Can somebody explain me why the following algorithm does not allow for single base pairs and only for base pairs that always come in stacks and how backtracking is carried out in it?

Nussinov algorithm for folding RNA sequences can be extended to allow only for stacked base pairs by introducing an auxiliary matrix C holding the score for entries closed by a base pair. For simplicity we ignore the bifurcating term. Hence the stem-loop version of the recursions is:

E(i; j) is the optimal (base pair) score on the subsequence I to j of some RNA sequence s. The auxiliary matrix C is only entered when bases s[i] and s[j] at position I and j can make up a base pair, which is one of the following: AU, UA, CG, GC, GU, UG. The minimal allowed loop length is 3 bases. Before the recursions are computed, all entries of the E matrix are initialized with 0, while all entries in the C matrix are initialized with 􀀀-infinity. For the energy score I of stacking the base pair (s[i + 1]; s[j 􀀀 1]) on top of the base pair (s[i]; s[j]), we use the reverse of the energy parameters:

All other base pair stackings not listed in the above table are forbidden and thus receive the least favorable energy score of 􀀀-infinity.