM in SMALLER ARRAY
    Find the index where to insert ITEM in LONGER ARRAY
    Add (the insertion location + the location in the short array) as the index in the mutable set.
Next item.

Batch insert all items.

The documentation for insertObjects:atIndexes: tells you that "the corresponding location specified in indexes after earlier insertions have been made." Which in your case with two sorted array mean all items with a lower index will already have been added and thus you should add the index of the object in the short array to the value returned from indexOfObject:inSortedRange:options:usingComparator:.

Another (probably very premature optimization) you can do is decrease the sortedRange for every item in the loop so that you don’t have to search through parts of the array that you know the item to be inserted is bigger than.

There are probably many other optimizations that can be made. You should still measure first! Hopefully this will get you started.