Assignment operators in C++ - Time & Space Complexity

Time Complexity: Assignment operators

O(n)

Understanding Time Complexity

We want to see how the time taken by assignment operators changes as the input size changes.

How does the cost of assigning values grow when working with bigger data?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int arr[1000];
for (int i = 0; i < 1000; i++) {
    arr[i] = i * 2;
}
int x = 5;
x = 10;

This code assigns values to each element of an array and then assigns a new value to a single variable.

Identify Repeating Operations

• Primary operation: Assignment inside the loop to each array element.
• How many times: 1000 times, once for each element.

How Execution Grows With Input

As the number of elements increases, the number of assignments grows in the same way.

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

Pattern observation: The number of assignments grows directly with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to assign values grows in a straight line as the number of items increases.

Common Mistake

[X] Wrong: "Assigning a single variable inside a loop makes the whole loop take constant time."

[OK] Correct: Even if the variable assignment is simple, doing it many times inside a loop adds up and grows with the number of repetitions.

Interview Connect

Understanding how simple assignments add up helps you explain how loops affect performance in real code.

Self-Check

"What if we replaced the array with a linked list and assigned values similarly? How would the time complexity change?"

Practice

1. Which of the following assignment operators adds the right value to the left variable and stores the result back in the left variable?

easy

A. +=

B. =

C. -=

D. *=

Solution

1. Step 1: Understand the meaning of +=

   The operator += adds the right side value to the left side variable and updates the variable with the new value.

2. Step 2: Compare with other operators

   = assigns a value, -= subtracts, and *= multiplies. Only += adds and assigns.

3. Final Answer:

   += -> Option A

4. Quick Check:

   Add and assign = += [OK]

Hint: Remember: += means add then assign [OK]

Common Mistakes:

• Confusing = with +=
• Thinking -= adds values
• Mixing *= with addition

2. Which of the following is the correct syntax to multiply variable x by 5 and store the result back in x?

easy

A. x =* 5;

B. x *= 5;

C. x = 5*;

D. x = 5 *;

Solution

1. Step 1: Identify the correct assignment operator syntax

   The operator to multiply and assign is *=, so x *= 5; is correct.

2. Step 2: Check other options for syntax errors

   x =* 5; and x = 5*; are invalid syntax. x = 5 *; is incomplete.

3. Final Answer:

   x *= 5; -> Option B

4. Quick Check:

   Multiply and assign = *= [OK]

Hint: Use operator before = for combined assignment [OK]

Common Mistakes:

• Placing * after = instead of before
• Leaving incomplete expressions
• Confusing with simple assignment =

3. What is the output of the following code?

int a = 10;
a += 5;
a -= 3;
std::cout << a;

medium

A. 12

B. 15

C. 8

D. 10

Solution

1. Step 1: Calculate a += 5;

   Starting with a = 10, adding 5 gives a = 15.

2. Step 2: Calculate a -= 3;

   Subtracting 3 from 15 gives a = 12.

3. Final Answer:

   12 -> Option A

4. Quick Check:

   10 + 5 - 3 = 12 [OK]

Hint: Apply each assignment step by step [OK]

Common Mistakes:

• Adding and subtracting in wrong order
• Confusing += and -= effects
• Ignoring the updated value after first operation

4. Identify the error in the following code snippet:

int x = 7;
x =+ 3;
std::cout << x;

medium

A. Syntax error due to incorrect operator

B. x will be 10

C. x will be 3

D. No error, output is 10

Solution

1. Step 1: Analyze x =+ 3;

   This is not the addition assignment +=. Instead, =+ means assign positive 3 to x.

2. Step 2: Determine the value of x after assignment

   x becomes 3, not 10, because =+ is just assignment with unary plus.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   =+ is assignment, not addition [OK]

Hint: Watch for =+ vs += difference [OK]

Common Mistakes:

• Confusing =+ with += operator
• Expecting addition instead of assignment
• Assuming output is sum without checking syntax

5. Given int n = 20;, which code snippet correctly divides n by 4 and then subtracts 2 from the result, updating n accordingly?

hard

A. n = n - 2 / 4;

B. n -= 2; n /= 4;

C. n = (n - 2) / 4;

D. n /= 4; n -= 2;

Solution

1. Step 1: Understand the required operations order

   First divide n by 4, then subtract 2 from the result, updating n each time.

2. Step 2: Check each option

   n /= 4; n -= 2; does n /= 4; then n -= 2;, matching the requirement. n -= 2; n /= 4; reverses order. n = (n - 2) / 4; subtracts first due to parentheses (18 / 4 = 4). n = n - 2 / 4; subtracts incorrectly.

3. Step 3: Confirm correct update

   n /= 4; n -= 2; updates n stepwise as requested.

4. Final Answer:

   n /= 4; n -= 2; -> Option D

5. Quick Check:

   Divide then subtract = n /= 4; n -= 2; [OK]

Hint: Follow operation order exactly [OK]

Common Mistakes:

• Reversing operation order
• Misunderstanding combined expressions
• Incorrect operator precedence assumptions