Stack applications (expression evaluation, backtracking) in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a stack in data structures?

A stack is a collection that follows the Last In, First Out (LIFO) principle, where the last element added is the first one to be removed.

intermediate

How does a stack help in expression evaluation?

Stacks help evaluate expressions by temporarily storing operators and operands, especially in converting infix expressions to postfix and then calculating the result.

beginner

What is backtracking in computer science?

Backtracking is a method of solving problems by trying possible options and undoing choices when they lead to dead ends, often using a stack to remember previous states.

intermediate

Why is a stack useful in backtracking algorithms?

A stack stores the sequence of choices or states, allowing the algorithm to return to previous points and try different options when a path fails.

intermediate

Explain how postfix expression evaluation uses a stack.

In postfix evaluation, operands are pushed onto the stack. When an operator appears, the required number of operands are popped, the operation is performed, and the result is pushed back. This continues until the expression is fully evaluated.

Which principle does a stack follow?

A Priority Based

B First In, First Out

C Last In, First Out

D Random Access

A stack follows the Last In, First Out (LIFO) principle.

In expression evaluation, what is the main use of a stack?

A To temporarily hold operators and operands

B To store variables permanently

C To sort numbers

D To store the final result only

Stacks temporarily hold operators and operands during expression evaluation.

What does backtracking do when it hits a dead end?

A Stops immediately

B Returns to a previous state to try another option

C Skips to the end

D Deletes all data

Backtracking returns to a previous state to try different options when a path fails.

Which expression type is easiest to evaluate using a stack?

A Postfix

B Prefix

C Infix

D Algebraic

Postfix expressions are straightforward to evaluate using a stack.

In backtracking, what data structure is commonly used to remember previous choices?

A Queue

B Array

C Linked List

D Stack

Stacks are used to remember previous choices in backtracking.

Describe how a stack is used to evaluate a postfix expression.

Think about how you handle numbers and operators step-by-step.

Explain why stacks are important in backtracking algorithms.

Consider how you might remember where you came from when exploring paths.

Practice

1. What is the main purpose of a stack in data structures?

easy

A. To store data randomly

B. To store data in first-in, first-out order

C. To store data in last-in, first-out order

D. To store data permanently

Solution

1. Step 1: Understand stack behavior

   A stack stores data so the last item added is the first one removed, called last-in, first-out (LIFO).

2. Step 2: Compare options with stack definition

   To store data in last-in, first-out order matches the LIFO behavior, while others describe different data structures or incorrect behavior.

3. Final Answer:

   To store data in last-in, first-out order -> Option C

4. Quick Check:

   Stack = LIFO order [OK]

Hint: Remember stack = last item in, first item out [OK]

Common Mistakes:

• Confusing stack with queue (FIFO)
• Thinking stack stores data randomly
• Assuming stack stores data permanently

2. Which of the following is the correct way to push an element x onto a stack named s?

easy

A. s.push(x)

B. s.pop(x)

C. s.enqueue(x)

D. s.insert(x)

Solution

1. Step 1: Identify stack operations

   Common stack operations are push (add), pop (remove), peek (view top).

2. Step 2: Match operation to pushing element

   To add element x, use push. Pop removes element. Enqueue is for queues. Insert is not standard stack method.

3. Final Answer:

   s.push(x) -> Option A

4. Quick Check:

   Push means add element [OK]

Hint: Push adds, pop removes from stack top [OK]

Common Mistakes:

• Using pop to add elements
• Confusing queue methods with stack
• Using non-standard method names

3. Consider the expression (3 + 2) * (4 - 1). Using a stack to evaluate this expression step-by-step, what is the final result?

medium

A. 15

B. 9

C. 21

D. Error

Solution

1. Step 1: Evaluate inside parentheses first

   (3 + 2) = 5 and (4 - 1) = 3

2. Step 2: Multiply the results

   5 * 3 = 15

3. Final Answer:

   15 -> Option A

4. Quick Check:

   (3+2)*(4-1) = 15 [OK]

Hint: Calculate parentheses first, then multiply [OK]

Common Mistakes:

• Ignoring parentheses order
• Adding instead of multiplying
• Confusing subtraction sign

4. A program uses a stack to check if brackets in an expression are balanced. Which of the following errors would cause the program to incorrectly say brackets are balanced?

medium

A. Pushing opening brackets onto the stack

B. Not popping from stack when a closing bracket is found

C. Ignoring characters other than brackets

D. Checking stack is empty at the end

Solution

1. Step 1: Understand bracket checking with stack

   Opening brackets are pushed; closing brackets pop the matching opening bracket.

2. Step 2: Identify error impact

   If popping is skipped on closing bracket, stack keeps extra openings, so program misses imbalance.

3. Final Answer:

   Not popping from stack when a closing bracket is found -> Option B

4. Quick Check:

   Pop on closing bracket needed [OK]

Hint: Pop stack on closing bracket to check balance [OK]

Common Mistakes:

• Forgetting to pop on closing bracket
• Pushing closing brackets instead of opening
• Not checking stack emptiness at end

5. In backtracking algorithms, how does a stack help in exploring possible solutions?

hard

A. By preventing any repeated steps automatically

B. By storing all solutions at once for quick access

C. By sorting the solutions in ascending order

D. By remembering choices and allowing undoing steps when a path fails

Solution

1. Step 1: Understand backtracking process

   Backtracking tries choices step-by-step and undoes them if they lead to failure.

2. Step 2: Role of stack in backtracking

   Stack stores the choices made so far, allowing the algorithm to go back (undo) when needed.

3. Final Answer:

   By remembering choices and allowing undoing steps when a path fails -> Option D

4. Quick Check:

   Stack = remember and undo choices [OK]

Hint: Stack tracks choices to backtrack easily [OK]

Common Mistakes:

• Thinking stack stores all solutions simultaneously
• Assuming stack sorts solutions
• Believing stack prevents repeated steps automatically