Logical operators in Java - Time & Space Complexity

Time Complexity: Logical operators

O(1)

Understanding Time Complexity

Logical operators combine true/false values to make decisions in code.

We want to see how using these operators affects how long the program takes to run.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

boolean a = true;
boolean b = false;
boolean c = true;

if ((a && b) || c) {
    System.out.println("Condition met");
} else {
    System.out.println("Condition not met");
}
    

This code checks a condition using logical AND and OR operators and prints a message.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single evaluation of logical operators.
• How many times: Exactly once per run, no loops or repeated checks.

How Execution Grows With Input

Since the code only evaluates a fixed number of logical conditions once, the work stays the same no matter what.

Input Size (n)	Approx. Operations
10	3 evaluations
100	3 evaluations
1000	3 evaluations

Pattern observation: The number of operations does not grow with input size; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means the time to run the code stays the same no matter how big the input is.

Common Mistake

[X] Wrong: "Logical operators slow down the program as input grows because they combine many conditions."

[OK] Correct: Logical operators here only check a fixed number of conditions once, so the time does not increase with input size.

Interview Connect

Understanding how simple logical checks run quickly helps you explain code efficiency clearly and confidently.

Self-Check

"What if we replaced the fixed booleans with a loop checking many conditions combined with logical operators? How would the time complexity change?"

Practice

1. Which logical operator in Java means "both conditions must be true"?

easy

A. && (AND)

B. || (OR)

C. ! (NOT)

D. ^ (XOR)

Solution

1. Step 1: Understand the meaning of logical AND

   The operator && means both conditions must be true for the whole expression to be true.

2. Step 2: Compare with other operators

   || means one or both true, ! reverses true/false, ^ means exclusive or (one true only).

3. Final Answer:

   && (AND) -> Option A

4. Quick Check:

   Both true = && [OK]

Hint: AND means both true, use && [OK]

Common Mistakes:

• Confusing || (OR) with && (AND)
• Thinking ! means AND
• Mixing up ^ with &&

2. Which of the following is the correct syntax to negate a boolean variable flag in Java?

easy

A. flag = not flag;

B. flag = !flag;

C. flag = ~flag;

D. flag = flag !=;

Solution

1. Step 1: Recall the NOT operator syntax

   In Java, the NOT operator is ! and placed before the boolean variable to reverse its value.

2. Step 2: Check each option

   flag = !flag; uses ! correctly. flag = not flag; uses 'not' which is invalid in Java. flag = ~flag; uses ~ which is bitwise NOT, not for booleans. flag = flag !=; is invalid syntax.

3. Final Answer:

   flag = !flag; -> Option B

4. Quick Check:

   Negate boolean with ! [OK]

Hint: Use ! before boolean to negate it [OK]

Common Mistakes:

• Using 'not' instead of !
• Using bitwise ~ on booleans
• Incorrect syntax like 'flag !=;'

3. What is the output of the following Java code?

boolean a = true;
boolean b = false;
System.out.println(a && b || !b);

medium

A. false

B. Compilation error

C. true

D. Runtime exception

Solution

1. Step 1: Evaluate the expression step-by-step

   a && b is true && false = false. !b is !false = true.

2. Step 2: Apply OR operator

   Now false || true = true.

3. Final Answer:

   true -> Option C

4. Quick Check:

   (true && false) || !false = true [OK]

Hint: Evaluate && first, then ||, then ! [OK]

Common Mistakes:

• Ignoring operator precedence
• Evaluating || before &&
• Confusing !b value

4. Identify the error in this Java code snippet:

boolean x = true;
boolean y = false;
if (x & | y) {
    System.out.println("Yes");
}

medium

A. Invalid use of & | operators together

B. Missing semicolon after if condition

C. Boolean variables cannot be used in if

D. No error, code runs fine

Solution

1. Step 1: Check the if condition syntax

   The condition uses '& |' which is not a valid operator combination in Java.

2. Step 2: Understand valid logical operators

   Valid operators are &&, ||, &, | but not combined as '& |'. This causes a syntax error.

3. Final Answer:

   Invalid use of & | operators together -> Option A

4. Quick Check:

   Operators & and | cannot be combined like '& |' [OK]

Hint: Use && or ||, not mixed & | [OK]

Common Mistakes:

• Confusing bitwise & with logical &&
• Combining & and | without operand
• Thinking no error occurs

5. You want to check if a number n is between 10 and 20 inclusive in Java. Which condition correctly uses logical operators?

hard

A. if (n > 10 && n < 20)

B. if (n >= 10 || n <= 20)

C. if (!(n < 10 && n > 20))

D. if (n >= 10 && n <= 20)

Solution

1. Step 1: Understand the range condition

   To check if n is between 10 and 20 inclusive, both conditions n >= 10 and n <= 20 must be true.

2. Step 2: Analyze each option

   if (n >= 10 || n <= 20) uses || which means either condition true, so it allows numbers outside the range. if (n >= 10 && n <= 20) uses && which correctly requires both conditions true. if (!(n < 10 && n > 20)) negates an impossible condition and is incorrect. if (n > 10 && n < 20) excludes 10 and 20 by using > and <.

3. Final Answer:

   if (n >= 10 && n <= 20) -> Option D

4. Quick Check:

   Both limits true = && [OK]

Hint: Use && to require both conditions true [OK]

Common Mistakes:

• Using || instead of && for range
• Excluding boundary values by using > or <
• Misusing negation for range check