Logical operators in conditions in Python - Time & Space Complexity

Time Complexity: Logical operators in conditions

O(n)

Understanding Time Complexity

Logical operators in conditions help decide which code runs based on true or false checks.

We want to see how these checks affect the time it takes for the program to run as input changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def check_values(nums, threshold):
    count = 0
    for num in nums:
        if num > threshold and num % 2 == 0:
            count += 1
    return count

This code counts how many numbers in a list are greater than a threshold and even.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each number in the list.
• How many times: Once for every number in the input list.

How Execution Grows With Input

As the list gets bigger, the program checks each number once.

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

Pattern observation: The number of checks grows directly with the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the list gets bigger.

Common Mistake

[X] Wrong: "Logical operators make the code run slower by multiplying the time."

[OK] Correct: The checks happen together for each item, so they add a small fixed cost, not extra loops.

Interview Connect

Understanding how conditions affect time helps you explain your code clearly and shows you know what happens as data grows.

Self-Check

"What if we changed the condition to use 'or' instead of 'and'? How would the time complexity change?"

Practice

1. Which logical operator in Python means all conditions must be true for the whole expression to be true?

easy

A. xor

B. and

C. not

D. or

Solution

1. Step 1: Understand the meaning of 'and'

   The and operator returns true only if both conditions are true.

2. Step 2: Compare with other operators

   or needs only one true condition, not reverses truth, and xor is not a Python keyword.

3. Final Answer:

   and -> Option B

4. Quick Check:

   All conditions true = and [OK]

Hint: Remember: 'and' means all must be true [OK]

Common Mistakes:

• Confusing 'and' with 'or'
• Thinking 'not' means all true
• Using 'xor' which is not a Python keyword

2. Which of the following is the correct syntax to check if variable x is NOT equal to 10 and variable y is greater than 5?

easy

A. if x != 10 and y > 5:

B. if x <> 10 and y > 5:

C. if x != 10 & y > 5:

D. if x != 10 or y > 5:

Solution

1. Step 1: Check the inequality operator

   != is the correct 'not equal' operator in Python; <> is invalid syntax.

2. Step 2: Check logical operator usage

   and correctly combines two conditions; & is a bitwise operator and or changes logic.

3. Final Answer:

   if x != 10 and y > 5: -> Option A

4. Quick Check:

   Correct inequality and 'and' syntax [OK]

Hint: Use '!=' for not equal and 'and' to combine conditions [OK]

Common Mistakes:

• Using '<>' instead of '!='
• Using '&' instead of 'and'
• Using 'or' when 'and' is needed

3. What will be the output of this code?

age = 20
has_id = False
if age >= 18 and has_id:
    print('Allowed')
else:
    print('Denied')

medium

A. SyntaxError

B. Allowed

C. Denied

D. No output

Solution

1. Step 1: Evaluate each condition

   age >= 18 is True since 20 >= 18, but has_id is False.

2. Step 2: Apply 'and' operator

   True and False is False, so the else block runs.

3. Final Answer:

   Denied -> Option C

4. Quick Check:

   True and False = False [OK]

Hint: Both conditions must be true for 'and' to print Allowed [OK]

Common Mistakes:

• Assuming one True is enough with 'and'
• Confusing 'and' with 'or'
• Ignoring boolean value of variables

4. Find the error in this code snippet:

if not x > 10 or y < 5
    print('Check passed')

medium

A. Missing colon ':' after condition

B. Wrong use of 'not' operator

C. Incorrect indentation

D. Using 'or' instead of 'and'

Solution

1. Step 1: Check syntax of if statement

   Python requires a colon ':' at the end of the if condition line.

2. Step 2: Review other parts

   The use of not and or is correct; indentation is not shown as wrong here.

3. Final Answer:

   Missing colon ':' after condition -> Option A

4. Quick Check:

   if statements need ':' [OK]

Hint: Always put ':' after if condition [OK]

Common Mistakes:

• Forgetting ':' after if
• Misusing 'not' operator
• Wrong indentation without colon

5. You want to check if a number n is either less than 0 or greater than 100, but NOT equal to -10. Which condition correctly uses logical operators?

hard

A. if n < 0 or (n > 100 and n != -10):

B. if n < 0 and n > 100 or n != -10:

C. if not (n < 0 or n > 100) and n == -10:

D. if (n < 0 or n > 100) and n != -10:

Solution

1. Step 1: Understand the condition requirements

   We want numbers less than 0 or greater than 100, but exclude -10.

2. Step 2: Analyze each option

   if (n < 0 or n > 100) and n != -10: correctly groups the or condition and excludes -10 with and n != -10. if n < 0 or (n > 100 and n != -10): excludes -10 only when >100, not <0 (e.g., n=-10 is true). if not (n < 0 or n > 100) and n == -10: reverses logic and checks for equal -10. if n < 0 and n > 100 or n != -10: mixes and/or incorrectly.

3. Final Answer:

   if (n < 0 or n > 100) and n != -10: -> Option D

4. Quick Check:

   Group or, then exclude -10 with and [OK]

Hint: Group or conditions, then exclude with and [OK]

Common Mistakes:

• Wrong grouping of conditions
• Misplacing 'not' or 'and'
• Confusing '!=' with '=='