Array Insertion at End in DSA Typescript - 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.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function insertAtEnd(arr: number[], value: number): void {
  arr[arr.length] = value;
}
    

This code adds a new value at the end of the array by placing it at the current length index.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single direct assignment to the array at the end index.
• How many times: Exactly once per insertion.

How Execution Grows With Input

Adding one item at the end takes the same small step no matter how big the array is.

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

Pattern observation: The time stays constant even as the array grows.

Final Time Complexity

Time Complexity: O(1)

This means adding an item at the end takes the same short time no matter how many items are already there.

Common Mistake

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

[OK] Correct: The insertion just places the new item at the next free spot without moving existing items.

Interview Connect

Knowing that adding at the end is quick helps you choose the right data structure and explain your choices clearly.

Self-Check

"What if the array needs to resize its storage when full? How would the time complexity change then?"

Practice

1. What does inserting an element at the end of an array do?

easy

A. Adds the element as the last item in the array

B. Removes the first element of the array

C. Replaces the first element with the new element

D. Sorts the array in ascending order

Solution

1. Step 1: Understand array insertion

   Inserting at the end means adding a new element after the last existing element.

2. Step 2: Effect on array

   The new element becomes the last item, increasing the array size by one.

3. Final Answer:

   Adds the element as the last item in the array -> Option A

4. Quick Check:

   Insertion at end = append last [OK]

Hint: Insertion at end means append after last element [OK]

Common Mistakes:

• Confusing insertion at end with removal
• Thinking insertion replaces elements
• Assuming insertion sorts the array

2. Which of the following is the correct TypeScript syntax to insert an element `5` at the end of array `arr`?

easy

A. arr.insert(5);

B. arr.add(5);

C. arr.push(5);

D. arr.append(5);

Solution

1. Step 1: Identify correct method for insertion at end

   In TypeScript (JavaScript), the method to add at the end is `push()`.

2. Step 2: Check other options

   Methods `add()`, `insert()`, and `append()` do not exist on arrays in TypeScript.

3. Final Answer:

   arr.push(5); -> Option C

4. Quick Check:

   Use push() to add at end [OK]

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

Common Mistakes:

• Using non-existent methods like add or append
• Confusing push() with pop()
• Trying to assign directly to arr[arr.length]

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

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

medium

A. [4, 1, 2, 3]

B. [1, 2, 3, 4]

C. [1, 2, 3]

D. [1, 2, 4, 3]

Solution

1. Step 1: Initial array state

   Array starts as [1, 2, 3].

2. Step 2: Apply push(4)

   push(4) adds 4 at the end, so array becomes [1, 2, 3, 4].

3. Final Answer:

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

4. Quick Check:

   push adds element at end [OK]

Hint: push() adds element at array end [OK]

Common Mistakes:

• Thinking push adds at start
• Confusing push with unshift
• Expecting array to remain unchanged

4. Identify the error in the following TypeScript code that tries to insert `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 method

B. Array nums is not declared properly

C. push method does not exist on arrays

D. Console.log syntax is incorrect

Solution

1. Step 1: Analyze push usage

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

2. Step 2: Effect of assignment

   This overwrites the push method, so no insertion happens and push is lost.

3. Final Answer:

   Using assignment instead of calling push method -> Option A

4. Quick Check:

   push must be called as a function [OK]

Hint: Call push() as a function, don't assign to it [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 an empty array `let data: number[] = [];`, which code snippet correctly inserts numbers 1 to 3 at the end of the array using a loop?

hard

A. for(let i = 0; i < 3; i++) { data.push(i); }

B. for(let i = 1; i <= 3; i++) { data[i] = i; }

C. for(let i = 1; i < 3; i++) { data.push(i); }

D. for(let i = 1; i <= 3; i++) { data.push(i); }

Solution

1. Step 1: Understand loop range and insertion

   We want to insert 1, 2, 3 at the end, so loop from 1 to 3 inclusive.

2. Step 2: Check each option

   A pushes 0,1,2 instead of 1,2,3.
   B assigns directly to indices 1,2,3 leaving index 0 empty.
   C uses push with i from 1 to 3, correctly adding 1,2,3.
   D loops from 1 to 2 only, missing 3.

3. Final Answer:

   for(let i = 1; i <= 3; i++) { data.push(i); } -> Option D

4. Quick Check:

   Loop 1 to 3 with push() adds correct elements [OK]

Hint: Loop from 1 to 3 and push each value [OK]

Common Mistakes:

• Using wrong loop range
• Assigning to array indices instead of push
• Starting loop at 0 instead of 1