Array Declaration and Initialization in DSA C# - Time & Space Complexity

Time Complexity: Array Declaration and Initialization

O(n)

Understanding Time Complexity

We want to understand how long it takes to create and fill an array when we declare it.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int[] numbers = new int[5];
for (int i = 0; i < numbers.Length; i++)
{
    numbers[i] = i * 2;
}
    

This code creates an array of 5 integers and fills it with values.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that assigns values to each array element.
• How many times: It runs once for each element, so 5 times here, but generally n times for size n.

How Execution Grows With Input

As the array size grows, the number of assignments grows the same way.

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

Pattern observation: The work grows directly with the number of elements.

Final Time Complexity

Time Complexity: O(n)

This means the time to fill the array grows in a straight line with the array size.

Common Mistake

[X] Wrong: "Declaring an array is instant and does not depend on size."

[OK] Correct: Actually, initializing the array elements takes time proportional to the size, because each element is set up.

Interview Connect

Understanding how array creation time grows helps you explain performance when working with collections in real projects.

Self-Check

"What if we declared the array but did not fill it with values? How would the time complexity change?"

Practice

1. Which of the following is the correct way to declare and initialize an integer array with 3 elements in C#?

easy

A. int[] numbers = new int[3] {1, 2, 3};

B. int numbers = new int[3] {1, 2, 3};

C. int numbers[] = {1, 2, 3};

D. int[] numbers = new int(3) {1, 2, 3};

Solution

1. Step 1: Understand array declaration syntax

   In C#, to declare an array, you use the type followed by square brackets, then assign with new keyword and specify size and elements.

2. Step 2: Check each option for correctness

   int[] numbers = new int[3] {1, 2, 3}; correctly declares an integer array with size 3 and initializes it with values 1, 2, 3. int numbers = new int[3] {1, 2, 3}; misses square brackets for array type. int numbers[] = {1, 2, 3}; is invalid syntax - square brackets must follow the type name, not the variable name. int[] numbers = new int(3) {1, 2, 3}; uses parentheses instead of square brackets which is invalid.

3. Final Answer:

   int[] numbers = new int[3] {1, 2, 3}; -> Option A

4. Quick Check:

   Correct array declaration uses int[] and new int[size] [OK]

Hint: Use type[] name = new type[size] {values}; for arrays [OK]

Common Mistakes:

• Forgetting square brackets [] after type
• Using parentheses () instead of [] for size
• Missing the new keyword
• Assigning array without brackets

2. Which of the following is a syntax error when declaring an array in C#?

easy

A. int[] arr = new int[5];

B. int[] arr = {1, 2, 3};

C. int arr[] = new int[5];

D. int[] arr = new int[] {1, 2, 3};

Solution

1. Step 1: Review C# array declaration syntax

   C# requires the square brackets to be placed after the type, not after the variable name. So int[] arr is correct, but int arr[] is invalid syntax.

2. Step 2: Check each option

   int[] arr = new int[5]; is correct standard syntax. int arr[] = new int[5]; uses C/C++ style int arr[] which is invalid in C#. int[] arr = {1, 2, 3}; is valid shorthand initialization. int[] arr = new int[] {1, 2, 3}; is also valid with explicit new int[].

3. Final Answer:

   int arr[] = new int[5]; -> Option C

4. Quick Check:

   Square brackets go after type, not variable name [OK]

Hint: Remember: In C#, brackets go after type, not variable name [OK]

Common Mistakes:

• Using C/C++ style array declaration
• Placing brackets after variable name
• Confusing array initialization syntax

3. You want to declare and initialize a string array with the names "Alice", "Bob", and "Charlie" in one line. Which of the following is the best way to do this in C#?

easy

A. string[] names = new string[3]; names = {"Alice", "Bob", "Charlie"};

B. string[] names = new string[] {"Alice", "Bob", "Charlie"};

C. string names[] = new string[3] {"Alice", "Bob", "Charlie"};

D. string names[] = {"Alice", "Bob", "Charlie"};

Solution

1. Step 1: Understand array declaration and initialization rules

   In C#, you can declare and initialize an array in one line using new string[] { ... } or shorthand { ... } only if declaration and initialization are combined.

2. Step 2: Evaluate each option

   string[] names = new string[3]; names = {"Alice", "Bob", "Charlie"}; tries to assign values after declaration without new, which is invalid. string names[] = {"Alice", "Bob", "Charlie"}; is invalid syntax with brackets after variable name. string names[] = new string[3] {"Alice", "Bob", "Charlie"}; uses invalid syntax with brackets after variable name. string[] names = new string[] {"Alice", "Bob", "Charlie"}; correctly declares and initializes in one line.

3. Final Answer:

   string[] names = new string[] {"Alice", "Bob", "Charlie"}; -> Option B

4. Quick Check:

   Use new string[] { ... } for clear array initialization [OK]

Hint: Use new string[] { ... } for clear one-line initialization [OK]

Common Mistakes:

• Assigning array values without new keyword after declaration
• Using C-style array syntax
• Confusing declaration and assignment

4. What will be the output of the following C# code?

int[] arr = new int[4] {10, 20, 30, 40};
Console.WriteLine(arr[2]);

medium

A. 30

B. 20

C. 40

D. IndexOutOfRangeException

Solution

1. Step 1: Understand array indexing

   Arrays in C# are zero-indexed, meaning the first element is at index 0. So arr[0] = 10, arr[1] = 20, arr[2] = 30, arr[3] = 40.

2. Step 2: Identify the value at index 2

   The code prints arr[2], which is the third element, value 30.

3. Final Answer:

   30 -> Option A

4. Quick Check:

   Zero-based index means arr[2] = 30 [OK]

Hint: Remember arrays start at index 0 in C# [OK]

Common Mistakes:

• Confusing index 2 with third element value
• Expecting 1-based indexing
• Mistaking array length for last index

5. Identify the error in the following C# code snippet:

int[] numbers = new int[3];
numbers = {1, 2, 3};

medium

A. No error, code runs fine

B. Array size mismatch error

C. Cannot assign values without new keyword

D. Syntax error due to missing new keyword in assignment

Solution

1. Step 1: Analyze array initialization and assignment

   In C#, you can initialize an array with values only at declaration or by using new int[] { ... }. Direct assignment like numbers = {1, 2, 3}; is invalid syntax.

2. Step 2: Identify the syntax error

   The second line misses the new int[] part, causing a syntax error.

3. Final Answer:

   Syntax error due to missing new keyword in assignment -> Option D

4. Quick Check:

   Array assignment requires new int[] { ... } [OK]

Hint: Use new int[] { ... } when assigning arrays after declaration [OK]

Common Mistakes:

• Assigning array values without new keyword
• Trying to reassign array with braces only
• Confusing initialization with assignment