Array Deletion at Middle Index in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does 'Array Deletion at Middle Index' mean?

It means removing the element located in the middle position of an array and shifting the remaining elements to fill the gap.

beginner

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

The middle index is found by dividing the length of the array by 2 and taking the floor value (integer division). For example, for 5 elements, middle index = 5 // 2 = 2.

beginner

What happens to the elements after deleting the middle element in an array?

All elements after the deleted middle element shift one position to the left to fill the empty space, reducing the array size by one.

intermediate

Why can't we just remove the middle element without shifting in an array?

Because arrays have fixed positions, removing an element leaves a gap. Shifting elements keeps the array continuous without empty spots.

intermediate

What is the time complexity of deleting an element at the middle index in an array?

The time complexity is O(n) because shifting elements after the deleted index requires moving up to n/2 elements in the worst case.

What is the middle index of an array with 7 elements?

A 5

B 4

C 2

D 3

Middle index = 7 // 2 = 3.

After deleting the middle element, what happens to the elements on the right side?

A They shift right by one position

B They stay in the same position

C They shift left by one position

D They are deleted too

Elements after the deleted index shift left to fill the gap.

What is the main reason for shifting elements after deletion in an array?

A To increase the array size

B To keep the array continuous without gaps

C To sort the array

D To reverse the array

Shifting keeps the array continuous and avoids empty spaces.

What is the time complexity of deleting an element at the middle index in an array?

A O(n)

B O(log n)

C O(1)

D O(n^2)

Shifting elements requires O(n) time.

If an array has 6 elements, what is the middle index to delete?

A 3

B 5

C 4

D 2

Middle index = 6 // 2 = 3.

Explain step-by-step how to delete the middle element from an array and update the array.

Think about how elements move to fill the empty space.

Describe why deleting an element in the middle of an array is more costly than deleting from the end.

Consider how arrays store elements in continuous memory.

Practice

1. What happens when you delete the middle element from an array with an odd number of elements?

easy

A. The element at the exact middle index is removed, and the array size decreases by one.

B. The first element is removed instead of the middle one.

C. The array size remains the same but the middle element is set to zero.

D. The last element is removed instead of the middle one.

Solution

1. Step 1: Identify the middle index in an odd-length array

   For an array with odd length n, the middle index is n//2 (integer division).

2. Step 2: Remove the element at the middle index

   Deleting the element at this index reduces the array size by one and shifts elements after it left.

3. Final Answer:

   The element at the exact middle index is removed, and the array size decreases by one. -> Option A

4. Quick Check:

   Middle element removed = The element at the exact middle index is removed, and the array size decreases by one. [OK]

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

Common Mistakes:

• Removing first or last element instead of middle
• Not reducing array size after deletion
• Confusing middle index calculation

2. Which of the following Python statements correctly deletes the middle element from a list named arr with odd length?

easy

A. arr.pop(len(arr))

B. del arr[len(arr)//2]

C. arr.remove(len(arr)//2)

D. arr.delete(len(arr)//2)

Solution

1. Step 1: Understand Python deletion syntax

   The del statement removes an element at a specific index from a list.

2. Step 2: Calculate middle index and delete

   Using len(arr)//2 gives the middle index for odd length. So del arr[len(arr)//2] deletes the middle element correctly.

3. Final Answer:

   del arr[len(arr)//2] -> Option B

4. Quick Check:

   Correct syntax for deletion = del arr[len(arr)//2] [OK]

Hint: Use del with index: del arr[len(arr)//2] [OK]

Common Mistakes:

• Using remove() which deletes by value, not index
• Using pop() with wrong index
• Using non-existent delete() method

3. What is the output of the following code?

arr = [10, 20, 30, 40, 50]
del arr[len(arr)//2]
print(arr)

medium

A. [10, 30, 40, 50]

B. [10, 20, 30, 40]

C. [20, 30, 40, 50]

D. [10, 20, 40, 50]

Solution

1. Step 1: Calculate middle index

   Length of arr is 5, so middle index = 5 // 2 = 2.

2. Step 2: Delete element at index 2 and print

   Element at index 2 is 30. After deletion, arr becomes [10, 20, 40, 50].

3. Final Answer:

   [10, 20, 40, 50] -> Option D

4. Quick Check:

   Deleted arr[2] = 30, remaining = [10, 20, 40, 50] [OK]

Hint: Middle index 2 in 5 elements; delete arr[2] [OK]

Common Mistakes:

• Deleting wrong index (like 3 or 1)
• Confusing element value with index
• Printing before deletion

4. The following code is intended to delete the middle element from an array arr. What is the error?

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

medium

A. It deletes the last element instead of the middle one.

B. It causes an IndexError because remove expects an index.

C. It deletes the element with value 2 instead of the middle index element.

D. There is no error; it deletes the middle element correctly.

Solution

1. Step 1: Understand remove() method behavior

   remove(x) deletes the first element with value x, not at index x.

2. Step 2: Analyze the argument passed to remove()

   len(arr)//2 = 5//2 = 2, so arr.remove(2) deletes element with value 2, not element at index 2.

3. Final Answer:

   It deletes the element with value 2 instead of the middle index element. -> Option C

4. Quick Check:

   remove deletes by value, not index = It deletes the element with value 2 instead of the middle index element. [OK]

Hint: remove() deletes by value, del deletes by index [OK]

Common Mistakes:

• Confusing remove() with del or pop()
• Expecting remove() to delete by index
• Not calculating middle index correctly

5. Given an array arr = [5, 10, 15, 20, 25, 30] with even length, which code correctly deletes the middle element(s) so that after deletion the array is [5, 10, 25, 30]?

hard

A. del arr[len(arr)//2 - 1]; del arr[len(arr)//2]

B. del arr[len(arr)//2]; del arr[len(arr)//2 - 1]

C. arr.pop(len(arr)//2); arr.pop(len(arr)//2 - 1)

D. arr.remove(len(arr)//2); arr.remove(len(arr)//2 - 1)

Solution

1. Step 1: Identify middle indices for even length array

   Length is 6, middle indices are 2 and 3 (0-based), values 15 and 20.

2. Step 2: Delete elements at indices 2 and 3 accounting for length change

   del arr[len(arr)//2 - 1] deletes index 2 (15), array becomes [5, 10, 20, 25, 30]. Then del arr[len(arr)//2] deletes new index 2 (20), resulting in [5, 10, 25, 30].

3. Final Answer:

   del arr[len(arr)//2 - 1]; del arr[len(arr)//2] -> Option A

4. Quick Check:

   del arr[2] then del arr[2] (after shift) = [5, 10, 25, 30] [OK]

Hint: For even length, delete lower middle index first then the new middle index [OK]

Common Mistakes:

• Deleting higher index first without adjusting for length change
• Using pop() in wrong order causing incorrect shifts
• Using remove() which deletes by value