Array Declaration and Initialization in DSA Typescript - Time & Space Complexity

Time Complexity: Array Declaration and Initialization

O(n)

Understanding Time Complexity

When we create and fill an array, we want to know how long it takes as the array grows.

We ask: How does the time to set up the array change with its size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const size = n;
const arr: number[] = new Array(size);
for (let i = 0; i < size; i++) {
  arr[i] = i * 2;
}
    

This code creates an array of size n 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: Exactly n times, once for each element.

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 size of the array.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

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

[OK] Correct: Even if the array space is reserved quickly, filling each element takes time proportional to the number of elements.

Interview Connect

Understanding how array setup time grows helps you explain efficiency clearly and shows you know what happens behind the scenes.

Self-Check

"What if we used a built-in method to fill the array instead of a loop? How would the time complexity change?"

Practice

1. Which of the following is the correct way to declare an array of numbers in TypeScript?

easy

A. const numbers: number[] = [1, 2, 3];

B. const numbers: number = [1, 2, 3];

C. const numbers: array = (1, 2, 3);

D. const numbers = {1, 2, 3};

Solution

1. Step 1: Understand TypeScript array syntax

   In TypeScript, arrays are declared using the type followed by square brackets, e.g., number[].

2. Step 2: Check each option's syntax

   const numbers: number[] = [1, 2, 3]; correctly declares an array of numbers. Options A, B, and D use incorrect syntax for arrays.

3. Final Answer:

   const numbers: number[] = [1, 2, 3]; -> Option A

4. Quick Check:

   Array declaration with type[] = correct syntax [OK]

Hint: Use type[] to declare arrays in TypeScript [OK]

Common Mistakes:

• Using type without [] for arrays
• Using parentheses instead of square brackets
• Using curly braces instead of square brackets

2. Which of the following is the correct syntax to initialize an empty array of strings in TypeScript?

easy

A. let names = string[];

B. let names: string = [];

C. let names: string[] = [];

D. let names: [] = string;

Solution

1. Step 1: Identify correct type annotation for empty string array

   To declare an empty array of strings, use string[] as the type and assign an empty array [].

2. Step 2: Validate each option

   let names: string[] = []; correctly uses let names: string[] = []. Others have syntax errors or wrong type placement.

3. Final Answer:

   let names: string[] = []; -> Option C

4. Quick Check:

   Empty array of strings = string[] = correct [OK]

Hint: Use type[] with empty brackets to declare empty arrays [OK]

Common Mistakes:

• Omitting [] after type for arrays
• Assigning type incorrectly after =
• Using invalid syntax like let names = string[];

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

const arr: number[] = [10, 20, 30];
arr[1] = 50;
console.log(arr);

medium

A. [10, 20, 30]

B. [10, 50, 30]

C. [50, 20, 30]

D. Error: Cannot assign to arr[1]

Solution

1. Step 1: Understand array element assignment

   Arrays allow changing elements by index. arr[1] changes the second element.

2. Step 2: Apply the assignment and print

   arr[1] = 50 changes the second element from 20 to 50. Printing arr shows [10, 50, 30].

3. Final Answer:

   [10, 50, 30] -> Option B

4. Quick Check:

   Index assignment updates array element [OK]

Hint: Array index starts at 0; arr[1] is second element [OK]

Common Mistakes:

• Thinking arrays are immutable
• Confusing index 1 with index 0
• Expecting syntax error on assignment

4. Identify the error in the following TypeScript array declaration:

let nums: number[] = (1, 2, 3);

medium

A. Array elements must be strings

B. Missing type annotation for nums

C. Using let instead of const

D. Using parentheses instead of square brackets for array initialization

Solution

1. Step 1: Check array initialization syntax

   Arrays must be initialized with square brackets []. Parentheses () create a comma expression, not an array.

2. Step 2: Identify the error

   Using (1, 2, 3) does not create an array but evaluates to 3. This is incorrect for array initialization.

3. Final Answer:

   Using parentheses instead of square brackets for array initialization -> Option D

4. Quick Check:

   Arrays use [] not () for initialization [OK]

Hint: Use [] for arrays, () is for grouping expressions [OK]

Common Mistakes:

• Confusing parentheses with brackets
• Ignoring type annotations
• Thinking let vs const causes error here

5. You want to declare and initialize a 2D array of numbers with 3 rows and 2 columns, all initialized to zero. Which is the correct TypeScript code?

hard

A. const matrix: number[][] = [[0, 0], [0, 0], [0, 0]];

B. const matrix: number[3][2] = [[0, 0], [0, 0], [0, 0]];

C. const matrix: number[] = [0, 0, 0, 0, 0, 0];

D. const matrix = new Array(3, 2).fill(0);

Solution

1. Step 1: Understand 2D array declaration in TypeScript

   2D arrays are arrays of arrays, so type is number[][].

2. Step 2: Check initialization for 3 rows and 2 columns

   const matrix: number[][] = [[0, 0], [0, 0], [0, 0]]; correctly initializes 3 arrays each with 2 zeros. const matrix: number[3][2] = [[0, 0], [0, 0], [0, 0]]; uses invalid syntax. const matrix: number[] = [0, 0, 0, 0, 0, 0]; is 1D array. const matrix = new Array(3, 2).fill(0); creates array with 2 elements, not 2D.

3. Final Answer:

   const matrix: number[][] = [[0, 0], [0, 0], [0, 0]]; -> Option A

4. Quick Check:

   2D array = array of arrays with type number[][] [OK]

Hint: 2D arrays use type number[][] and nested brackets [OK]

Common Mistakes:

• Using number[3][2] which is invalid in TypeScript
• Confusing 1D and 2D array initialization
• Using new Array with multiple arguments incorrectly