Expression trees are a type of binary tree that can be used to store print and evaluate mathematical expressions.

For this assignment, you will implement an ExpressionTree Class. The ExpressionTree class will need to be able to parse a mathematical expression, load it into a binary tree, print the expression in Postfix or Infix notation, and evaluate the expression. You should also write code to test your ExpressionTree class or use the provided test code: ExpressionTreeTest.cpp Download ExpressionTreeTest.cpp$.$

ExpressionTree Class

Must support the following public methods:

ExpressionTree$()-$ default constructor creates an empty expression tree

ExpressionTree$($std::string expr$)-$ Creates an expression tree from the given string expression

setExpression$($std::string expr$)-$ Clears the expression tree and stores the given expression in a new tree

getResult$()-$ return the results of evaluating the expression tree

printParseTreeInOrder$($std::ostream&$)-$ outputs the tree to the ostream& using an in$-$order traversal

printParseTreePostOrder$($std::ostream&$)-$ outputs the tree to the ostream& using post$-$order traversal

Parsing Building and Evaluating ExpressionTrees

The core of this assignment revolves around takExpression trees are a type of binary tree that can be used to store print and evaluate mathematical expressions.

For this assignment, you will implement an ExpressionTree Class. The ExpressionTree class will need to be able to parse a mathematical expression, load it into a binary tree, print the expression in Postfix or Infix notation, and evaluate the expression.$$ You should also write code to test your ExpressionTree class or use the provided test code: ExpressionTreeTest.cpp Download ExpressionTreeTest.cpp$.$

ExpressionTree Class

Must support the following public methods:

ExpressionTree$()-$ default constructor creates an empty expression treeExpressionTree$($std::string expr$)-$ Creates an expression tree from the given string expressionsetExpression$($std::string expr$)-$ Clears the expression tree and stores the given expression in a new treegetResult$()-$ return the results of evaluating the expression treeprintParseTreeInOrder$($std::ostream&$)-$ outputs the tree to the ostream& using an in$-$order traversalprintParseTreePostOrder$($std::ostream&$)-$ outputs the tree to the ostream& using post$-$order traversal

Parsing Building and Evaluating ExpressionTrees

The core of this assignment revolves around taking a statement like:$((((3+12)-7)*120)/(2+3))$ and converting it into a tree like this:$$

Building the expression tree can be done recursively like follows:

If the character is a $\text{'}(\text{'}$ create a node and place it on the left of your currentNode, move to the next character in the expression and recursively go left from the currentNode.

if the character is a digit, continue reading from the string until you encounter a non$-$digit character. Each time concatenate the new digit character into a temporary string. Store that temp string in your currentNode data and then return.

If the character is an operator store the operator in the currentNode data, create a new node and place it on the right of your currentNode, move to the next character in the expression and recursively go right from the currentNode.

if the character is a $\text{'})\text{'},$ just return.

Evaluating the expression tree can also be done recursively like follows:

If the node is null the result is $0\mathrm{.}0$

If the node is a number the result is that number

If the node is an operator the result is the recursive result of the left subtree and right subtree combined using the given operator

$--$

My is code in C$++$