Therefore, only one determinant of size \( N/2 \) is involved in each calculation of \( R \) and update of the inverse matrix. The scaling of each transition then becomes:

$$ O_R(N/2)+O_\mathrm{inverse}(N^2/4) $$

and the time scaling when the transitions for all \( N \) particles are put together:

$$ O_R(N^2/2)+O_\mathrm{inverse}(N^3/4) $$

which gives the same reduction as in the case of moving all particles at once.