The principles stacks used to validate expression syntax are also critical for determining the precise order of operations in arithmetic expressions.
- While we, as humans, understand the precedence rules necessary to evaluate
A + B * C, computers require a more explicit, unambiguous representation. - Stacks are foundational for converting human-readable Infix expressions into formats that are easily evaluated by a machine, such as Postfix or Prefix notations.
- Why Notation Matters for Stacks: Standard mathematical notation (Infix) is inherently ambiguous without applying external precedence rules (e.g., multiplication before addition). By converting to Postfix, we eliminate the need for parentheses and complex rule lookups, relying purely on the FILO structure of the stack for operation ordering.
Expression Notation Comparison
| Notation | Operator Position | Example (A + B * C) |
Stack Relevance |
|---|---|---|---|
| Infix | Between Operands | A + B * C |
Requires manual Precedence Rules |
| Postfix (RPN) | After Operands | A B C * + |
Optimal for Stack Evaluation |
| Prefix (Polish) | Before Operands | + A * B C |
Also uses stacks, read Right-to-Left |