In video games, especially those in the roleplaying genre, it is common that characters in the game are

advanced in power through the use of a skill tree. Generally, a skill tree defines the prerequisite for the

various skills that your character in the game might acquire. For example, in a hypothetical game, if

the Shield Bash, Defensive Stance, and Shield Ally skills all require that your character first have the skill

Shield Proficiency, then this might be represented by the following skill tree:

More formally, a skill in the skill tree can only be gained if the character first gains all of the skills

which are ancestors of that skill in the tree$\mathrm{.}1$

Your Tasks

Your task in this question is to write a class called SkillTree which extends BasicMAryTree$280$

$($an m$-$ary tree of Skill objects; a complete Skill.java is provided$).$ A template for the SkillTree

class is provided. It contains a constructor and a couple of useful methods. You will add additional

methods to this class in the following steps, which you should complete in order:

$($a$)$ Write a main$()$ method in the SkillTree class in which you construct your own skill tree for your

own hypothetical video game. Your tree must contain at least $10$ skills. However, for the sanity

of everyone involved, try to keep it under $15$ skills. Be creative! There is no reason why any

two students should hand in exactly the same $($or even very similar$)$ skill trees, nor should you

just duplicate the skill tree shown in the sample output. Print your tree to the console using the

toStringByLevel$()$ method inherited from BasicMAryTree$280.$

$($b$)$ Write a method in the SkillTree class called skillDependencies which takes a skill name as

input and returns an instance of LinkedList$280$ which contains all the of the skills which

are prerequisites for obtaining the input skill $($including the input skill itself!$).$ A RuntimeException

exception should be thrown if the tree does not contain the given skill. A good implementation

approach for this method is to use a recursive traversal of the tree to find the named skill, and

then add skills to the output list as the recursion unwinds. Tutorial $3$ includes some discussion of

recursive traversal of m$-$ary trees. Add to your main$()$ program a few tests of this method, and

print out the lists that is returned $($you can use the list$$s toString$()$ method for this$).$ Be sure to

test the case where the named skill does not exist in the tree.

$($c$)$ Write a method in the SkillTree class called skillTotalCost which takes a skill name as in$-$

put and returns the total number of skill points that a player must invest to obtain the given

skill. If the named skill is not in the skill tree, then the skillTotalCost method should throw

a RuntimeException exception. Hint: this method is quite easy to implement if you make use of the

previously implemented skillDependencies method.

For example, in the above skill tree, if a character wants the Shield Ally skill they would need to

spend $1$ skill point to get Shield Proficiency, and then spend $3$ skill points to get Shield Ally for an $($In the video game world, the term $$skill tree$$ sometimes refers to things that actually aren$$t trees; a noteworthy example is the skill tree in the ARPG Path Of Exile, which, if you click the link, can see is clearly not a tree, even though they call it that. Here in question $2,$ we used the term $$skill trees$$ to mean skill trees that are, in fact, actual trees.$)$ overall investment of $1+3=4$ points, so for the above tree, skillTotalCost$("$Shield Ally"$)$

should return $4.$ Note that the Skill object contains the cost of the skill.

Add to your main$()$ program a few tests of skillTotalCost, and print out the total costs returned.

Be sure to test the case where the named skill does not exist in the tree.

$($d$)$ Run your main$()$ program. Cut and paste the console output to a text file and submit it with your

assignment.