Question

Consider the binary tree given below. What will be the corresponding infix expression to this? 

• A. ((a + b + c * d) % (f \^ g) / (g - h))
• B. (a - b) - (c * d) % ((f \^ i) + (g / h))
• C. ((a + b) - (c * d)) % ((f \^ g) / (h - i))
• D. ((a + b) - (c * d)) / ((f \^ g) / (h - i))

Hint:

In an expression tree, the operators are located at the internal nodes, and the operands are at the leaf nodes. Use infix traversal to determine the corresponding expression.

Answer 1

The Correct Option is C

Step 1: Analyze the Binary Tree Structure.
Internal nodes represent operators, while leaf nodes represent operands. The sequence of operations is determined by an infix traversal: left operand, operator, right operand.

Step 2: Execute Infix Traversal. 
The provided binary tree translates to the following infix expression: 

- Root node (`-`) applies to its left and right subtrees. 

- The left subtree (rooted at `+`) yields the expression `(a + b)`. 

- The right subtree (rooted at `*`) yields the expression `(c * d)`. 

- The rightmost subtree (rooted at `/`) represents the expression `(g - h)`. 

- The root operator `%` combines the left sub-expression `(a + b) - (c * d)` and the right sub-expression `(f ^ g) / (h - i)`. 

The complete infix expression is: \[ ((a + b) - (c * d)) % ((f ^ g) / (h - i)) \]

Step 3: Final Determination. 
The accurate infix expression corresponds to option (3).