Applying the stack's LIFO principle to validate correctly nested brackets in expressions.
After mastering the fundamental push and pop operations, we can now apply the stack's FILO principle to solve real-world sequential problems. One common application that relies heavily on structured pairing is validating expression syntax, known as the Bracket Balancing Problem.
This problem requires checking if every opening delimiter (e.g., `(`, `{`, `[`) has a corresponding closing delimiter in the correct order. The stack is perfectly suited because the most recently opened bracket must always be the first one closed.
Example of a Balanced Expression: The global example {[()]} demonstrates perfect nesting.
The Stack Logic for Balancing:
- Opening Delimiter (`(`, `[`, `{`): Treat this as an item entering the required sequence. We push it onto the stack.
- Closing Delimiter (`)`, `]`, `}`): Treat this as an item leaving the sequence. We perform a pop operation and compare the popped opening bracket against the current closing bracket.
- Matching: If they match (e.g., `)` closes `(`), the sequence is valid so far, and we continue.
- Mismatched or Underflow: If they mismatch, or if a closing delimiter is found when the stack is empty (Underflow), the expression is immediately unbalanced.
- Final Check: After processing the entire expression, the stack must be empty.
Bracket Balancing Conditions
| Condition | Action / Result |
|---|---|
| Encounter opening bracket $(, [, \{$ | Push to stack. |
| Encounter closing bracket $), ], \}$ | Pop and check for match. |
| Mismatch or pop from empty stack | Unbalanced |
| End of string, stack is not empty | Unbalanced |
| End of string, stack is empty | Balanced |