Arithmetic operators in Go - Time & Space Complexity

Time Complexity: Arithmetic operators

O(n)

Understanding Time Complexity

We want to see how the time to run arithmetic operations changes as we do more of them.

How does the number of calculations grow when we increase the input size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func sumArray(nums []int) int {
    total := 0
    for _, num := range nums {
        total += num
    }
    return total
}
    

This code adds up all numbers in a list using arithmetic operators inside a loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Addition inside the loop (total += num)
• How many times: Once for each number in the list

How Execution Grows With Input

Each number in the list causes one addition operation.

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

Pattern observation: The number of operations grows directly with the number of items.

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: "Arithmetic operations inside a loop are instant and don't affect time."

[OK] Correct: Even simple additions take time, and doing them many times adds up as the list grows.

Interview Connect

Understanding how loops with arithmetic operations scale helps you explain efficiency clearly and confidently.

Self-Check

"What if we replaced the loop with nested loops doing additions? How would the time complexity change?"

Practice

1. Which arithmetic operator in Go is used to find the remainder of a division?

easy

A. /

B. +

C. *

D. %

Solution

1. Step 1: Understand the remainder operation

   The remainder operator returns what is left after division.

2. Step 2: Identify the correct operator in Go

   In Go, the remainder operator is represented by the percent sign '%'.

3. Final Answer:

   % -> Option D

4. Quick Check:

   Remainder = % [OK]

Hint: Remainder uses % like in many languages [OK]

Common Mistakes:

• Confusing division / with remainder %
• Using * for remainder
• Using + for remainder

2. Which of the following is the correct way to write a multiplication operation in Go?

easy

A. a x b

B. a . b

C. a * b

D. a & b

Solution

1. Step 1: Recall Go's multiplication syntax

   Go uses the asterisk '*' symbol for multiplication.

2. Step 2: Check each option

   Only 'a * b' uses the correct multiplication operator.

3. Final Answer:

   a * b -> Option C

4. Quick Check:

   Multiplication = * [OK]

Hint: Use * for multiplication, not x or & [OK]

Common Mistakes:

• Using 'x' instead of '*'
• Using '.' or '&' for multiplication
• Confusing syntax with other languages

3. What is the output of this Go code?

package main
import "fmt"
func main() {
  a := 7
  b := 3
  fmt.Println(a / b)
}

medium

A. 2.3333333

B. 2

C. 3

D. 0

Solution

1. Step 1: Identify variable types and operation

   Both a and b are integers, so division is integer division.

2. Step 2: Calculate integer division result

   7 divided by 3 is 2.333..., but integer division drops decimals, so result is 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Integer division 7/3 = 2 [OK]

Hint: Integer division drops decimals, result is int [OK]

Common Mistakes:

• Expecting float result
• Confusing integer division with float division
• Using wrong operator

4. Find the error in this Go code snippet:

package main
import "fmt"
func main() {
  x := 10
  y := 0
  fmt.Println(x / y)
}

medium

A. Division by zero causes runtime panic

B. Syntax error: missing semicolon

C. Variable y is not declared

D. No error, prints 0

Solution

1. Step 1: Analyze the division operation

   The code divides x by y, where y is zero.

2. Step 2: Understand Go's behavior on division by zero

   Dividing by zero causes a runtime panic (error) in Go.

3. Final Answer:

   Division by zero causes runtime panic -> Option A

4. Quick Check:

   Division by zero = runtime panic [OK]

Hint: Never divide by zero; it crashes the program [OK]

Common Mistakes:

• Thinking it prints 0
• Expecting compile-time error
• Ignoring runtime panic

5. Given the Go code below, what is the output?

package main
import "fmt"
func main() {
  a := 15
  b := 4
  c := a % b
  d := a / b
  fmt.Println(c + d)
}

hard

A. 6

B. 3

C. 19

D. 4

Solution

1. Step 1: Calculate remainder c = a % b

   15 % 4 equals 3 because 4*3=12 and 15-12=3.

2. Step 2: Calculate integer division d = a / b

   15 / 4 equals 3 because integer division drops decimals.

3. Step 3: Add c + d

   3 + 3 equals 6.

4. Final Answer:

   6 -> Option A

5. Quick Check:

   15 % 4 = 3, 15 / 4 = 3, 3 + 3 = 6 [OK]

Hint: Add remainder and integer division results carefully [OK]

Common Mistakes:

• Miscomputing remainder
• Using float division instead of integer
• Adding wrong values