Question

6. For the following expression, 5 + 8 * (3 – 2) * 6 – 10 / 2

(i) Convert to the corresponding postfix expression. Show your steps clearly.

(ii) Build the expression tree and show the result of preorder traversal.

Answer 1

The converted postfix expression for 5 + 8 * (3 – 2) * 6 – 10 / 2 is 5 8 1 * 6 * + 10 2 / -. The expression tree is built upon this postfix expression, and its preorder traversal is 5 8 6 1 * * + 2 10 / -.

Step-by-step explanation:

Postfix Expression Conversion:

To convert the given infix expression 5 + 8 * (3 – 2) * 6 – 10 / 2 to its corresponding postfix expression, we need to follow the order of operations, also known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

1. Inside the brackets (3 - 2) is evaluated first, which gives 1.
2. Then the multiplication 8 * 1 and division 10 / 2 are evaluated to give 8 and 5, respectively.
3. The resulting infix expression is now 5 + 8 * 6 - 5.
4. The multiplication is done next, which transforms the expression to 5 + 48 - 5.
5. Lastly, perform the addition and subtraction in sequence.

The postfix expression is 5 8 1 * 6 * + 10 2 / -.

Expression Tree and Preorder Traversal:

Building the expression tree:

• Create a binary tree with operators as internal nodes and operands as leaves.
• Traverse the expression and construct the tree following the postfix representation.

The preorder traversal of the built tree is the sequence in which we visit the root node first, then recursively do a preorder traversal of the left subtree, followed by a preorder traversal of the right subtree. The result for our expression tree is 5 8 6 1 * * + 2 10 / -.