Determine an LCS of $1,0,1,0,0,1,0,1$ and $0,1,0,1,1,0,1,1,0.$

Moreover, as discussed in our class, generalize the recursive formula used in the

textbook Eq$.15\mathrm{.}9($p$\mathrm{.}393)$ to the following one:

$$

$$

$$

$+==$

$==$

$=$

max$([1,1](),[,1],[1,])$ if $,0,$

$0$ if $0$ or $0,$

$[,]$

c i j x y c i j c i j i j

i j

c i j

i j

$($xi $==$ yj is $1$ if xi $=$ yj or $0$ if not$),$ so that all LCS$$s of two sequences can be found. Use

the recursive formula to find all the LCS$$s$.$