YAMS can execute 4 types of merges :

1. tails to head
2. heads to tail
3. both to head
4. both to tail

Of course if they are called in random order, the data will be sorted anyway but it wouldn't be efficient, likely close to O(n²). So this is how to use them more efficiently.

Let's simply consider the final size of all the possible moves : there are 3 sizes M, H and T, the sums of consecutive pairs of runs:

There are 3! = 6 possible permutations when we sort their values (ignoring equal results for a moment) and only 4 moves. 4 tests are enough to decide the move since some combinations are degenerate:

The algorithm is most efficient by always choosing to operate on the pair that will give the smallest run. In the case M where there are two possible outcomes, it chooses the direction where the following merge will also give the smallest run as well.