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

Time Complexity: Array Deletion at Beginning

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove the first item from an array.

How does the work grow when 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 the rest left.

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 shift happens n-1 times.

How Execution Grows With Input

When the array size grows, the number of shifts grows almost the same way.

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

Pattern observation: The work grows roughly in a straight line with the array size.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the first element grows directly with the array size.

Common Mistake

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

[OK] Correct: Removing the first element requires moving all other elements, so it takes longer as the array grows.

Interview Connect

Knowing this helps you choose the right data structure when you need fast removals at the start, like using a linked list instead of an array.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity of deleting the first element change?"

Practice

1. What does the shift() method do to an array in JavaScript?

easy

A. Adds an element at the end

B. Removes the last element and returns it

C. Adds an element at the beginning

D. Removes the first element and returns it

Solution

1. Step 1: Understand the shift() method

   The shift() method removes the first element from an array and returns that element.

2. Step 2: Compare with other array methods

   pop() removes the last element, unshift() adds at the beginning, and push() adds at the end.

3. Final Answer:

   Removes the first element and returns it -> Option D

4. Quick Check:

   shift() removes first element [OK]

Hint: Remember: shift = remove from start [OK]

Common Mistakes:

• Confusing shift() with pop()
• Thinking shift() adds elements
• Mixing shift() with unshift()

2. Which of the following is the correct syntax to remove the first element from an array arr in JavaScript?

easy

A. arr.shift()

B. arr.delete(0)

C. arr.unshift()

D. arr.pop()

Solution

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

   The method to remove the first element is shift().

2. Step 2: Check other options

   pop() removes last element, unshift() adds elements at start, and delete is not a valid array method.

3. Final Answer:

   arr.shift() -> Option A

4. Quick Check:

   Use shift() to remove first element [OK]

Hint: Use arr.shift() to remove first element [OK]

Common Mistakes:

• Using pop() instead of shift()
• Trying to use delete() on arrays
• Confusing unshift() with shift()

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

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

medium

A. [20, 30, 40] and 10

B. [10, 20, 30] and 40

C. [20, 30, 40] and 40

D. [10, 20, 30] and 10

Solution

1. Step 1: Apply shift() on the array

   shift() removes the first element (10) from arr and returns it.

2. Step 2: Check the updated array and removed value

   After removal, arr becomes [20, 30, 40], and removed stores 10.

3. Final Answer:

   [20, 30, 40] and 10 -> Option A

4. Quick Check:

   shift() removes first element 10 [OK]

Hint: shift() returns removed first element [OK]

Common Mistakes:

• Expecting last element removed
• Confusing returned value with array
• Not updating array after shift()

4. Find the error in the following code that tries to remove the first element from array nums:

let nums = [5, 10, 15];
nums.remove(0);
console.log(nums);

medium

A. remove() removes last element, not first

B. remove() is not a valid array method

C. remove() requires two arguments

D. Code is correct and works fine

Solution

1. Step 1: Check the method used

   The method remove() does not exist for JavaScript arrays.

2. Step 2: Identify correct method to remove first element

   To remove the first element, use shift() instead of remove().

3. Final Answer:

   remove() is not a valid array method -> Option B

4. Quick Check:

   Use shift() to remove first element, not remove() [OK]

Hint: Use shift(), not remove(), to delete first element [OK]

Common Mistakes:

• Using remove() instead of shift()
• Assuming remove() exists in JS arrays
• Not checking method names carefully

5. Given an array data = [1, 2, 3, 4, 5], you want to remove the first two elements efficiently. Which code snippet correctly achieves this?

hard

A. data.shift(2);

B. data.pop(); data.pop();

C. data.splice(0, 2);

D. data.slice(2);

Solution

1. Step 1: Understand each method's effect

   shift(2) is invalid; shift() removes one element from start and takes no arguments. splice(0, 2) removes two elements starting at index 0 in one call. pop() removes from end, not start. slice(2) returns a new array without first two elements but does not modify original.

2. Step 2: Choose the best method to remove first two elements

   splice(0, 2) removes first two elements efficiently and modifies the original array.

3. Final Answer:

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

4. Quick Check:

   splice(0, 2) removes first two elements [OK]

Hint: Use splice(0, 2) to remove first two elements at once [OK]

Common Mistakes:

• Using pop() which removes from end
• Using slice() which does not modify original array
• Using shift(2) which is invalid