Array Insertion at End in DSA C - Time & Space Complexity

Time Complexity: Array Insertion at End

O(1)

Understanding Time Complexity

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

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void insertAtEnd(int arr[], int *size, int capacity, int value) {
    if (*size < capacity) {
        arr[*size] = value;
        (*size)++;
    }
}
    

This code adds a new value at the end of the array if there is space available.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning the new value to the last position in the array.
• How many times: Exactly once per insertion.

How Execution Grows With Input

Adding one item at the end always takes the same small number of steps, no matter how big the array is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time stays the same even if the array grows larger.

Final Time Complexity

Time Complexity: O(1)

This means adding an item at the end takes a fixed amount of time regardless of array size.

Common Mistake

[X] Wrong: "Adding at the end takes longer as the array gets bigger because we have to move all elements."

[OK] Correct: We do not move existing elements when adding at the end; we just place the new item in the next free spot.

Interview Connect

Knowing that adding at the end is quick helps you explain why some data structures are faster for certain tasks.

Self-Check

"What if the array is full and we need to resize it before adding? How would the time complexity change?"

Practice

1. What happens when you insert an element at the end of an array in C if the array has enough space?

easy

A. The element is added at the last position and the array size increases by one.

B. The element replaces the first element of the array.

C. The array size remains the same and the element is ignored.

D. The array is sorted automatically after insertion.

Solution

1. Step 1: Understand array insertion at end

   When an element is inserted at the end, it is placed at the next free index if space is available.

2. Step 2: Effect on array size

   The logical size of the array increases by one because a new element is added.

3. Final Answer:

   The element is added at the last position and the array size increases by one. -> Option A

4. Quick Check:

   Insert at end adds element and increases size [OK]

Hint: Insert at end adds element at next free index [OK]

Common Mistakes:

• Thinking array size changes physically (fixed size in C)
• Assuming insertion replaces existing elements
• Believing array sorts automatically after insertion

2. Which of the following is the correct syntax to insert an element 'x' at the end of an array 'arr' with current size 'n' in C?

easy

A. arr[n+1] = x; n++;

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

C. arr[n-1] = x; n++;

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

Solution

1. Step 1: Identify correct index for insertion

   The next free position is at index 'n' since array indexing starts at 0 and current size is 'n'.

2. Step 2: Update size after insertion

   After inserting, increment 'n' to reflect the new size.

3. Final Answer:

   arr[n] = x; n++; -> Option B

4. Quick Check:

   Insert at arr[n], then increment n [OK]

Hint: Insert at arr[n], then increase size n [OK]

Common Mistakes:

• Using arr[n+1] causes out-of-bounds error
• Using arr[n-1] overwrites last element
• Confusing element and index positions

3. What will be the output of the following C code?

int arr[5] = {1, 2, 3};
int n = 3;
arr[n] = 4;
n++;
for(int i = 0; i < n; i++) {
    printf("%d ", arr[i]);
}

medium

A. 1 2 3 4

B. 1 2 3

C. 1 2 3 0

D. Compilation error

Solution

1. Step 1: Insert element at arr[3]

   arr[3] is assigned 4, so array becomes {1, 2, 3, 4, ?}.

2. Step 2: Increment size and print elements

   n becomes 4, loop prints arr[0] to arr[3]: 1 2 3 4.

3. Final Answer:

   1 2 3 4 -> Option A

4. Quick Check:

   Inserted 4 at end, printed all elements [OK]

Hint: Insert at arr[n], increment n, print up to n [OK]

Common Mistakes:

• Ignoring increment of n, printing only first 3 elements
• Assuming uninitialized arr[3] is zero
• Confusing array size and capacity

4. Find the error in the following code snippet that inserts an element at the end of an array:

int arr[5] = {10, 20, 30};
int n = 3;
arr[n+1] = 40;
n++;

medium

A. Array initialization is incorrect.

B. The size 'n' is not incremented correctly.

C. No error, code works fine.

D. The element is inserted at wrong index (arr[n+1] instead of arr[n]).

Solution

1. Step 1: Check insertion index

   Inserting at arr[n+1] means arr[4], skipping arr[3], which is incorrect for sequential insertion.

2. Step 2: Consequence of wrong index

   This causes a gap in the array; correct index is arr[n].

3. Final Answer:

   The element is inserted at wrong index (arr[n+1] instead of arr[n]). -> Option D

4. Quick Check:

   Insert at arr[n], not arr[n+1] [OK]

Hint: Insert at arr[n], not arr[n+1] to avoid errors [OK]

Common Mistakes:

• Using arr[n+1] instead of arr[n]
• Not updating size after insertion
• Ignoring array bounds

5. Given an array int arr[6] = {5, 10, 15, 20}; with current size n = 4, which code snippet correctly inserts the element 25 at the end and prints the updated array?

medium

A. arr[n-1] = 25; n++; for(int i=0; i

B. arr[n+1] = 25; n++; for(int i=0; i

C. arr[n] = 25; n++; for(int i=0; i

D. arr[5] = 25; n = 5; for(int i=0; i

Solution

1. Step 1: Identify correct insertion index

   Current size n=4 (indices 0-3 used), so end insertion at arr[4] (arr[n]), then n=5.

2. Step 2: Evaluate options

   A: arr[4]=25, n=5, prints 5 10 15 20 25 [correct].
   B: arr[5]=25, n=5, prints 0-4 (5 10 15 20 <uninit>) [misses 25].
   C: arr[3]=25 overwrites 20 [wrong].
   D: arr[5]=25, n=5, prints 0-4 [misses 25].

3. Final Answer:

   arr[n] = 25; n++; for(int i=0; i -> Option C

4. Quick Check:

   Insert at arr[n], n++, print 0 to n-1 [OK]

Hint: Insert at next free index, update size, print all elements [OK]

Common Mistakes:

• Inserting at wrong index causing overwrite
• Not updating size correctly
• Printing wrong number of elements