Stack applications (expression evaluation, backtracking) in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Expression Evaluation Using Stacks

Consider the infix expression: (3 + 4) * 5 - 6. When evaluating this expression using two stacks (one for operators and one for operands), what is the value on the operand stack just before the final subtraction operation is applied?

A 35

B 29

C 20

D 7

💡 Hint

Evaluate the expression step-by-step, applying operator precedence and parentheses.

The expression evaluates as follows: (3 + 4) = 7, then 7 * 5 = 35, finally 35 - 6 = 29. Just before the subtraction, the operand stack holds 35.

❓ Reasoning

intermediate

Backtracking with Stacks in Maze Solving

In a maze-solving algorithm using backtracking with a stack, what does pushing a position onto the stack represent?

A Storing the shortest path found so far

B Deleting a path that leads to a dead end

C Marking a position as visited and exploring it later

D Recording a path choice to return to if a dead end is reached

💡 Hint

Think about how backtracking remembers where to return after exploring a path.

Pushing a position onto the stack records a choice point. If the path leads to a dead end, the algorithm can pop the stack to backtrack to that position and try another path.

🔍 Analysis

advanced

Output of Postfix Expression Evaluation

What is the result of evaluating the postfix expression 6 2 3 + - 3 8 2 / + * using a stack?

A 30

B 36

C 7

D 24

💡 Hint

Process the postfix expression from left to right, pushing numbers and applying operators.

Step-by-step evaluation:
Push 6 → [6]
Push 2 → [6, 2]
Push 3 → [6, 2, 3]
+ : pop 3, 2; 2 + 3 = 5; push 5 → [6, 5]
- : pop 5, 6; 6 - 5 = 1; push 1 → [1]
Push 3 → [1, 3]
Push 8 → [1, 3, 8]
Push 2 → [1, 3, 8, 2]
/ : pop 2, 8; 8 / 2 = 4; push 4 → [1, 3, 4]
+ : pop 4, 3; 3 + 4 = 7; push 7 → [1, 7]
* : pop 7, 1; 1 * 7 = 7; push 7 → [7]
Final result: 7

❓ Comparison

advanced

Comparing Stack and Recursion in Backtracking

Which statement best describes the relationship between using an explicit stack and recursion for backtracking algorithms?

A Recursion uses the call stack implicitly, while an explicit stack replaces this with manual control

B Recursion is always more memory efficient than using an explicit stack

C Recursion and explicit stacks are unrelated concepts in backtracking

D An explicit stack cannot handle backtracking as effectively as recursion

💡 Hint

Think about how function calls are managed in recursion versus manual stack usage.

Recursion uses the system's call stack to remember states, while using an explicit stack means managing these states manually. Both achieve backtracking but differ in control and sometimes efficiency.

📋 Factual

expert

Error Identification in Expression Evaluation Algorithm

In an algorithm that evaluates arithmetic expressions using stacks, which of the following errors will occur if the operator stack is popped without checking if it is empty?

A SyntaxError because the expression is malformed

B StackUnderflowError or equivalent runtime error due to popping from an empty stack

C Logical error but no runtime error occurs

D No error; the algorithm handles empty stacks automatically

💡 Hint

Consider what happens when you try to remove an item from an empty container.

Popping from an empty stack causes a runtime error such as StackUnderflowError or IndexError, depending on the implementation. This must be checked to avoid crashes.