Array Insertion at Middle Index in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does 'inserting an element at the middle index of an array' mean?

It means adding a new element right in the center of the array, shifting the elements after it one position to the right.

beginner

How do you find the middle index of an array with an even number of elements?

You divide the length of the array by 2. For example, if the array has 4 elements, the middle index is 2.

intermediate

Why do we need to shift elements when inserting in the middle of an array?

Because arrays have fixed positions, to insert a new element in the middle, we move all elements from that position to the right by one to make space.

intermediate

What is the time complexity of inserting an element in the middle of an array?

It is O(n) because in the worst case, you may need to shift half of the elements to the right.

beginner

TypeScript code snippet: How to insert element 99 at the middle index of array [10, 20, 30, 40]?

const arr = [10, 20, 30, 40];
const mid = Math.floor(arr.length / 2);
arr.splice(mid, 0, 99);
// Result: [10, 20, 99, 30, 40]

What does the splice method do when used as arr.splice(index, 0, element)?

A Clears the array

B Inserts element at index without removing any elements

C Replaces element at index

D Removes element at index

Using splice with 0 as the second argument inserts the new element at the given index without deleting any existing elements.

If an array has 5 elements, what is the middle index to insert a new element?

A 3

B 4

C 1

D 2

Middle index is floor of length divided by 2, so floor(5/2) = 2.

What happens to elements after the middle index when inserting a new element there?

A They shift right by one position

B They shift left by one position

C They get deleted

D They stay in the same place

Elements after the insertion point move right to make space for the new element.

Which of these is the correct way to find the middle index in TypeScript?

A Math.ceil(arr.length / 2)

B arr.length / 2

C Math.floor(arr.length / 2)

D arr.length - 1

Math.floor ensures the middle index is an integer, suitable for array indexing.

What is the time complexity of inserting an element at the middle of an array?

A O(n)

B O(1)

C O(log n)

D O(n^2)

Insertion requires shifting elements, which takes linear time proportional to the array size.

Explain step-by-step how to insert an element at the middle index of an array.

Think about how arrays store elements in order and what happens when you add a new one in the middle.

Describe the impact on performance when inserting elements in the middle of large arrays.

Consider how many elements move when you insert in the middle versus at the end.

Practice

1. What does inserting an element at the middle index of an array mean?

easy

A. Adding the element exactly in the center position of the array

B. Adding the element at the start of the array

C. Adding the element at the end of the array

D. Replacing the middle element with a new element

Solution

1. Step 1: Understand array indexing

   Arrays have positions starting from 0 to length-1. The middle index is usually length/2 (rounded down).

2. Step 2: Define insertion at middle

   Inserting at middle means placing the new element at this middle index, shifting elements after it to the right.

3. Final Answer:

   Adding the element exactly in the center position of the array -> Option A

4. Quick Check:

   Middle insertion = center position [OK]

Hint: Middle index = array length divided by 2 [OK]

Common Mistakes:

• Confusing insertion with replacement
• Inserting at start or end instead of middle
• Not shifting elements after insertion

2. Which of the following TypeScript code snippets correctly inserts the value 99 at the middle index of array arr?

easy

A. arr.unshift(99);

B. arr.push(99);

C. arr.splice(Math.floor(arr.length / 2), 0, 99);

D. arr[ Math.floor(arr.length / 2) ] = 99;

Solution

1. Step 1: Understand splice method

   splice(index, 0, value) inserts value at index without removing elements.

2. Step 2: Check other options

   push adds at end, unshift adds at start, direct assignment replaces element.

3. Final Answer:

   arr.splice(Math.floor(arr.length / 2), 0, 99); -> Option C

4. Quick Check:

   splice with 0 delete count inserts [OK]

Hint: Use splice(index, 0, value) to insert without removal [OK]

Common Mistakes:

• Using push or unshift instead of splice
• Replacing element instead of inserting
• Incorrect index calculation

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

const arr = [10, 20, 30, 40];
arr.splice(Math.floor(arr.length / 2), 0, 25);
console.log(arr);

medium

A. [10, 20, 30, 25, 40]

B. [10, 20, 25, 30, 40]

C. [10, 25, 20, 30, 40]

D. [25, 10, 20, 30, 40]

Solution

1. Step 1: Calculate middle index

   arr.length = 4, middle index = Math.floor(4/2) = 2.

2. Step 2: Insert 25 at index 2

   splice(2, 0, 25) inserts 25 before element at index 2 (which is 30), shifting elements right.

3. Final Answer:

   [10, 20, 25, 30, 40] -> Option B

4. Quick Check:

   Inserted 25 at index 2 [OK]

Hint: Middle index = floor(length/2), splice inserts at that index [OK]

Common Mistakes:

• Inserting at wrong index
• Replacing element instead of inserting
• Misunderstanding splice parameters

4. What is the output of the following TypeScript code?

const nums = [1, 2, 3, 4, 5];
const mid = nums.length / 2;
nums.splice(mid, 0, 50);
console.log(nums);

medium

A. [1, 50, 2, 3, 4, 5]

B. [1, 2, 3, 4, 5, 50]

C. [1, 2, 3, 50, 4, 5]

D. [1, 2, 50, 3, 4, 5]

Solution

1. Step 1: Check mid calculation

   nums.length = 5, mid = 5 / 2 = 2.5 (a float).

2. Step 2: Understand splice behavior

   splice coerces 2.5 to integer 2 (ToInteger(2.5) = 2). Inserts 50 at index 2, shifting 3,4,5 right: [1, 2, 50, 3, 4, 5].

3. Final Answer:

   [1, 2, 50, 3, 4, 5] -> Option D

4. Quick Check:

   Float index coerced to 2 [OK]

Hint: Always floor length/2 for middle index [OK]

Common Mistakes:

• Confusing with unshift (insert at start)
• Confusing with push (append at end)
• Inserting at index 3 instead of 2

5. Given an array arr = [5, 10, 15, 20, 25], write a TypeScript function insertMiddle that inserts a given value exactly in the middle of the array. What will be the array after calling insertMiddle(arr, 12)?

hard

A. [5, 10, 12, 15, 20, 25]

B. [5, 10, 15, 12, 20, 25]

C. [12, 5, 10, 15, 20, 25]

D. [5, 10, 15, 20, 25, 12]

Solution

1. Step 1: Calculate middle index for odd length

   arr.length = 5, middle index = Math.floor(5/2) = 2.

2. Step 2: Insert 12 at index 2

   Using splice(2, 0, 12) inserts 12 before element at index 2 (which is 15), shifting elements right.

3. Final Answer:

   [5, 10, 12, 15, 20, 25] -> Option A

4. Quick Check:

   Inserted 12 at middle index 2 [OK]

Hint: Use Math.floor(length/2) for middle insertion [OK]

Common Mistakes:

• Inserting at wrong index for odd length
• Appending instead of inserting
• Replacing element instead of inserting