Array initialization in C - Time & Space Complexity

Time Complexity: Array initialization

O(n)

Understanding Time Complexity

When we create and fill an array, the time it takes depends on how many items we add.

We want to know how the work grows as the array size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int arr[1000];
for (int i = 0; i < 1000; i++) {
    arr[i] = 0;
}
    

This code sets each element of an array with 1000 items to zero.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Setting each array element to zero inside the loop.
• How many times: Exactly 1000 times, once for each element.

How Execution Grows With Input

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

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

Pattern observation: Doubling the array size doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to initialize grows directly with the number of elements.

Common Mistake

[X] Wrong: "Initializing an array is instant no matter the size."

[OK] Correct: Each element must be set one by one, so bigger arrays take more time.

Interview Connect

Understanding how array initialization scales helps you explain performance in real code.

Self-Check

"What if we initialize the array with a fixed value using a library function? How would the time complexity change?"

Practice

1. Which of the following correctly declares and initializes an integer array of size 3 with values 1, 2, and 3 in C?

easy

A. int arr = {1, 2, 3};

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

C. int arr[3] = (1, 2, 3);

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

Solution

1. Step 1: Understand array declaration syntax

   In C, arrays are declared with a type, name, and size in square brackets, e.g., int arr[3].

2. Step 2: Check initialization format

   Initialization uses curly braces with comma-separated values, e.g., {1, 2, 3}.

3. Final Answer:

   int arr[3] = {1, 2, 3}; -> Option B

4. Quick Check:

   Correct array declaration and initialization [OK]

Hint: Use curly braces {} with size in brackets [] for arrays [OK]

Common Mistakes:

• Missing square brackets for size
• Using parentheses instead of braces
• Assigning array without braces

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

easy

A. int nums[4] = {10, 20, 30, 40};

B. int nums[5] = {0};

C. int nums[] = {5, 6, 7};

D. int nums[3] = {1, 2, 3, 4};

Solution

1. Step 1: Check array size and initializer count

   Array size is 3 but initializer has 4 values, which is invalid in C.

2. Step 2: Verify other options

   int nums[4] = {10, 20, 30, 40}; matches size and values, C infers size from initializer, B zero-initializes first element and rest are zero.

3. Final Answer:

   int nums[3] = {1, 2, 3, 4}; -> Option D

4. Quick Check:

   Initializer count > array size causes syntax error [OK]

Hint: Initializer list cannot exceed declared array size [OK]

Common Mistakes:

• Providing more initial values than array size
• Omitting size but giving initializer with extra values
• Using wrong braces

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

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

medium

A. 1 2 0 0 0

B. 1 2 garbage garbage garbage

C. 1 2 3 4 5

D. Compilation error

Solution

1. Step 1: Understand partial initialization

   When fewer values are given, remaining elements are set to zero automatically.

2. Step 2: Check printed values

   arr[0] = 1, arr[1] = 2, arr[2], arr[3], arr[4] = 0 each.

3. Final Answer:

   1 2 0 0 0 -> Option A

4. Quick Check:

   Partial init fills rest with zero [OK]

Hint: Uninitialized array elements default to zero if partially initialized [OK]

Common Mistakes:

• Assuming uninitialized elements have garbage values
• Expecting compilation error for partial init
• Confusing array size with initializer count

4. Identify the error in the following C code snippet:

int data[3];
data = {1, 2, 3};

medium

A. Missing semicolon after array declaration.

B. Array size must be omitted when initializing.

C. Arrays cannot be assigned values after declaration like this.

D. Braces should be parentheses for assignment.

Solution

1. Step 1: Understand array assignment rules

   In C, arrays cannot be assigned values after declaration using = and braces.

2. Step 2: Check other options

   Semicolon is present, size can be specified, braces are correct for initialization but not assignment.

3. Final Answer:

   Arrays cannot be assigned values after declaration like this. -> Option C

4. Quick Check:

   Array assignment after declaration is invalid [OK]

Hint: Arrays must be initialized at declaration, not assigned later [OK]

Common Mistakes:

• Trying to assign array with braces after declaration
• Confusing array assignment with pointer assignment
• Using parentheses instead of braces

5. You want to create an integer array of size 6 where the first two elements are 10 and 20, and the rest are zeros. Which of the following is the best way to initialize it in C?

hard

A. int arr[6] = {0}; arr[0] = 10; arr[1] = 20;

B. int arr[6] = {10, 20, 0, 0, 0, 0};

C. int arr[6] = {10, 20};

D. int arr[6]; arr[0] = 10; arr[1] = 20;

Solution

1. Step 1: Analyze partial initialization

   int arr[6] = {10, 20}; partially initializes first two elements; rest are zero by default, so it works.

2. Step 2: Compare with explicit zero initialization and assignment

   int arr[6] = {0}; arr[0] = 10; arr[1] = 20; explicitly zeroes all elements then assigns first two, ensuring clarity and no garbage.

3. Step 3: Evaluate best practice

   int arr[6] = {0}; arr[0] = 10; arr[1] = 20; is best for clarity and safety; int arr[6] = {10, 20}; works but less explicit; int arr[6] = {10, 20, 0, 0, 0, 0}; is verbose; int arr[6]; arr[0] = 10; arr[1] = 20; leaves uninitialized elements.

4. Final Answer:

   int arr[6] = {0}; arr[0] = 10; arr[1] = 20; -> Option A

5. Quick Check:

   Explicit zero init then assign first elements [OK]

Hint: Zero initialize first, then assign specific elements for clarity [OK]

Common Mistakes:

• Assuming partial init always safe without explicit zero
• Not initializing array before assignment
• Overwriting zeros with uninitialized values