Array Insertion at End in DSA Java - 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.

public class ArrayInsertion {
    public static int insertAtEnd(int[] arr, int size, int value) {
        arr[size] = value;  // Insert value at the end
        return size + 1;    // Return new size
    }
}
    

This code adds a new value at the end of an array and returns the updated size.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single direct assignment to the array at the last index.
• How many times: Exactly once per insertion.

How Execution Grows With Input

Adding one item at the end always takes the same amount of work, no matter how big the array is.

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

Pattern observation: The work stays the same even as the array grows larger.

Final Time Complexity

Time Complexity: O(1)

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

Common Mistake

[X] Wrong: "Adding at the end takes longer as the array grows 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 directly at the next free spot.

Interview Connect

Knowing that adding at the end of an array is quick helps you understand when arrays are a good choice for storing data.

Self-Check

"What if the array is full and we need to create a bigger array to insert the new item? How would the time complexity change?"

Practice

1. What happens when you insert an element at the end of a fixed-size array in Java without resizing?

easy

A. The insertion throws an error if the array is full

B. The element is added at the next free position if available

C. The array automatically resizes to fit the new element

D. The element replaces the last element if the array is full

Solution

1. Step 1: Understand fixed-size array behavior

   Java arrays have a fixed size and cannot grow automatically. Attempting arr[size] where size == length throws ArrayIndexOutOfBoundsException.

2. Step 2: Inserting at end when full

   Standard insertion arr[size++] = element; if full (size == arr.length), accesses arr[length] and throws runtime error.

3. Final Answer:

   The insertion throws an error if the array is full -> Option A

4. Quick Check:

   Fixed-size array throws error when full [OK]

Hint: Fixed arrays don't resize; throws error if full [OK]

Common Mistakes:

• Assuming arrays resize automatically
• Thinking insertion overwrites last element
• Believing new element is added beyond array size

2. Which of the following is the correct syntax to insert an element at the end of an array in Java if the array has space?

easy

A. arr[size] = newElement; size++;

B. arr[arr.length - 1] = newElement;

C. arr[arr.length] = newElement;

D. arr.add(newElement);

Solution

1. Step 1: Understand array indexing and size tracking

   Arrays use zero-based indexing; last index is length-1. We track current size separately.

2. Step 2: Insert element at next free position

   Use size as index to insert, then increment size to reflect new element count.

3. Final Answer:

   arr[size] = newElement; size++; -> Option A

4. Quick Check:

   Use size as index and increment after insertion [OK]

Hint: Use size variable as index, then increment size [OK]

Common Mistakes:

• Using arr.length as index (out of bounds)
• Trying to use arr.add() which is for lists
• Overwriting last element without size tracking

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

int[] arr = new int[5];
int size = 0;
arr[size++] = 10;
arr[size++] = 20;
arr[size++] = 30;
System.out.print(java.util.Arrays.toString(arr));

medium

A. [10, 20, 30]

B. [10, 20, 30, 0, 0]

C. [10, 20, 30, 30, 30]

D. [0, 10, 20, 30, 0]

Solution

1. Step 1: Trace insertions with size increment

   Elements 10, 20, 30 are inserted at indexes 0, 1, 2 respectively; size increments after each insertion.

2. Step 2: Understand default array values

   Remaining positions (indexes 3 and 4) remain 0 as default for int arrays.

3. Final Answer:

   [10, 20, 30, 0, 0] -> Option B

4. Quick Check:

   Inserted elements at start; rest are zeros [OK]

Hint: Inserted elements fill start; rest remain default zero [OK]

Common Mistakes:

• Assuming array shrinks to inserted elements only
• Confusing index positions
• Expecting uninitialized elements to be null

4. Identify the error in the following code that tries to insert an element at the end of an array:

int[] arr = new int[3];
int size = 3;
arr[size] = 5;

medium

A. Compilation error due to wrong syntax

B. No error; element inserted at the end

C. ArrayIndexOutOfBoundsException because size equals array length

D. Logical error; element overwrites first element

Solution

1. Step 1: Check array size and index used

   Array length is 3, valid indexes are 0,1,2. Using index 3 causes error.

2. Step 2: Understand runtime exception

   Accessing arr[3] throws ArrayIndexOutOfBoundsException at runtime.

3. Final Answer:

   ArrayIndexOutOfBoundsException because size equals array length -> Option C

4. Quick Check:

   Index equals length causes runtime error [OK]

Hint: Index must be less than array length to avoid error [OK]

Common Mistakes:

• Assuming index == length is valid
• Expecting compile-time error instead of runtime
• Ignoring size variable correctness

5. You have an integer array of size 4: int[] arr = {1, 2, 3, 4}; and a variable size = 4;. You want to insert 5 at the end but the array is full. Which approach correctly adds 5 at the end without losing existing data?

hard

A. Overwrite arr[3] with 5 directly

B. Increase size variable to 5 and assign arr[4] = 5

C. Use arr[size] = 5 without resizing

D. Create a new array of size 5, copy old elements, then add 5 at index 4

Solution

1. Step 1: Recognize fixed array size limitation

   Original array size is 4; cannot add element beyond index 3 without resizing.

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

   Create new array of size 5, copy existing elements, then insert 5 at index 4.

3. Final Answer:

   Create a new array of size 5, copy old elements, then add 5 at index 4 -> Option D

4. Quick Check:

   Resize by new array and copy before insertion [OK]

Hint: Resize array by copying before adding new element [OK]

Common Mistakes:

• Trying to insert without resizing
• Overwriting last element losing data
• Assuming size variable controls array length