Array Deletion at Beginning in DSA Typescript - Time & Space Complexity

Time Complexity: Array Deletion at Beginning

O(n)

Understanding Time Complexity

When we remove the first item from an array, the computer must adjust the rest of the items.

We want to know how the time to do this changes as the array gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const arr = [1, 2, 3, 4, 5];
arr.shift(); // removes the first element
console.log(arr);
    

This code removes the first element from the array and shifts all other elements left by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Shifting all elements after the first one to the left by one position.
• How many times: For an array of size n, this shifting happens n-1 times.

How Execution Grows With Input

As the array grows, the number of elements to shift grows almost the same.

Input Size (n)	Approx. Operations (shifts)
10	9
100	99
1000	999

Pattern observation: The operations grow roughly in a straight line with the size of the array.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the first element grows directly with the number of items in the array.

Common Mistake

[X] Wrong: "Removing the first element is always fast and constant time like removing the last element."

[OK] Correct: Because after removing the first element, all other elements must move one step left, which takes time proportional to the array size.

Interview Connect

Understanding this helps you explain why some operations on arrays can be slower than expected and when to choose other data structures like linked lists.

Self-Check

"What if we changed the array to a linked list? How would the time complexity of deleting the first element change?"

Practice

1. What does deleting the first element of an array using array.shift() do to the array?

easy

A. Removes the last element of the array

B. Removes the first element and shifts all other elements left

C. Deletes the entire array

D. Adds a new element at the beginning

Solution

1. Step 1: Understand shift() method

   The shift() method removes the first element of the array.

2. Step 2: Effect on array elements

   After removal, all other elements move one position to the left to fill the gap.

3. Final Answer:

   Removes the first element and shifts all other elements left -> Option B

4. Quick Check:

   shift() removes first element [OK]

Hint: Remember: shift() removes from start, pop() removes from end [OK]

Common Mistakes:

• Confusing shift() with pop()
• Thinking shift() deletes entire array
• Assuming shift() adds elements

2. Which of the following is the correct syntax to remove the first element from an array named nums in TypeScript?

easy

A. nums.shift()

B. nums.removeFirst()

C. nums.pop()

D. nums.delete(0)

Solution

1. Step 1: Identify the method to remove first element

   The correct method to remove the first element in TypeScript arrays is shift().

2. Step 2: Check other options

   pop() removes last element, removeFirst() and delete(0) are invalid methods.

3. Final Answer:

   nums.shift() -> Option A

4. Quick Check:

   Use shift() to remove first element [OK]

Hint: Use shift() to remove first element, pop() for last [OK]

Common Mistakes:

• Using pop() instead of shift()
• Using non-existent methods like removeFirst()
• Trying to delete with delete(0) which is invalid

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

let arr = [10, 20, 30, 40];
arr.shift();
console.log(arr);

medium

A. [40]

B. [10, 20, 30, 40]

C. [30, 40]

D. [20, 30, 40]

Solution

1. Step 1: Initial array and shift operation

   The array starts as [10, 20, 30, 40]. Calling shift() removes the first element 10.

2. Step 2: Resulting array after shift

   After removal, the array becomes [20, 30, 40].

3. Final Answer:

   [20, 30, 40] -> Option D

4. Quick Check:

   shift() removes first element, rest remain [OK]

Hint: shift() removes first element, so array starts from second element [OK]

Common Mistakes:

• Expecting original array unchanged
• Thinking shift() removes last element
• Confusing output with pop() effect

4. Consider this TypeScript code snippet:

let numbers = [5, 10, 15];
numbers.shift;
console.log(numbers);

What is the issue and how to fix it?

medium

A. Missing parentheses after shift; fix by using numbers.shift()

B. shift is not a valid method; use pop() instead

C. Array is empty; no fix needed

D. shift() removes last element; use unshift() instead

Solution

1. Step 1: Identify the method call mistake

   The code uses numbers.shift without parentheses, so the method is not called.

2. Step 2: Correct method call syntax

   Adding parentheses numbers.shift() calls the method and removes the first element.

3. Final Answer:

   Missing parentheses after shift; fix by using numbers.shift() -> Option A

4. Quick Check:

   Method calls need parentheses [OK]

Hint: Always add () to call methods like shift() [OK]

Common Mistakes:

• Forgetting parentheses on method calls
• Using pop() instead of shift() incorrectly
• Misunderstanding shift() removes first element

5. You have an array let fruits = ['apple', 'banana', 'cherry', 'date'];. You want to remove the first two fruits efficiently. Which code snippet correctly does this?

hard

A. fruits.shift(2);

B. fruits.pop(); fruits.pop();

C. fruits.splice(0, 2);

D. fruits.delete(0); fruits.delete(1);

Solution

1. Step 1: Understand removing multiple elements

   fruits.shift(2); fruits.shift(2); is incorrect: shift() takes no arguments (ignores 2) and removes only the first element.

2. Step 2: Using splice for efficient removal

   splice(0, 2) removes two elements starting at index 0 in one operation.

3. Step 3: Check other options

   pop() removes from end, delete() is invalid for arrays.

4. Final Answer:

   fruits.splice(0, 2); -> Option C

5. Quick Check:

   Use splice to remove multiple from start efficiently [OK]

Hint: Use splice(0, n) to remove n elements from start at once [OK]

Common Mistakes:

• Using shift(2) which only removes one element
• Using pop() which removes from end
• Using invalid delete() method