Array Insertion at Middle Index in DSA Python - Execution Trace

Concept Flow - Array Insertion at Middle Index

Start with original array

↓

Calculate middle index = length // 2

↓

Shift elements right from end to middle

↓

Insert new element at middle index

↓

Array updated with new element in middle

This flow shows how to insert a new element in the middle of an array by shifting elements right and placing the new element at the middle index.

Execution Sample

DSA Python

arr = [10, 20, 30, 40, 50]
mid = len(arr) // 2
new_val = 25
arr.append(0)  # Increase array size by 1 to accommodate new element
for i in range(len(arr)-2, mid-1, -1):
    arr[i+1] = arr[i]
arr[mid] = new_val

This code inserts 25 into the middle of the array by shifting elements right from the middle index.

Execution Table

Step	Operation	Index i	Array State	Pointer Changes	Visual State
1	Calculate middle index	-	[10, 20, 30, 40, 50]	mid = 2	10 -> 20 -> 30 -> 40 -> 50 -> null
2	Start shifting elements right	4	[10, 20, 30, 40, 50, 50]	arr[5] = arr[4]	10 -> 20 -> 30 -> 40 -> 50 -> 50 -> null
3	Shift element right	3	[10, 20, 30, 40, 40, 50]	arr[4] = arr[3]	10 -> 20 -> 30 -> 40 -> 40 -> 50 -> null
4	Shift element right	2	[10, 20, 30, 30, 40, 50]	arr[3] = arr[2]	10 -> 20 -> 30 -> 30 -> 40 -> 50 -> null
5	Insert new element	2	[10, 20, 25, 30, 40, 50]	arr[2] = 25	10 -> 20 -> 25 -> 30 -> 40 -> 50 -> null
6	End	-	[10, 20, 25, 30, 40, 50]	-	10 -> 20 -> 25 -> 30 -> 40 -> 50 -> null

💡 All elements shifted right from index 2, new element inserted at middle index 2

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
arr	[10, 20, 30, 40, 50]	[10, 20, 30, 40, 50, 50]	[10, 20, 30, 40, 40, 50]	[10, 20, 30, 30, 40, 50]	[10, 20, 25, 30, 40, 50]	[10, 20, 25, 30, 40, 50]
mid	2	2	2	2	2	2
i	-	4	3	2	2	-

Key Moments - 3 Insights

Why do we shift elements starting from the end towards the middle?

We shift elements from the end to avoid overwriting values before moving them. See execution_table steps 2 to 4 where elements are moved right one by one.

Why is the middle index calculated as length // 2?

Using integer division ensures the middle index is an integer position in the array. This is shown in execution_table step 1 where mid = 2 for length 5.

What happens if we insert without shifting elements first?

Without shifting, the element at the middle index would be overwritten and lost. The shifting steps (2-4) prevent this by making space.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the array state?

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

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

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

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

💡 Hint

Check the 'Array State' column at step 3 in the execution_table.

At which step is the new element inserted into the array?

A Step 4

B Step 5

C Step 2

D Step 6

💡 Hint

Look for the operation 'Insert new element' in the execution_table.

If the array length was 6 instead of 5, what would be the middle index?

A 3

B 4

C 2

D 5

💡 Hint

Middle index is calculated as length // 2, see variable_tracker for 'mid'.

Concept Snapshot

Array Insertion at Middle Index:
- Calculate middle index as length // 2
- Shift elements right from end to middle
- Insert new element at middle index
- Shifting prevents overwriting existing elements
- Resulting array size increases by 1

Full Transcript

This concept shows how to insert a new element into the middle of an array. First, we find the middle index by dividing the array length by two using integer division. Then, starting from the last element, we shift each element one position to the right until we reach the middle index. This creates space at the middle index. Finally, we place the new element at the middle index. This process ensures no data is lost by overwriting. The array size increases by one after insertion.