Balanced Parentheses Problem Using Stack in DSA Python - 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 changes as the input string grows.

How does the number of steps grow when the string gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def is_balanced(s: str) -> bool:
    stack = []
    pairs = {')': '(', ']': '[', '}': '{'}
    for char in s:
        if char in '([{':
            stack.append(char)
        elif char in ')]}':
            if not stack or stack.pop() != pairs[char]:
                return False
    return not stack

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

Identify Repeating Operations

• 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 string gets longer, the number of steps grows directly with the number of characters.

Input Size (n)	Approx. Operations
10	About 10 checks and stack operations
100	About 100 checks and stack operations
1000	About 1000 checks and stack operations

Pattern observation: The work grows in a straight line with input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to check balanced parentheses grows linearly with the length of the string.

Common Mistake

[X] Wrong: "Because of the stack operations, the time complexity is more than linear, maybe quadratic."

[OK] Correct: Each character is processed once, and stack push/pop are constant time, so total time stays linear.

Interview Connect

Understanding this linear time check shows you can analyze how data structures like stacks help solve problems efficiently.

Self-Check

"What if we checked for balanced parentheses without using a stack, by scanning multiple times? How would the time complexity change?"

Practice

1. What does the Balanced Parentheses problem using a stack check for in a string?

easy

A. Whether every opening bracket has a matching closing bracket in correct order

B. If the string contains only alphabets

C. If the string length is even

D. Whether the string contains any numbers

Solution

1. Step 1: Understand the problem goal

   The Balanced Parentheses problem checks if all opening brackets like '(' have a matching closing bracket ')' in the correct order.

2. Step 2: Role of stack in checking

   A stack helps track opening brackets and ensures each one is closed properly in sequence.

3. Final Answer:

   Whether every opening bracket has a matching closing bracket in correct order -> Option A

4. Quick Check:

   Balanced parentheses = matching pairs in order [OK]

Hint: Stack tracks openings; match with closings in order [OK]

Common Mistakes:

• Thinking it checks string length
• Confusing with character types
• Ignoring order of brackets

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

easy

A. stack.push(x)

B. stack.append(x)

C. stack.add(x)

D. stack.insert(x)

Solution

1. Step 1: Recall Python list methods for stack

   Python uses list to implement stack; to add an element on top, use append().

2. Step 2: Check each option

   add() and push() are not list methods; insert() adds at specific index, not top.

3. Final Answer:

   stack.append(x) -> Option B

4. Quick Check:

   Use append() to push in Python stack [OK]

Hint: Use append() to push in Python stack [OK]

Common Mistakes:

• Using push() which is not a Python list method
• Using add() which is for sets
• Using insert() without index

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

def is_balanced(s):
    stack = []
    for char in s:
        if char == '(': stack.append(char)
        elif char == ')':
            if not stack: return False
            stack.pop()
    return not stack

print(is_balanced('(()())'))
print(is_balanced('(()'))

medium

A. True\nFalse

B. False\nTrue

C. True\nTrue

D. False\nFalse

Solution

1. Step 1: Trace first input '(()())'

   Push '(' three times, pop ')' three times, stack empty at end, returns True.

2. Step 2: Trace second input '(()'

   Push '(' twice, one ')' pops one '(', stack not empty at end, returns False.

3. Final Answer:

   True\nFalse -> Option A

4. Quick Check:

   Balanced string returns True, unbalanced returns False [OK]

Hint: Empty stack at end means balanced parentheses [OK]

Common Mistakes:

• Not checking stack empty at end
• Returning true too early
• Ignoring unmatched openings

4. Find the error in this code snippet for checking balanced parentheses:

def check_balance(s):
    stack = []
    for ch in s:
        if ch == '(': stack.push(ch)
        elif ch == ')':
            if stack == []: return False
            stack.pop()
    return len(stack) == 0

medium

A. Using '==' to check empty stack is wrong

B. Missing return statement inside the loop

C. stack.push(ch) is invalid; use stack.append(ch) instead

D. pop() should be called before checking stack empty

Solution

1. Step 1: Identify stack method error

   Python list has no push() method; append() should be used to add elements.

2. Step 2: Verify other parts

   Return statements and empty checks are correct; pop() after check is correct.

3. Final Answer:

   stack.push(ch) is invalid; use stack.append(ch) instead -> Option C

4. Quick Check:

   Use append() to add in Python list stack [OK]

Hint: Use append() not push() for Python list stack [OK]

Common Mistakes:

• Using push() instead of append()
• Checking stack emptiness incorrectly
• Calling pop() without checking stack

5. Given the string s = '{[()()]}', which modification is needed in the balanced parentheses stack algorithm to correctly check this string?

hard

A. Only check for parentheses '()' and ignore other brackets

B. Count total number of brackets without matching pairs

C. Use a queue instead of a stack to check balance

D. Add support for multiple types of brackets and match pairs accordingly

Solution

1. Step 1: Identify bracket types in string

   The string contains curly braces {}, square brackets [], and parentheses ().

2. Step 2: Modify algorithm for multiple bracket types

   The stack algorithm must track each opening bracket type and match it with the correct closing bracket type.

3. Final Answer:

   Add support for multiple types of brackets and match pairs accordingly -> Option D

4. Quick Check:

   Match bracket types correctly for balanced check [OK]

Hint: Match each opening bracket with its correct closing type [OK]

Common Mistakes:

• Checking only parentheses and ignoring others
• Using queue instead of stack
• Counting brackets without matching