Array Insertion at Middle Index in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output after inserting at the middle index?

Given the array and insertion code below, what is the printed array after insertion?

DSA Python

arr = [10, 20, 30, 40, 50]
mid = len(arr) // 2
arr.insert(mid, 25)
print(arr)

A [10, 20, 25, 30, 40, 50]

B [10, 20, 30, 25, 40, 50]

C [10, 20, 30, 40, 25, 50]

D [25, 10, 20, 30, 40, 50]

💡 Hint

Remember that insert() adds the element before the given index.

The middle index is 2 (5 // 2). Inserting 25 at index 2 places it before the element 30.

❓ Predict Output

intermediate

What is the output after inserting in an even-length array?

What will be printed after inserting 15 at the middle index of the array below?

DSA Python

arr = [5, 10, 20, 25]
mid = len(arr) // 2
arr.insert(mid, 15)
print(arr)

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

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

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

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

💡 Hint

For even length, middle index is length divided by 2.

Length is 4, middle index is 2. Inserting 15 at index 2 places it before 20.

🔧 Debug

advanced

Why does this insertion code raise an error?

Identify the error in the code below and what error it raises.

DSA Python

arr = [1, 2, 3]
mid = len(arr) // 2
arr.insert(mid 4)
print(arr)

A No error, prints [1, 2, 4, 3]

B TypeError because insert() expects only one argument

C IndexError because mid is out of range

D SyntaxError due to missing comma in insert() arguments

💡 Hint

Check the syntax of the insert() method call.

The insert() method requires two arguments separated by a comma. Missing comma causes SyntaxError.

❓ Predict Output

advanced

What is the output after multiple insertions at middle?

What is the final array after these insertions?

DSA Python

arr = [100, 200, 300, 400]
mid = (len(arr) + 1) // 2
arr.insert(mid, 150)
mid = (len(arr) + 1) // 2
arr.insert(mid, 250)
print(arr)

A [100, 150, 200, 250, 300, 400]

B [100, 200, 150, 300, 250, 400]

C [100, 200, 150, 250, 300, 400]

D [150, 100, 200, 250, 300, 400]

💡 Hint

Recalculate middle index after each insertion.

First insertion at index 2 adds 150 before 300. Array becomes [100, 200, 150, 300, 400].

New middle index is 3. Insert 250 at index 3 before 300.

Final array: [100, 200, 150, 250, 300, 400].

🧠 Conceptual

expert

How does insertion at middle index affect time complexity?

Consider an array of size n. What is the time complexity of inserting an element at the middle index?

A O(1) because insertion is direct at the middle index

B O(n) because elements after middle must be shifted

C O(log n) because binary search is used to find middle

D O(n^2) because all elements are copied twice

💡 Hint

Think about what happens to elements after the insertion point.

Inserting in the middle requires shifting all elements after the insertion point one step right, which takes O(n) time.

Practice

1. What is the middle index of an array with 7 elements when inserting a new element?

easy

A. 3

B. 4

C. 2

D. 5

Solution

1. Step 1: Calculate middle index for odd length array

   For an array of length 7, middle index = length // 2 = 7 // 2 = 3.

2. Step 2: Understand insertion position

   Inserting at index 3 places the new element exactly in the middle.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Middle index = length // 2 = 3 [OK]

Hint: Middle index = length // 2 for insertion [OK]

Common Mistakes:

• Using length // 2 + 1 for middle index
• Using length // 2 - 1 for middle index
• Confusing middle index with last index

2. Which of the following Python statements correctly inserts the value 10 at the middle index of list arr = [1, 2, 3, 4]?

easy

A. arr.insert(0, 10)

B. arr.insert(len(arr), 10)

C. arr.insert(len(arr) // 2, 10)

D. arr.append(10)

Solution

1. Step 1: Calculate middle index for arr

   Length of arr is 4, middle index = 4 // 2 = 2.

2. Step 2: Use insert method at middle index

   arr.insert(2, 10) inserts 10 at index 2, which is the middle.

3. Final Answer:

   arr.insert(len(arr) // 2, 10) -> Option C

4. Quick Check:

   Use insert at middle index = len(arr)//2 [OK]

Hint: Use arr.insert(len(arr)//2, value) to insert in middle [OK]

Common Mistakes:

• Using append() which adds at end
• Using insert(len(arr), value) which adds at end
• Using insert(0, value) which adds at start

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

arr = [5, 10, 15, 20]
mid = len(arr) // 2
arr.insert(mid, 12)
print(arr)

medium

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

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

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

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

Solution

1. Step 1: Calculate middle index

   Length of arr is 4, so mid = 4 // 2 = 2.

2. Step 2: Insert 12 at index 2

   arr.insert(2, 12) inserts 12 before element at index 2 (which is 15).

3. Final Answer:

   [5, 10, 12, 15, 20] -> Option B

4. Quick Check:

   Insert at mid index shifts elements right [OK]

Hint: Insert at mid index shifts elements right [OK]

Common Mistakes:

• Inserting at wrong index causing misplaced element
• Appending instead of inserting
• Confusing index with value

4. Find the error in the code below that tries to insert 99 in the middle of arr = [1, 2, 3, 4, 5]:

arr = [1, 2, 3, 4, 5]
mid = len(arr) / 2
arr.insert(mid, 99)
print(arr)

medium

A. Using '/' instead of '//' for middle index calculation

B. Using insert() instead of append() method

C. Not defining arr before insertion

D. Using print() incorrectly

Solution

1. Step 1: Check middle index calculation

   len(arr) / 2 returns a float (2.5), but insert() requires an integer index.

2. Step 2: Correct middle index calculation

   Use integer division '//' to get integer index: mid = len(arr) // 2 = 2.

3. Final Answer:

   Using '/' instead of '//' for middle index calculation -> Option A

4. Quick Check:

   Index must be int, use '//' not '/' [OK]

Hint: Use '//' for integer division to get valid index [OK]

Common Mistakes:

• Using '/' causing TypeError
• Forgetting to calculate middle index
• Using append() instead of insert()

5. Given arr = [2, 4, 6, 8, 10, 12], write code to insert the value 7 exactly in the middle so that the array remains sorted. What will be the final array?

hard

A. [2, 4, 7, 6, 8, 10, 12]

B. [2, 4, 6, 8, 7, 10, 12]

C. [7, 2, 4, 6, 8, 10, 12]

D. [2, 4, 6, 7, 8, 10, 12]

Solution

1. Step 1: Calculate middle index for even length array

   Length is 6, middle index = 6 // 2 = 3.

2. Step 2: Insert 7 at index 3 to keep array sorted

   Inserting 7 at index 3 places it between 6 and 8, maintaining sorted order.

3. Final Answer:

   [2, 4, 6, 7, 8, 10, 12] -> Option D

4. Quick Check:

   Insert 7 at middle index 3 to keep sorted [OK]

Hint: Insert at middle index to keep sorted order [OK]

Common Mistakes:

• Inserting 7 at wrong index breaking order
• Appending 7 at end
• Inserting 7 at start