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.