1. Binary Expression Trees
(a data structure used to store algebraic expressions)
infix expression: a / b + (c - d) * e
parenthesize fully:
((a / b) + ((c - d) * e))
**Each binary expression (within parentheses) can be represented by a tree where the root is the operator and the children are the operands.** +
/ * a b e c d

2. Perform a preorder traversal on above tree:+
/ * a b e c d
Perform a preorder traversal on above tree:
+ / a b * - c d e
Perform a postorder traversal on above tree:
a b / c d - e * +

3. +
/ * a b e c d
Write pseudocode for a recursive traversal, similar to thestandard inorder traversal, to display the infix expression fully parenthesized.
private void displayInfix(curr) // requires all tokens to be chars
{if (isLeaf(curr) print curr.data;
else {print '(';
displayInfix(curr.left);
print curr.data;
displayInfix(curr.right);
print ')';}

4. Write pseudocode for a recursive method that evaluates a binary expression tree.
private int evalTree(curr) //assumes operands are strings
{ if isLeaf(curr) return Integer.parseInt(curr.data);
else {
switch curr.data
case '*': return evalTree(curr.left) * evalTree(curr.left):
break;
case '/': return evalTree(curr.left) / evalTree(curr.left):
case '+': return evalTree(curr.left) + evalTree(curr.left):
case '-': return evalTree(curr.left) - evalTree(curr.left): }