Let us consider a comparison$-$based algorithm for sorting a set of elements.

Select one or moresa Sorting $4$ elements requires $5$ comparisonsb. The optimal algorithm for sorting $4$ elements can simply be performed by only comparing and exchanging $($if necessary$)$ some pairs of elementsc. The optimal algorithm for sorting $6$ elements can simply be performed by only comparing and exchanging $($if necessary$)$ some pairs of elementsd. The optimal algorithm for sorting $5$ elements requires $70$ comparisons