Balanced Parentheses Problem Using Stack in DSA C# - Time & Space Complexity

Time Complexity: Balanced Parentheses Problem Using Stack

O(n)

Understanding Time Complexity

We want to know how the time needed to check balanced parentheses grows as the input string gets longer.

How does the number of steps change when the input size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public bool IsBalanced(string s) {
    Stack<char> stack = new Stack<char>();
    foreach (char c in s) {
        if (c == '(') {
            stack.Push(c);
        } else if (c == ')') {
            if (stack.Count == 0) return false;
            stack.Pop();
        }
    }
    return stack.Count == 0;
}
    

This code checks if parentheses in a string are balanced using a stack.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character in the string once.
• How many times: Exactly once for each character (n times for string length n).

How Execution Grows With Input

As the input string gets longer, the number of steps grows directly with its length.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The steps increase in a straight line as input size increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to check balanced parentheses grows linearly with the input size.

Common Mistake

[X] Wrong: "The time complexity is quadratic because of the stack operations inside the loop."

[OK] Correct: Each stack operation (push/pop) takes constant time, so they don't multiply the loop's time; the loop still runs once per character.

Interview Connect

Understanding this linear time check helps you solve many real problems involving matching pairs efficiently.

Self-Check

"What if we changed the input to include multiple types of brackets (like {}, [], ())? How would the time complexity change?"

Practice

1. What is the main purpose of using a stack in the Balanced Parentheses Problem?

easy

A. To count the total number of parentheses in the string

B. To keep track of opening parentheses and match them with closing ones

C. To reverse the order of parentheses in the string

D. To sort the parentheses based on their type

Solution

1. Step 1: Understand the role of stack in parentheses matching

   A stack helps keep track of opening parentheses so that each closing parenthesis can be matched correctly in order.

2. Step 2: Identify why other options are incorrect

   Counting or reversing parentheses does not solve the matching problem, and sorting is unrelated to balance checking.

3. Final Answer:

   To keep track of opening parentheses and match them with closing ones -> Option B

4. Quick Check:

   Stack tracks openings for matching closings [OK]

Hint: Stack stores openings to match closings in order [OK]

Common Mistakes:

• Thinking stack counts parentheses instead of matching
• Confusing stack with queue for this problem
• Assuming stack reverses parentheses order

2. Which of the following C# code snippets correctly pushes an opening parenthesis onto a stack named stack?

easy

A. stack.Push('(');

B. stack.Add('(');

C. stack.Insert('(');

D. stack.Enqueue('(');

Solution

1. Step 1: Recall stack method to add elements

   In C#, the method to add an element to a stack is Push().

2. Step 2: Identify incorrect methods

   Add() and Insert() are not stack methods; Enqueue() is for queues.

3. Final Answer:

   stack.Push('('); -> Option A

4. Quick Check:

   Use Push() to add to stack [OK]

Hint: Use Push() to add elements to stack in C# [OK]

Common Mistakes:

• Using queue methods like Enqueue() on stack
• Trying to use Add() or Insert() which don't exist for stack
• Confusing stack with list methods

3. What will be the output of the following C# code snippet?

string input = "({[]})";
Stack<char> stack = new Stack<char>();
foreach (char c in input) {
  if (c == '(' || c == '{' || c == '[') {
    stack.Push(c);
  } else {
    if (stack.Count == 0) {
      Console.WriteLine("Unbalanced");
      return;
    }
    char top = stack.Pop();
    if ((c == ')' && top != '(') || (c == '}' && top != '{') || (c == ']' && top != '[')) {
      Console.WriteLine("Unbalanced");
      return;
    }
  }
}
if (stack.Count == 0) Console.WriteLine("Balanced"); else Console.WriteLine("Unbalanced");

medium

A. Runtime Error

B. Unbalanced

C. No Output

D. Balanced

Solution

1. Step 1: Trace the input string character by character

   Opening brackets '(', '{', '[' are pushed onto the stack. Closing brackets pop and check matching. The input "({[]})" is perfectly nested.

2. Step 2: Check stack emptiness after processing

   After processing all characters, stack is empty, so output is "Balanced".

3. Final Answer:

   Balanced -> Option D

4. Quick Check:

   All pairs matched, stack empty = Balanced [OK]

Hint: Match each closing with last opening using stack [OK]

Common Mistakes:

• Not checking stack empty before popping
• Mismatching bracket pairs
• Ignoring stack emptiness at end

4. Identify the bug in the following C# code snippet for checking balanced parentheses:

Stack<char> stack = new Stack<char>();
foreach (char c in input) {
  if (c == '(' || c == '{' || c == '[') {
    stack.Push(c);
  } else {
    char top = stack.Pop();
    if ((c == ')' && top != '(') || (c == '}' && top != '{') || (c == ']' && top != '[')) {
      return false;
    }
  }
}
return stack.Count == 0;

medium

A. Not returning true when balanced

B. Incorrect matching of parentheses pairs

C. Missing check if stack is empty before Pop()

D. Using stack.Push() instead of Pop() for closing brackets

Solution

1. Step 1: Check for stack underflow before popping

   The code pops from stack without checking if it's empty, which can cause runtime error if closing bracket appears first.

2. Step 2: Confirm matching logic is correct

   Matching pairs are correctly checked, and return false if mismatch occurs.

3. Final Answer:

   Missing check if stack is empty before Pop() -> Option C

4. Quick Check:

   Always check stack empty before Pop() [OK]

Hint: Check stack empty before Pop() to avoid errors [OK]

Common Mistakes:

• Popping from empty stack causing exceptions
• Ignoring stack.Count == 0 before Pop()
• Confusing Push and Pop methods

5. Given the string "[{()}]({[]})", which of the following modifications to the balanced parentheses algorithm will correctly handle this input and return true?

Options:
A) Ignore all characters except parentheses.
B) Use a stack and match pairs as usual.
C) Use two stacks, one for opening and one for closing parentheses.
D) Use a queue instead of a stack to track parentheses.

hard

A. Use a stack and match pairs as usual.

B. Ignore all characters except parentheses.

C. Use two stacks, one for opening and one for closing parentheses.

D. Use a queue instead of a stack to track parentheses.

Solution

1. Step 1: Understand the input and algorithm

   The input contains only parentheses characters. The standard stack-based matching algorithm works for nested and sequential pairs.

2. Step 2: Evaluate each option's correctness

   Use a stack and match pairs as usual. is correct as it uses the standard stack approach. Ignore all characters except parentheses. is irrelevant since input has only parentheses. Use two stacks, one for opening and one for closing parentheses. complicates unnecessarily. Use a queue instead of a stack to track parentheses. fails because queue does not track last opening bracket.

3. Final Answer:

   Use a stack and match pairs as usual. -> Option A

4. Quick Check:

   Standard stack method handles nested pairs [OK]

Hint: Standard stack method works for all balanced parentheses [OK]

Common Mistakes:

• Trying to use queue which breaks matching order
• Overcomplicating with multiple stacks
• Ignoring characters that are not parentheses