Algorithm Design

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Chapter 6 Dynamic Programming
For our purposes, a single-stranded RNA molecule can be viewed as a
sequence of n symbols (bases) drawn from the alphabet [A, C, G, U}.3 Let B =
bib2.. ¯ b n be a single-stranded RNA molecule, where each bi ~ [A, C, G, U).
To a first approximation, one can model its secondary structure as follows. As
usual, we require that A pairs with U, and C pairs with G; we also require
that each base can pair with at most one other base--in other words, the set
of base pairs forms a matching. It also turns out that secondary structures are
(again, to a first approximation) "knot-flee," which we will formalize as a kind
of noncrossing condition below.
Thus, concretely, we say that a secondary structure on B is a set of pairs
n}, that satisfies the following conditions.
(i) (No sharp tams.) The ends of each pair in S are separated by at least four
intervening bases; that is, if (i,j) ~ S, then i