Array Insertion at Beginning in DSA C#

Mental Model

To insert a new item at the start of an array, we must move all existing items one step to the right to make space.

Analogy: Imagine a row of chairs with people sitting. To add a new person at the first chair, everyone must stand up and move one chair to the right, freeing the first chair.

Index: 0   1   2   3   4
Array: [1]->[2]->[3]->[4]->[5]
Insert new value 0 at index 0

Dry Run Walkthrough

Input: array: [1, 2, 3, 4, 5], insert value 0 at beginning

Goal: Insert 0 at the start and shift all elements right

Step 1: Shift element at index 4 (5) to index 5

[1]->[2]->[3]->[4]->[5]->[5]
Indexes: 0 1 2 3 4 5

Why: Make space at the end to avoid overwriting data

Step 2: Shift element at index 3 (4) to index 4

[1]->[2]->[3]->[4]->[4]->[5]
Indexes: 0 1 2 3 4 5

Why: Move elements right to free index 0

Step 3: Shift element at index 2 (3) to index 3

[1]->[2]->[3]->[3]->[4]->[5]
Indexes: 0 1 2 3 4 5

Why: Continue shifting elements right

Step 4: Shift element at index 1 (2) to index 2

[1]->[2]->[2]->[3]->[4]->[5]
Indexes: 0 1 2 3 4 5

Why: Keep shifting elements right

Step 5: Shift element at index 0 (1) to index 1

[1]->[1]->[2]->[3]->[4]->[5]
Indexes: 0 1 2 3 4 5

Why: Final shift to free index 0

Step 6: Insert new value 0 at index 0

[0]->[1]->[2]->[3]->[4]->[5]
Indexes: 0 1 2 3 4 5

Why: Place new value at the beginning

Result:

[0]->[1]->[2]->[3]->[4]->[5]

Annotated Code

DSA C#

using System;

class ArrayInsertion
{
    public static int[] InsertAtBeginning(int[] arr, int value)
    {
        int n = arr.Length;
        int[] newArr = new int[n + 1];
        // Shift elements right by one
        for (int i = n - 1; i >= 0; i--)
        {
            newArr[i + 1] = arr[i];
        }
        // Insert new value at index 0
        newArr[0] = value;
        return newArr;
    }

    static void Main()
    {
        int[] arr = {1, 2, 3, 4, 5};
        int valueToInsert = 0;
        int[] result = InsertAtBeginning(arr, valueToInsert);
        // Print array
        for (int i = 0; i < result.Length; i++)
        {
            Console.Write(result[i]);
            if (i != result.Length - 1) Console.Write(" -> ");
        }
        Console.WriteLine();
    }
}

for (int i = n - 1; i >= 0; i--) { newArr[i + 1] = arr[i]; }

Shift all elements one position right to make space at index 0

newArr[0] = value;

Insert the new value at the beginning of the array

Output

0 -> 1 -> 2 -> 3 -> 4 -> 5

Complexity Analysis

Time: O(n) because we must move all n elements one step to the right

Space: O(n) because we create a new array with one extra space

vs Alternative: In-place insertion is not possible in fixed-size arrays without overwriting, so creating a new array is necessary

Edge Cases

empty array

Returns a new array with only the inserted value

DSA C#

int n = arr.Length;

single element array

Shifts the single element right and inserts new value at start

DSA C#

for (int i = n - 1; i >= 0; i--)

When to Use This Pattern

When you need to add an element at the start of a fixed-size array, use shifting and a new array to avoid overwriting data.

Common Mistakes

Mistake: Shifting elements left to right instead of right to left causes overwriting data
Fix: Always shift elements from the end towards the start to preserve data

Summary

Inserts a new element at the beginning of an array by shifting existing elements right.

Use when you need to add an item at the start but arrays have fixed size.

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

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