n Prolog, you are going to write a maze solver. You will write the rule:

solve$($X$,$ Y$)$

where X is the starting point and Y is the ending point. It will determine if there is a

path between those points using facts in the form of:

path$($a$,$b$).$

Where a is the starting point of the path and b is the ending point. Paths in this

question are directional. This means that path$($a$,$b$)$ means there is a path from a to

b but not b to a$.$

Example Facts:

path$($a$,$b$).$

path$($b$,$c$).$

path$($c$,$d$).$

path$($e$,$f$).$

Example queries:

$$ solve$($a$,$b$)$: would result in true. There is a direct path.

$$ solve$($b$,$a$)$: would be false.

$$ solve$($a$,$d$)$: would be true. Path is a$-$b$-$c$-$d$.$

$$ solve$($a$,$f$)$: would be false.

Your solution should work for any length path.

$2.$ Now modify your solution to allow paths to be bi$-$directional. So path$($a$,$b$),$ allow

travel from a to b and b to a$.$

$3.$ Now modify your solution to add distance of the path.The for of solve will be:

solve$($X$,$ Y$,$ D$)$

Where D is now the number of paths it took.

For example using the facts above, solve$($a$,$b$,$D would say D is $1.$ solve$($a$,$d$,$D$)$

would be $3.$

$1$

$4.$ Now modify that solution to allow for paths to have different lengths. Path would not

be in the form:

path$($a$,$b$,10).$

Where $10$ is the distance of that path.

Example Facts:

path$($a$,$b$\mathrm{.}20).$

path$($b$,$c$,10).$

path$($c$,$d$,100).$

path$($e$,$f$,5).$

Example queries:

$$ solve$($a$,$b$,$D$)$: would result in true and D of $20$

$$ solve$($b$,$a$,$D$)$: would result in true and D of $20$

$$ solve$($a$,$d$,$D$)$: would be true and a D of $130.$

$$ solve$($a$,$f$,$D$)$: would be false.

$5.$ Does your solution handle infinite circular paths? For instance with bidirectional paths,

you can have a path from a to c of $($a$,$b$,$c$)$ and $($a$,$b$,$a$,$b$,$c$)$ and $($a$,$b$,$a$,$b$,$a$,$b$,$c$).$ Explain

how you would handle this. You do not need to write the code for it$.$