All of the following functions that operate on trees should be recursive.
Some functions that you may need are provided in the file
`Cons.java` . This assignment may be done in Java or in Lisp.

- Write a function
`maxbt(Object tree)`that finds the maximum value in a binary tree of`Integer`. For this function, we will assume that both the`first`and`rest`of a`Cons`can be subtrees. We will assume that every element of the tree is a`Cons`(which can be tested with`consp`and then cast as`(Cons)`),`null`, or`Integer`. We will assume that every`Integer`is greater than`Integer.MIN_VALUE`.

Example:`(maxbt '((1 7) (-3 2) (((8)))) ) = 8` - An algebraic expression can be written as a linked list tree:
an expression is either a number (
`Integer`or`Double`), a symbol (`String`), or a list`(`*op lhs rhs*`)`where*op*is an operator (`String`) and*lhs*(left-hand side) and*rhs*(right-hand side) are expressions. The functions`op`,`lhs`and`rhs`are provided. Write a function`Cons vars(Object expr)`that returns a set of the variables in an expression. Note that the*op*and numbers are not variables. The result is a set (list) of variables in any order; the`union`function is provided.

Example:`(vars '(= f (* m a))) = (f m a)` - Write a function
`boolean occurs(Object value, Object tree)`that tests whether the`value`occurs anywhere in the expression`tree`. We will assume that the`value`has a`.equals()`method and is not a Cons.

Example:`(occurs 'm '(= f (* m a))) = true` - Write a function
`Integer eval(Object tree)`that evaluates (finds the value of) an expression tree where the leaves are`Integer`. The value of an`Integer`expression is the expression itself. If the expression is a`Cons`, first find the value of its arguments (`lhs`and`rhs`), then perform the operation denoted by the`op`. The possible operations are`+ - * / expt`.`(expt x n)`raises x to the power`n`; a function`pow`is provided. Note that`-`could have either one operand (minus) or two operands (difference); all other operations are assumed to be binary.

Note: if you use Lisp, call your function`myeval`;`eval`is the Lisp interpreter.

Example:`(eval '(+ 3 (* 5 7))) = 38` - Write a function
`Integer eval(Object tree, Cons bindings)`that evaluates an expression tree where the leaves are Integer or are variables whose values are given in the`bindings`.`bindings`is an association list,`((var value) ...)`, that gives values for variables. This version of`eval`is an easy extension of the previous one. The function`assoc`is provided.

Example:`(eval '(+ 3 (* 5 b)) '((b 7))) = 38` - Write a function
`Cons english(Object tree)`that translates an expression tree into a list of English words (Strings). If the tree is a leaf, the translation is just a list of that tree. For an expression, make a list containing`"the"`, an appropriate English word for the operator, and the operands connected by`"of"`and`"and"`. The`english`program should only use operations such as`cons`,`list`,`append`,`first`,`rest`,`op`,`lhs`,`rhs`etc.; it should not use any String operations.

Example:`(english '(+ 3 (* b 7))) = (the sum of 3 and the product of b and 7)` - There is a close relationship between programming languages
and trees. A compiler performs
*parsing*, which converts a character string in a programming language to a tree.*Unparsing*, converting a tree to a program, is also useful. Write a function`String tojava(Object tree)`that translates an expression tree to a String that is a line of Java code. The line of Java code should be terminated by a semicolon character. We will assume that the expression can contain the operators`= + - * /`as well as single-argument functions such as`sin`.Operators have

*precedence*, which determines the order in which operations are performed when an expression is not parenthesized. We will assume that`=`has precedence 1,`+ -`have precedence 5, and`* /`have precedence 6. A subexpression needs to be parenthesized if its precedence is less than or equal to the precedence of its surroundings; otherwise, it should not be parenthesized. Make an auxiliary function that includes precedence as an argument. The starting precedence can be 0, so that any operator will be higher in precedence.

Example:`(tojava '(= x (* (+ a b) c))) = "x=(a+b)*c;"`We will assume that a unary minus should always be parenthesized, and that it has a precedence of 6.

For functions that are not in the operator list, such as

`sin`, make the name be`Math.`followed by the function name, and make a function call form. For example,`(sin x)`would become`"Math.sin(x)"`.