Q11Data Structures

The problem demands the conversion of the specific infix expression A + B - (C + D) / E * F - (G + H) / I into postfix notation. We strictly adhere to standard mathematical operator precedence (Multiplication/Division * / > Addition/Subtraction + -) and left-to-right associativity.

Step-by-Step Conversion Trace

Step 1 (Parenthetical Resolution): We immediately resolve the deepest, explicitly bracketed sub-expressions first to establish baseline terms.

First bracket: (C + D) mathematically converts to C D +.

Second bracket: (G + H) mathematically converts to G H +.

The overall expression temporarily simplifies to: A + B - [C D +] / E * F - [G H +] / I

Step 2 (Multiplication and Division - Left to Right): We now scan the entire simplified expression strictly from left to right, hunting exclusively for the higher precedence / and * operators.

Found division: [C D +] / E. The operator shifts to the right, yielding C D + E /.

The expression is now: A + B - [C D + E /] * F - [G H +] / I

Continuing the scan, we find multiplication involving the previous result: [C D + E /] * F. This converts to C D + E / F *.

The expression is now: A + B - [C D + E / F *] - [G H +] / I

Continuing the scan, we find the final division: [G H +] / I. This converts to G H + I /.

The expression is now fully devoid of high-precedence operators: A + B - [C D + E / F *] - [G H + I /]

Step 3 (Addition and Subtraction - Left to Right): Finally, we resolve the remaining + and - operators, strictly adhering to left-to-right processing.

First, the leading addition: A + B converts to A B +.

The expression is: [A B +] - [C D + E / F *] - [G H + I /]

Second, the first subtraction: [A B +] - [C D + E / F *] converts to A B + C D + E / F * -.

The expression is: [A B + C D + E / F * -] - [G H + I /]

Third, the final, global subtraction: [...Left Term...] - [G H + I /] converts to A B + C D + E / F * - G H + I / -.

The definitive, syntactically correct Postfix expression is: A B + C D + E / F * - G H + I / -