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

Recall & Review

beginner

What does 'Array Insertion at Beginning' mean?

It means adding a new element at the very first position of an array, shifting all other elements one place to the right.

beginner

Why do we need to shift elements when inserting at the beginning of an array?

Because arrays have fixed positions, to insert at the start, all existing elements must move one step right to make space for the new element.

intermediate

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

The time complexity is O(n), where n is the number of elements, because all elements must be shifted one position.

beginner

Show the steps to insert 5 at the beginning of array [1, 2, 3, 4].

Step 1: Shift 4 to position 5
Step 2: Shift 3 to position 4
Step 3: Shift 2 to position 3
Step 4: Shift 1 to position 2
Step 5: Insert 5 at position 1
Result: [5, 1, 2, 3, 4]

intermediate

What happens if the array is full when inserting at the beginning?

If the array is full, you cannot insert a new element unless you resize the array or remove an element first.

What is the first step when inserting an element at the beginning of an array?

A Shift all elements one position to the right

B Replace the first element

C Add element at the end

D Delete the last element

To insert at the beginning, all elements must move right to make space.

What is the time complexity of inserting at the beginning of an array with n elements?

A O(n^2)

B O(1)

C O(log n)

D O(n)

All n elements must be shifted, so time complexity is O(n).

If an array has elements [10, 20, 30] and you insert 5 at the beginning, what is the new array?

A [5, 20, 30]

B [10, 20, 30, 5]

C [5, 10, 20, 30]

D [10, 5, 20, 30]

The new element 5 goes at the start, shifting others right.

What must you check before inserting at the beginning of an array?

A If the array has space

B If the array is sorted

C If the array is empty

D If the array is reversed

You must ensure there is space to insert a new element.

Which data structure allows faster insertion at the beginning than an array?

A Stack

B Linked List

C Queue

D Heap

Linked lists can insert at the beginning in O(1) time without shifting.

Explain how to insert an element at the beginning of an array and why shifting is necessary.

Think about the positions of elements and how arrays store data.

Describe what happens if you try to insert at the beginning of a full array and how to handle it.

Consider array capacity and memory.

Practice

1. What happens when you insert an element at the beginning of an array in C++?

easy

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

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

C. The array size decreases by one.

D. The array elements are sorted automatically.

Solution

1. Step 1: Understand array structure

   An array stores elements in continuous memory locations.

2. Step 2: Effect of insertion at beginning

   To insert at the start, all elements must move right to free the first position.

3. Final Answer:

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

4. Quick Check:

   Insertion at start shifts elements right = B [OK]

Hint: Insertion at start shifts elements right to free first slot [OK]

Common Mistakes:

• Thinking new element replaces first without shifting
• Assuming array size decreases
• Believing array sorts automatically

2. Which of the following is the correct syntax to insert an element `x` at the beginning of an array `arr` of size `n` in C++ (assuming enough space)?

easy

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

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

C. for(int i = n; i > 0; i--) arr[i] = arr[i-1]; arr[0] = x; n++;

D. arr[n] = x; n++;

Solution

1. Step 1: Shift elements right from end

   Loop from last index `n` down to 1, moving each element to the right by one.

2. Step 2: Insert new element at index 0 and increase size

   Place `x` at `arr[0]` and increment `n`.

3. Final Answer:

   for(int i = n; i > 0; i--) arr[i] = arr[i-1]; arr[0] = x; n++; -> Option C

4. Quick Check:

   Shift right from end, insert at 0 = C [OK]

Hint: Shift from end to start, then insert at zero index [OK]

Common Mistakes:

• Shifting from start to end overwrites data
• Not incrementing array size
• Inserting without shifting elements

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

int arr[5] = {2, 4, 6, 8, 10};
int n = 5;
int x = 1;
for(int i = n; i > 0; i--) {
  arr[i] = arr[i-1];
}
arr[0] = x;
n++;
for(int i = 0; i < n; i++) {
  std::cout << arr[i] << " ";
}

medium

A. 2 4 6 8 10 1

B. 1 2 4 6 8 10

C. 1 2 4 6 8

D. 2 4 6 8 10

Solution

1. Step 1: Shift elements right to make space

   Elements move right: arr[5]=arr[4]=10, arr[4]=arr[3]=8, arr[3]=arr[2]=6, arr[2]=arr[1]=4, arr[1]=arr[0]=2.

2. Step 2: Insert 1 at arr[0] and print

   arr[0]=1, array becomes [1,2,4,6,8,10], printed with space.

3. Final Answer:

   1 2 4 6 8 10 -> Option B

4. Quick Check:

   Shift right + insert 1 at start = A [OK]

Hint: Shift right, insert new at zero, print all elements [OK]

Common Mistakes:

• Not shifting elements correctly
• Printing old array size
• Inserting at wrong index

4. Identify the error in this code snippet that inserts `x` at the beginning of array `arr` of size `n`:

for(int i = 0; i < n; i++) {
  arr[i+1] = arr[i];
}
arr[0] = x;
n++;

medium

A. Loop shifts elements left instead of right, overwriting data.

B. Array size `n` is not incremented after insertion.

C. New element is inserted at wrong index.

D. Loop should start from `n` and go down to 1 to avoid overwrite.

Solution

1. Step 1: Analyze loop direction

   Loop moves from 0 to n-1, shifting elements forward, overwriting original data.

2. Step 2: Correct loop direction

   Loop must run backward from n to 1 to shift elements safely without overwrite.

3. Final Answer:

   Loop should start from `n` and go down to 1 to avoid overwrite. -> Option D

4. Quick Check:

   Backward loop prevents overwrite = D [OK]

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

Common Mistakes:

• Shifting elements forward overwrites data
• Forgetting to increment array size
• Inserting element at wrong position

5. Given an array `arr` of size `n` with elements sorted in ascending order, how can you insert a new element `x` at the beginning and keep the array sorted?

hard

A. If `x` is smaller than `arr[0]`, shift elements right and insert `x` at start; else find correct position.

B. Insert `x` at the beginning and then sort the entire array again.

C. Always insert `x` at the beginning without shifting elements.

D. Replace the last element with `x` if `x` is smaller than last element.

Solution

1. Step 1: Check if `x` is smaller than first element

   If yes, shift all elements right and insert `x` at index 0 to keep order.

2. Step 2: If `x` is not smallest, find correct position

   Find proper index to insert `x` to maintain sorted order, not necessarily at start.

3. Final Answer:

   If `x` is smaller than `arr[0]`, shift elements right and insert `x` at start; else find correct position. -> Option A

4. Quick Check:

   Insert at start only if smaller, else find position = A [OK]

Hint: Insert at start only if smaller; else find correct sorted position [OK]

Common Mistakes:

• Always inserting at start breaks sorting
• Sorting entire array after insertion wastes time
• Replacing last element loses data