Array Insertion at Beginning in DSA C# - Time & Space Complexity

Time Complexity: Array Insertion at Beginning

O(n)

Understanding Time Complexity

We want to understand how long it takes to add a new item at the start of an array.

How does the time needed change as the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int[] InsertAtBeginning(int[] arr, int value) {
    int n = arr.Length;
    int[] newArr = new int[n + 1];
    newArr[0] = value;
    for (int i = 0; i < n; i++) {
        newArr[i + 1] = arr[i];
    }
    return newArr;
}
    

This code creates a new array and copies all elements from the old array, shifting them right to insert the new value at the start.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop copying each element from the old array to the new array.
• How many times: Exactly once for each element in the original array (n times).

How Execution Grows With Input

As the array size grows, the number of copy steps grows the same way.

Input Size (n)	Approx. Operations
10	About 10 copy steps
100	About 100 copy steps
1000	About 1000 copy steps

Pattern observation: The work grows directly with the number of items; doubling the array size roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the beginning grows linearly with the array size.

Common Mistake

[X] Wrong: "Inserting at the start of an array is always fast and constant time like adding at the end."

[OK] Correct: Because arrays need to move all existing items to make space at the start, so the time grows with the array size.

Interview Connect

Knowing this helps you explain why arrays are not ideal for frequent insertions at the start, and shows you understand how data structure choices affect performance.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity change?"

Practice

1. What happens when you insert an element at the beginning of a fixed-size array in C#?

easy

A. The last element is removed and the new element is added at the start.

B. The new element replaces the first element without shifting others.

C. The array size automatically increases to fit the new element.

D. All existing elements shift one position to the right to make space.

Solution

1. Step 1: Understand fixed-size array behavior

   In C#, arrays have fixed size, so to insert at the beginning, elements must shift right.

2. Step 2: Effect of insertion at index 0

   The element at index 0 is replaced by the new element, and all others move one index higher.

3. Final Answer:

   All existing elements shift one position to the right to make space. -> Option D

4. Quick Check:

   Insert at start = shift right [OK]

Hint: Insert at start means shift all elements right [OK]

Common Mistakes:

• Thinking array size grows automatically
• Replacing first element without shifting
• Removing last element silently

2. Which of the following C# code snippets correctly inserts an integer 5 at the beginning of an array arr of size 5, shifting elements right?

easy

A. for (int i = arr.Length - 1; i > 0; i--) { arr[i] = arr[i - 1]; } arr[0] = 5;

B. for (int i = 0; i < arr.Length - 1; i++) { arr[i] = arr[i + 1]; } arr[arr.Length - 1] = 5;

C. arr[0] = 5; // No shifting needed

D. arr[arr.Length] = 5; // Add at end

Solution

1. Step 1: Identify correct loop for shifting right

   Loop must start from the end and move elements one step right to avoid overwriting.

2. Step 2: Assign new value at index 0

   After shifting, assign 5 to arr[0].

3. Final Answer:

   for (int i = arr.Length - 1; i > 0; i--) { arr[i] = arr[i - 1]; } arr[0] = 5; -> Option A

4. Quick Check:

   Shift right from end, then insert [OK]

Hint: Shift from end to start to avoid overwrite [OK]

Common Mistakes:

• Shifting left instead of right
• Assigning without shifting
• Using invalid index arr.Length

3. What is the output of the following C# code?

int[] arr = {10, 20, 30, 40, 50};
for (int i = arr.Length - 1; i > 0; i--) {
    arr[i] = arr[i - 1];
}
arr[0] = 5;
foreach (int num in arr) {
    Console.Write(num + " ");
}

medium

A. 5 10 20 30 50

B. 5 10 20 30 40

C. 5 20 30 40 50

D. 10 5 20 30 40

Solution

1. Step 1: Shift elements right

   Elements move right: arr[4]=arr[3]=40, arr[3]=arr[2]=30, arr[2]=arr[1]=20, arr[1]=arr[0]=10

2. Step 2: Insert 5 at index 0

   arr[0] = 5

3. Final Answer:

   5 10 20 30 40 -> Option B

4. Quick Check:

   Shift right + insert 5 at start = 5 10 20 30 40 [OK]

Hint: Trace shifts from end, then insert new value [OK]

Common Mistakes:

• Not shifting elements correctly
• Overwriting elements before shifting
• Incorrect final array print

4. The following code attempts to insert 99 at the beginning of an array arr but produces incorrect output. What is the error?

int[] arr = {1, 2, 3, 4, 5};
for (int i = 0; i < arr.Length - 1; i++) {
    arr[i + 1] = arr[i];
}
arr[0] = 99;

medium

A. The loop shifts elements left instead of right, overwriting data.

B. The assignment to arr[0] should be inside the loop.

C. The loop index range is incorrect; it should start from the end.

D. The array size is too small to insert a new element.

Solution

1. Step 1: Analyze loop direction and range

   The loop starts from 0 and moves forward, causing overwriting of elements.

2. Step 2: Correct loop should start from end

   To shift right safely, loop must start from last index and move backward.

3. Final Answer:

   The loop index range is incorrect; it should start from the end. -> Option C

4. Quick Check:

   Shift right requires backward loop [OK]

Hint: Shift right needs backward loop from end [OK]

Common Mistakes:

• Looping forward overwrites elements
• Assigning new value inside loop
• Ignoring fixed array size

5. You have an array arr = new int[6] {0, 1, 2, 3, 4, 5} and want to insert a new element 99 at the beginning without losing any data. Which approach correctly handles this?

hard

A. Create a new array of size 7, set arr2[0] = 99, then copy all elements of arr to arr2 starting at index 1.

B. Shift all elements right by one and assign 99 to arr[0], but last element is lost.

C. Replace arr[0] with 99 directly without shifting elements.

D. Use a List<int> instead of array to insert at beginning easily.

Solution

1. Step 1: Understand fixed array size limitation

   Original array size is 6, so inserting without losing data requires a bigger array.

2. Step 2: Create new larger array and copy elements

   Create new array size 7, assign 99 at index 0, then copy original elements starting at index 1.

3. Final Answer:

   Create a new array of size 7, set arr2[0] = 99, then copy all elements of arr to arr2 starting at index 1. -> Option A

4. Quick Check:

   New bigger array + copy elements = safe insertion [OK]

Hint: Use bigger array and copy to insert without loss [OK]

Common Mistakes:

• Trying to insert in fixed-size array losing last element
• Replacing without shifting
• Ignoring better data structures like List