Loop execution flow in Java - Time & Space Complexity

Time Complexity: Loop execution flow

O(n)

Understanding Time Complexity

Loops run code multiple times, so their speed depends on how many times they repeat.

We want to know how the total work grows as the loop runs more times.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for (int i = 0; i < n; i++) {
    System.out.println(i);
}
    

This code prints numbers from 0 up to n-1, running the print statement once each loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The print statement inside the for loop.
• How many times: Exactly n times, once per loop cycle.

How Execution Grows With Input

As n gets bigger, the number of print actions grows the same way.

Input Size (n)	Approx. Operations
10	10 prints
100	100 prints
1000	1000 prints

Pattern observation: The work grows directly with n, so doubling n doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line with the number of loop cycles.

Common Mistake

[X] Wrong: "The loop runs faster because it just prints simple numbers."

[OK] Correct: Even simple actions inside the loop add up, so the total time still grows with n.

Interview Connect

Understanding how loops affect time helps you explain code speed clearly and confidently in interviews.

Self-Check

"What if we added a nested loop inside this loop? How would the time complexity change?"

Practice

1. What does a for loop in Java primarily do?

easy

A. Executes code only once

B. Stops the program immediately

C. Repeats a block of code a specific number of times

D. Creates a new variable

Solution

1. Step 1: Understand the purpose of a for loop and compare options

   A for loop is designed to repeat a block of code multiple times based on a condition. Only "Repeats a block of code a specific number of times" correctly describes it.

2. Final Answer:

   Repeats a block of code a specific number of times -> Option C

3. Quick Check:

   for loop = repeat code [OK]

Hint: For loops repeat code a set number of times [OK]

Common Mistakes:

• Thinking for loops run only once
• Confusing loops with variable declarations
• Believing loops stop the program

2. Which of the following is the correct syntax for a basic while loop in Java?

easy

A. while (condition); { // code }

B. while condition { // code }

C. while: (condition) { // code }

D. while (condition) { // code }

Solution

1. Step 1: Recall Java while loop syntax and check options

   The correct syntax requires parentheses around the condition and braces for the code block. Only "while (condition) { // code }" matches: while (condition) { // code }.

2. Final Answer:

   while (condition) { // code } -> Option D

3. Quick Check:

   while loop syntax = parentheses + braces [OK]

Hint: While loops need parentheses and braces [OK]

Common Mistakes:

• Omitting parentheses around condition
• Adding semicolon after while condition
• Using colon instead of parentheses

3. What will be the output of this Java code?

int count = 0;
while (count < 3) {
  System.out.print(count + " ");
  count++;
}

medium

A. 0 1 2

B. 1 2 3

C. 0 1 2 3

D. 3 2 1

Solution

1. Step 1: Analyze the loop condition and trace iterations

   The loop runs while count is less than 3, starting from 0. It prints 0, then increments to 1; prints 1, increments to 2; prints 2, increments to 3; then stops because 3 is not less than 3.

2. Final Answer:

   0 1 2 -> Option A

3. Quick Check:

   Prints 0,1,2 then stops [OK]

Hint: Count starts at 0 and stops before 3 [OK]

Common Mistakes:

• Including 3 in output
• Starting count from 1
• Printing in reverse order

4. Identify the error in this loop code:

int i = 0;
while (i < 5) {
  System.out.println(i);
}

medium

A. Missing increment of i inside the loop

B. Incorrect loop condition syntax

C. Missing semicolon after while

D. Variable i should be declared inside the loop

Solution

1. Step 1: Check loop control variable and consequences

   The variable i is initialized but never changed inside the loop. Without incrementing i, the condition i < 5 is always true, causing an infinite loop.

2. Final Answer:

   Missing increment of i inside the loop -> Option A

3. Quick Check:

   Loop needs variable update to stop [OK]

Hint: Always update loop variable to avoid infinite loops [OK]

Common Mistakes:

• Forgetting to increment loop variable
• Misplacing semicolons
• Declaring variable inside loop unnecessarily

5. Consider this code snippet:

int sum = 0;
for (int i = 1; i <= 5; i++) {
  if (i == 3) continue;
  sum += i;
}
System.out.println(sum);

What is the output and why?

hard

A. 15 because all numbers 1 to 5 are added

B. 12 because number 3 is skipped in addition

C. 10 because only numbers less than 3 are added

D. Error due to incorrect use of continue

Solution

1. Step 1: Trace the loop and effect of continue

   The loop runs from 1 to 5. When i equals 3, continue skips the addition for that iteration. Sum = 1 + 2 + 4 + 5 = 12 because 3 is skipped.

2. Final Answer:

   12 because number 3 is skipped in addition -> Option B

3. Quick Check:

   continue skips 3, sum = 12 [OK]

Hint: Continue skips current loop iteration [OK]

Common Mistakes:

• Adding 3 despite continue
• Thinking continue causes error
• Summing only numbers less than 3