3.)

We know a connected acyclic graph is called a Tree.  So the given alkane or saturated hydrocarbon can be intuitively deemed as a tree.

Following are some facts that we would need to devise an algorithm for the given problem:-

1.    Any tree with \(v\) vertices has \(v-1\) edges.

2.    Sum of degrees of all the vertices is equal to twice the number of edges in the Tree.

            \(\equiv\deg\left(v_1\right)+\deg\left(v_2\right)+....+\deg\left(v_k\right)\ =\ 2\left(k-1\right)\)

So considering each of carbon and hydrogen atoms as vertices and the bonds between them as the edges we can consider the molecule to be a tree.

We are given \(k\) carbon atoms and \(l\ \) hydrogen atoms. So we have \(k+l\) vertices and thus with \(k+l-1\) edges.

And we know the degree of Carbon atom at maximum can be 4 and for Hydrogen atom it can be 1.

Since there are k vertices with degree 4 and l vertices with degree 1, we can write

                                                    \(4k+l=2\left(k+l-1\right)\)

                                                \(\Rightarrow l=2k+2\)

                                                \(\Rightarrow k=\frac{\left(l-2\right)}{2}\)

ALGORITHM

        \(return\ null\)

         \(return\ \frac{\left(l-2\right)}{2}\)