Array Insertion at Middle Index in DSA Python

Mental Model

To insert a new value in the middle of an array, we shift all elements from that position to the right by one place to make space.

Analogy: Imagine a row of chairs with people sitting. To add a new person in the middle, everyone from that spot onward stands up and moves one chair to the right, freeing a chair in the middle.

Index: 0   1   2   3   4
Array: [1] [2] [3] [4] [5]

Dry Run Walkthrough

Input: array: [1, 2, 3, 4, 5], insert value 99 at index 2

Goal: Insert 99 at index 2 and shift elements right to keep order

Step 1: Start shifting elements from the last index to index 2 one step right

Index: 0   1   2   3   4   5
Array: [1] [2] [3] [4] [5] [5]

Why: We copy the last element to the next free spot to avoid overwriting

Step 2: Shift element at index 3 to index 4

Index: 0   1   2   3   4   5
Array: [1] [2] [3] [4] [4] [5]

Why: Continue shifting elements right to make space at index 2

Step 3: Shift element at index 2 to index 3

Index: 0   1   2   3   4   5
Array: [1] [2] [3] [3] [4] [5]

Why: Final shift to free index 2 for new value

Step 4: Insert value 99 at index 2

Index: 0   1   2   3   4   5
Array: [1] [2] [99] [3] [4] [5]

Why: Place new value in the freed spot

Result:

Index: 0   1   2   3   4   5
Array: [1] [2] [99] [3] [4] [5]

Annotated Code

DSA Python

class ArrayInsertion:
    def __init__(self, arr):
        self.arr = arr
        self.size = len(arr)

    def insert_at_middle(self, index, value):
        # Shift elements right from the end to index
        self.arr.append(0)  # Increase size by one
        for i in range(self.size, index, -1):
            self.arr[i] = self.arr[i - 1]  # Shift right
        self.arr[index] = value  # Insert new value
        self.size += 1

    def __str__(self):
        return ' -> '.join(str(x) for x in self.arr) + ' -> null'

# Driver code
array = [1, 2, 3, 4, 5]
obj = ArrayInsertion(array)
obj.insert_at_middle(2, 99)
print(obj)

self.arr.append(0) # Increase size by one

Expand array size by adding a placeholder at the end

for i in range(self.size, index, -1):

Loop backward from last element to index to shift elements right

self.arr[i] = self.arr[i - 1] # Shift right

Move element one position right to free space

self.arr[index] = value # Insert new value

Place the new value at the target index

self.size += 1

Update size to reflect new element

Output

1 -> 2 -> 99 -> 3 -> 4 -> 5 -> null

Complexity Analysis

Time: O(n) because in the worst case we shift half of the elements to the right

Space: O(1) because insertion is done in place with only one extra slot added

vs Alternative: Compared to creating a new array and copying all elements, this method is more space efficient but still requires shifting elements which takes linear time

Edge Cases

Insert at index 0 (start of array)

All elements shift right, new value placed at start

DSA Python

for i in range(self.size, index, -1):

Insert at last index (end of array)

No shifting needed, new value appended

DSA Python

for i in range(self.size, index, -1):

Insert into empty array

Array grows to size 1 with new value

DSA Python

self.arr.append(0)

When to Use This Pattern

When you need to add an element inside an array and keep order, think about shifting elements right to make space before insertion.

Common Mistakes

Mistake: Shifting elements left to right causing overwriting of data
Fix: Always shift elements from right to left (end to index) to avoid overwriting

Mistake: Not increasing array size before shifting
Fix: Append a placeholder to increase array size before shifting elements

Summary

It inserts a new value at a given middle index by shifting elements right to make space.

Use it when you want to add an element inside an array without losing existing data order.

The key is to shift elements from the end towards the insertion point to avoid overwriting.

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