Array Insertion at End in DSA Go - Time & Space Complexity

Time Complexity: Array Insertion at End

O(1) amortized

Understanding Time Complexity

We want to understand how long it takes to add an item at the end of an array.

How does the time needed change as the array grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

package main

import "fmt"

func insertAtEnd(arr []int, val int) []int {
    arr = append(arr, val)
    return arr
}

func main() {
    arr := []int{1, 2, 3}
    arr = insertAtEnd(arr, 4)
    fmt.Println(arr)
}

This code adds a new value at the end of an integer array using Go's append function.

Identify Repeating Operations

• Primary operation: Adding one element at the end of the array.
• How many times: Once per insertion.

How Execution Grows With Input

Adding one element usually takes the same short time, but sometimes it takes longer if the array needs more space.

Input Size (n)	Approx. Operations
10	About 1 operation
100	About 1 operation
1000	About 1 operation

Pattern observation: Most insertions are quick, but occasionally the array grows and copying happens, making that insertion slower.

Final Time Complexity

Time Complexity: O(1) amortized

This means each insertion usually takes the same small amount of time, but sometimes it takes longer when the array grows.

Common Mistake

[X] Wrong: "Every insertion at the end takes longer as the array grows because it copies all elements each time."

[OK] Correct: The array only copies when it runs out of space, which happens rarely. Most insertions are very fast.

Interview Connect

Understanding this helps you explain how dynamic arrays work and why adding at the end is efficient most of the time.

Self-Check

"What if we changed the array to a linked list? How would the time complexity of insertion at the end change?"

Practice

1. What happens when you insert an element at the end of a fixed-size array in Go?

easy

A. You cannot insert because arrays have fixed size

B. The element replaces the first element

C. The element is added and array size increases automatically

D. The array is converted to a slice automatically

Solution

1. Step 1: Understand Go array size

   Arrays in Go have a fixed size defined at declaration and cannot grow.

2. Step 2: Effect of insertion at end

   Since size is fixed, you cannot add new elements beyond the declared size.

3. Final Answer:

   You cannot insert because arrays have fixed size -> Option A

4. Quick Check:

   Fixed size array = no insertion beyond size [OK]

Hint: Arrays have fixed size; no automatic growth on insertion [OK]

Common Mistakes:

• Thinking arrays can grow automatically
• Confusing arrays with slices
• Assuming insertion replaces last element

2. Which of the following is the correct way to append an element 10 to a slice named nums in Go?

easy

A. nums = nums + 10

B. nums.append(10)

C. append(nums, 10)

D. nums = append(nums, 10)

Solution

1. Step 1: Recall Go slice append syntax

   In Go, append returns a new slice with the element added, so assignment is needed.

2. Step 2: Check each option

   nums = append(nums, 10) correctly assigns the result of append to nums. Others are invalid syntax or missing assignment.

3. Final Answer:

   nums = append(nums, 10) -> Option D

4. Quick Check:

   Use append with assignment to add element [OK]

Hint: Always assign append result back to slice variable [OK]

Common Mistakes:

• Not assigning append result back
• Using method call syntax like nums.append()
• Trying to add with + operator

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

nums := []int{1, 2, 3}
nums = append(nums, 4)
fmt.Println(nums)

medium

A. [1 2 3]

B. [4 1 2 3]

C. [1 2 3 4]

D. Compilation error

Solution

1. Step 1: Understand initial slice and append

   nums starts as [1 2 3]. append(nums, 4) adds 4 at the end.

2. Step 2: Print the updated slice

   After append, nums becomes [1 2 3 4], which is printed.

3. Final Answer:

   [1 2 3 4] -> Option C

4. Quick Check:

   Appending 4 adds it at end [OK]

Hint: append adds element at end, print shows updated slice [OK]

Common Mistakes:

• Expecting original slice without new element
• Thinking append adds at start
• Confusing slice with array syntax

4. Identify the error in the following Go code that tries to insert 5 at the end of an array:

arr := [3]int{1, 2, 3}
arr = append(arr, 5)
fmt.Println(arr)

medium

A. Cannot use append on array; append works only on slices

B. Array size is too small; must declare larger array

C. Missing import for fmt package

D. Syntax error in array declaration

Solution

1. Step 1: Check type of arr

   arr is declared as an array [3]int, which has fixed size and no append method.

2. Step 2: Understand append usage

   append works only on slices, not arrays. Using append on array causes error.

3. Final Answer:

   Cannot use append on array; append works only on slices -> Option A

4. Quick Check:

   append requires slice, not array [OK]

Hint: append works only on slices, not fixed-size arrays [OK]

Common Mistakes:

• Trying to append to fixed-size array
• Ignoring difference between array and slice
• Assuming append auto-converts array to slice

5. Given a slice data := []int{2, 4, 6}, which code snippet correctly inserts the value 8 at the end and then doubles all elements?

hard

A. data = append(data, 8)
for _, v := range data {
v *= 2
}
fmt.Println(data)

B. data = append(data, 8)
for i := range data {
data[i] *= 2
}
fmt.Println(data)

C. data = append(data, 8)
for i := 0; i < len(data); i++ {
data[i] = data[i] + 2
}
fmt.Println(data)

D. data = append(data, 8)
for i := range data {
data[i] = data[i] / 2
}
fmt.Println(data)

Solution

1. Step 1: Append 8 to slice

   data = append(data, 8) adds 8 at the end, making data [2 4 6 8].

2. Step 2: Double each element correctly

   Using for i := range data and data[i] *= 2 doubles each element in place.

3. Step 3: Check other options

   data = append(data, 8) for _, v := range data { v *= 2 } fmt.Println(data) doubles copy of value, not original slice. Options C and D do wrong math.

4. Final Answer:

   data = append(data, 8) for i := range data { data[i] *= 2 } fmt.Println(data) -> Option B

5. Quick Check:

   Append then modify elements by index [OK]

Hint: Modify slice elements by index, not by value copy [OK]

Common Mistakes:

• Modifying value copy in range instead of slice element
• Using wrong arithmetic operation
• Not assigning append result back