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

Time Complexity: Array Insertion at End

O(1)

Understanding Time Complexity

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

This helps us know how fast this operation is as the array grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const arr = [];
function insertAtEnd(value) {
  arr[arr.length] = value;
}

insertAtEnd(5);
insertAtEnd(10);
insertAtEnd(15);
    

This code adds new values to the end of an array one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding one item at the end of the array.
• How many times: Each call adds exactly one item, no loops inside.

How Execution Grows With Input

Adding one item takes about the same time no matter how big the array is.

Input Size (n)	Approx. Operations
10	10 insertions, each quick
100	100 insertions, each quick
1000	1000 insertions, each quick

Pattern observation: Time per insertion stays about the same as array grows.

Final Time Complexity

Time Complexity: O(1)

This means adding an item at the end takes a constant amount of time, no matter the array size.

Common Mistake

[X] Wrong: "Adding at the end takes longer as the array grows because it has to move all items."

[OK] Correct: Arrays keep track of their length, so adding at the end just places the item there without moving others.

Interview Connect

Knowing that adding at the end is fast helps you choose the right data structure and explain your code clearly in interviews.

Self-Check

"What if we had to insert at the beginning of the array instead? How would the time complexity change?"

Practice

1. What does the push() method do when used on a JavaScript array?

easy

A. Adds one or more elements to the end of the array

B. Removes the first element from the array

C. Sorts the array in ascending order

D. Reverses the order of elements in the array

Solution

1. Step 1: Understand the purpose of push()

   The push() method is designed to add elements to the end of an array.

2. Step 2: Compare with other array methods

   Other methods like shift() remove elements, sort() orders elements, and reverse() changes order, but push() only adds at the end.

3. Final Answer:

   Adds one or more elements to the end of the array -> Option A

4. Quick Check:

   push() adds elements at end [OK]

Hint: Remember: push adds at the end, pop removes from end [OK]

Common Mistakes:

• Confusing push() with pop() which removes elements
• Thinking push() adds elements at the start
• Mixing push() with sort() or reverse()

2. Which of the following is the correct syntax to add the element 5 at the end of array arr?

easy

A. arr.add(5);

B. arr.append(5);

C. arr.insertEnd(5);

D. arr.push(5);

Solution

1. Step 1: Recall JavaScript array methods

   JavaScript arrays use push() to add elements at the end.

2. Step 2: Check each option's validity

   add(), insertEnd(), and append() are not valid JavaScript array methods.

3. Final Answer:

   arr.push(5); -> Option D

4. Quick Check:

   Correct syntax for adding at end is push() [OK]

Hint: Use push() to add elements at array end [OK]

Common Mistakes:

• Using non-existent methods like add() or append()
• Confusing push() with unshift() which adds at start
• Missing parentheses in method call

3. What will be the output of the following code?

let arr = [1, 2, 3];
arr.push(4);
console.log(arr);

medium

A. [1, 2, 3]

B. [4, 1, 2, 3]

C. [1, 2, 3, 4]

D. Error

Solution

1. Step 1: Understand initial array and push operation

   The array starts as [1, 2, 3]. The push(4) adds 4 at the end.

2. Step 2: Determine final array content

   After push, the array becomes [1, 2, 3, 4].

3. Final Answer:

   [1, 2, 3, 4] -> Option C

4. Quick Check:

   push(4) adds 4 at end [OK]

Hint: push() adds element at end, so array grows rightwards [OK]

Common Mistakes:

• Thinking push adds element at start
• Expecting original array unchanged
• Confusing push with unshift

4. Identify the error in the following code snippet that tries to add 10 at the end of array nums:

let nums = [1, 2, 3];
nums.push = 10;
console.log(nums);

medium

A. Using assignment instead of calling push as a function

B. Array nums is not defined

C. push method does not exist on arrays

D. Missing semicolon after push

Solution

1. Step 1: Analyze the push usage

   The code assigns 10 to nums.push instead of calling nums.push(10).

2. Step 2: Understand consequences of assignment

   This overwrites the push method with a number, so push no longer works as a function.

3. Final Answer:

   Using assignment instead of calling push as a function -> Option A

4. Quick Check:

   push must be called as a function, not assigned [OK]

Hint: Always call push() with parentheses to add elements [OK]

Common Mistakes:

• Assigning value to push instead of calling it
• Forgetting parentheses after push
• Assuming push is a property, not a method

5. Given the code below, what will be the final state of arr?

let arr = [10];
arr.push(20);
arr.push(30, 40);
arr.push();

hard

A. [10, 20, [30, 40]]

B. [10, 20, 30, 40]

C. [10, 20, 30, 40, undefined]

D. [10, 20, 30]

Solution

1. Step 1: Trace each push call

   Initial array: [10]. arr.push(20) adds 20 -> [10, 20]. arr.push(30, 40) adds both 30 and 40 -> [10, 20, 30, 40]. arr.push() with no arguments adds nothing.

2. Step 2: Confirm final array state

   No undefined or nested arrays are added. Final array is [10, 20, 30, 40].

3. Final Answer:

   [10, 20, 30, 40] -> Option B

4. Quick Check:

   push() adds all args at end; no args means no change [OK]

Hint: push() adds all arguments; no args means no change [OK]

Common Mistakes:

• Thinking push() with no args adds undefined
• Assuming push(30, 40) adds an array instead of separate elements
• Confusing nested arrays with multiple arguments