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

Recall & Review

beginner

What is the first step when inserting an element into the middle of an array?

Find the middle index where the new element will be inserted. For an array of size n, middle index is usually n/2 (integer division).

beginner

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, all elements from the middle index to the end must be moved one position to the right to make space.

beginner

In C++, what happens if you try to insert an element in a fixed-size array without shifting elements?

The new element will overwrite the existing element at that position, causing data loss and incorrect array contents.

intermediate

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

O(n) because shifting half of the elements (approximately n/2) to the right takes linear time.

beginner

Show the steps to insert 99 into the middle of array [10, 20, 30, 40, 50].

1. Find middle index: 5/2 = 2.
2. Shift elements from index 2 to right: [10, 20, 30, 30, 40, 50].
3. Insert 99 at index 2: [10, 20, 99, 30, 40, 50].

What is the middle index of an array with 8 elements (0-based indexing)?

A 3

B 5

C 4

D 2

Middle index = 8/2 = 4 (integer division).

When inserting an element in the middle of an array, what must you do before placing the new element?

A Shift elements to the right

B Delete the last element

C Replace the middle element directly

D Shift elements to the left

Elements from the middle index to the end must be shifted right to make space.

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

A O(log n)

B O(n)

C O(1)

D O(n log n)

Shifting elements takes linear time proportional to the number of elements.

If an array has 5 elements, what is the middle index for insertion?

A 4

B 1

C 3

D 2

Middle index = 5/2 = 2 (integer division).

What happens if you insert an element in the middle of a fixed-size array without shifting elements?

A Elements after middle are lost or overwritten

B Array throws an error

C Array size increases automatically

D Nothing happens

Without shifting, the new element overwrites the existing element at that position.

Explain the process of inserting an element into the middle of an array step-by-step.

Think about how to make space for the new element.

Describe why inserting in the middle of an array is slower than inserting at the end.

Consider what happens to existing elements.

Practice

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

easy

A. Adding a new element exactly in the center, shifting others right

B. Replacing the middle element with a new one

C. Adding a new element at the end of the array

D. Removing the middle element from the array

Solution

1. Step 1: Understand middle index insertion

   Inserting at the middle means placing a new element at the center position, pushing existing elements right.

2. Step 2: Differentiate from other operations

   Replacing or removing elements is not insertion; adding at the end is not middle insertion.

3. Final Answer:

   Adding a new element exactly in the center, shifting others right -> Option A

4. Quick Check:

   Middle insertion means insert and shift right [OK]

Hint: Middle insertion shifts elements right from center [OK]

Common Mistakes:

• Thinking insertion replaces the middle element
• Confusing insertion with appending at the end
• Assuming middle means removing element

2. Which of the following C++ code snippets correctly inserts an element `x` at the middle index of array `arr` of size `n`?

easy

A. arr[n] = x; for(int i = n/2; i < n; i++) arr[i] = arr[i+1];

B. for(int i = 0; i < n/2; i++) arr[i] = arr[i+1]; arr[n/2] = x;

C. arr[n/2] = x; for(int i = n/2; i < n; i++) arr[i+1] = arr[i];

D. for(int i = n; i > n/2; i--) arr[i] = arr[i-1]; arr[n/2] = x;

Solution

1. Step 1: Shift elements right from middle index

   Loop from end (n) down to middle (n/2 + 1) shifting elements right to make space.

2. Step 2: Insert element at middle index

   Assign new element x at index n/2 after shifting.

3. Final Answer:

   for(int i = n; i > n/2; i--) arr[i] = arr[i-1]; arr[n/2] = x; -> Option D

4. Quick Check:

   Shift right then insert at middle [OK]

Hint: Shift elements right from end to middle before insert [OK]

Common Mistakes:

• Shifting elements left instead of right
• Inserting before shifting elements
• Incorrect loop direction causing overwrite

3. What is the output array after inserting 99 at the middle index of arr = {10, 20, 30, 40, 50} using the correct insertion method?

medium

A. [10, 20, 30, 40, 99, 50]

B. [10, 20, 99, 30, 40, 50]

C. [10, 20, 30, 99, 40, 50]

D. [10, 20, 30, 40, 50, 99]

Solution

1. Step 1: Calculate middle index

   Array size n=5, middle index = n/2 = 2 (0-based indexing).

2. Step 2: Shift elements right and insert 99

   Shift elements from index 4 to 2 right by one position, then insert 99 at index 2.

3. Final Answer:

   [10, 20, 99, 30, 40, 50] -> Option B

4. Quick Check:

   Insert at index 2 shifts right [OK]

Hint: Middle index = size/2; shift right, then insert [OK]

Common Mistakes:

• Inserting at wrong index (like 3 or 4)
• Not shifting elements before insertion
• Appending at the end instead of middle

4. Identify the error in the following code snippet that inserts element `x` at the middle index of array `arr` of size `n`:

for(int i = n/2; i < n; i++) {
  arr[i+1] = arr[i];
}
arr[n/2] = x;

medium

A. Loop shifts elements left instead of right

B. Index out of bounds when accessing arr[i+1]

C. Loop direction causes overwriting elements

D. No error, code works correctly

Solution

1. Step 1: Analyze loop direction and effect

   The loop moves forward from middle to end, copying arr[i] to arr[i+1], overwriting elements before they are moved.

2. Step 2: Identify correct approach

   Elements must be shifted right starting from the end backward to avoid overwriting data.

3. Final Answer:

   Loop direction causes overwriting elements -> Option C

4. Quick Check:

   Shift right must go backward to avoid overwrite [OK]

Hint: Shift elements right backward from end to middle [OK]

Common Mistakes:

• Shifting elements forward causing data loss
• Ignoring array bounds when shifting
• Assuming forward loop works for shifting right

5. Given an array arr = {5, 10, 15, 20, 25, 30} of size 6, after inserting element 99 at the middle index, what will be the final array?

hard

A. [5, 10, 15, 99, 20, 25, 30]

B. [5, 10, 99, 15, 20, 25, 30]

C. [5, 10, 15, 20, 99, 25, 30]

D. [5, 10, 15, 20, 25, 30, 99]

Solution

1. Step 1: Calculate middle index for even-sized array

   Array size n=6, middle index = n/2 = 3 (0-based indexing).

2. Step 2: Shift elements right from index 5 to 3

   Shift elements at indices 5,4,3 one position right to make space at index 3.

3. Step 3: Insert 99 at middle index

   Place 99 at index 3 after shifting.

4. Final Answer:

   [5, 10, 15, 99, 20, 25, 30] -> Option A

5. Quick Check:

   Insert at index 3 shifts right [OK]

Hint: For even size, middle = size/2; shift right, then insert [OK]

Common Mistakes:

• Inserting at index 2 instead of 3
• Not shifting elements before insertion
• Appending at the end instead of middle