Remove Duplicates from Sorted Array Two Pointer in DSA Javascript - Time & Space Complexity

Time Complexity: Remove Duplicates from Sorted Array Two Pointer

O(n)

Understanding Time Complexity

We want to understand how the time needed changes when removing duplicates from a sorted array using two pointers.

How does the number of steps grow as the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function removeDuplicates(nums) {
  let i = 0;
  for (let j = 1; j < nums.length; j++) {
    if (nums[j] !== nums[i]) {
      i++;
      nums[i] = nums[j];
    }
  }
  return i + 1;
}
    

This code moves through the array once, shifting unique values forward to remove duplicates.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: One loop that goes through the array from start to end once.
• How many times: Exactly once for each element after the first, so roughly n-1 times for array size n.

How Execution Grows With Input

As the array gets bigger, the loop runs once for each element, so the steps grow directly with the size.

Input Size (n)	Approx. Operations
10	About 9 checks and moves
100	About 99 checks and moves
1000	About 999 checks and moves

Pattern observation: The number of operations grows in a straight line with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to remove duplicates grows directly with the number of elements in the array.

Common Mistake

[X] Wrong: "Because there are two pointers, the time complexity is O(n²)."

[OK] Correct: Both pointers move forward only, never backward, so the loop runs just once through the array, making it O(n), not O(n²).

Interview Connect

Understanding this pattern helps you solve many array problems efficiently by using two pointers to avoid extra loops.

Self-Check

"What if the array was not sorted? How would the time complexity change if we still tried to remove duplicates this way?"

Practice

1. What is the main purpose of using the two-pointer technique in removing duplicates from a sorted array?

easy

A. To reverse the array while removing duplicates

B. To sort the array again after duplicates are removed

C. To count the total number of duplicates in the array

D. To efficiently overwrite duplicates and keep unique elements at the start

Solution

1. Step 1: Understand the two-pointer technique

   One pointer tracks the position to place the next unique element, the other scans the array.

2. Step 2: Purpose of the technique

   It overwrites duplicates by placing unique elements at the front, avoiding extra space.

3. Final Answer:

   To efficiently overwrite duplicates and keep unique elements at the start -> Option D

4. Quick Check:

   Two-pointer = overwrite duplicates [OK]

Hint: Two pointers: one scans, one writes unique values [OK]

Common Mistakes:

• Thinking it sorts the array again
• Confusing counting duplicates with removing them
• Assuming it reverses the array

2. Which of the following is the correct syntax to initialize two pointers for removing duplicates from a sorted array nums in JavaScript?

easy

A. let i = 1, j = 0;

B. let i = 0, j = 1;

C. let i = 0, j = 0;

D. let i = 1, j = 1;

Solution

1. Step 1: Identify pointer roles

   Pointer i tracks last unique element index, j scans from next element.

2. Step 2: Correct initialization

   i starts at 0 (first element), j starts at 1 (second element) to compare.

3. Final Answer:

   let i = 0, j = 1; -> Option B

4. Quick Check:

   i=0, j=1 start positions [OK]

Hint: Start i at 0, j at 1 to compare neighbors [OK]

Common Mistakes:

• Starting both pointers at 0
• Swapping i and j initialization
• Starting both pointers at 1

3. What will be the output array after removing duplicates using the two-pointer method on nums = [1, 1, 2, 2, 3]?

medium

A. [1, 2, 3]

B. [1, 1, 2, 3]

C. [1, 2, 2, 3]

D. [1, 3, 2]

Solution

1. Step 1: Traverse and compare elements

   Start with i=0, j=1. Compare nums[j] with nums[i]. If different, increment i and copy nums[j].

2. Step 2: Update array with unique elements

   After processing, unique elements at start are [1, 2, 3].

3. Final Answer:

   [1, 2, 3] -> Option A

4. Quick Check:

   Unique sorted elements = [1, 2, 3] [OK]

Hint: Unique elements stay at front in sorted order [OK]

Common Mistakes:

• Leaving duplicates in the output
• Mixing order of elements
• Not updating the array in place

4. Consider this code snippet for removing duplicates from a sorted array nums. What is the bug?

let i = 0;
for (let j = 1; j < nums.length; j++) {
  if (nums[j] !== nums[i]) {
    i = j;
    nums[i] = nums[j];
  }
}
return i + 1;

medium

A. Pointer i should be incremented, not assigned j

B. The loop should start from j = 0

C. The comparison should be nums[j] === nums[i]

D. Return statement should be i instead of i + 1

Solution

1. Step 1: Analyze pointer update

   i should move forward by incrementing to next unique position, not jump to j.

2. Step 2: Correct pointer increment

   Use i++ to move i forward, then assign nums[i] = nums[j].

3. Final Answer:

   Pointer i should be incremented, not assigned j -> Option A

4. Quick Check:

   i++ to move pointer forward [OK]

Hint: Increment i to place unique elements, don't assign j to i [OK]

Common Mistakes:

• Assigning i = j instead of i++
• Starting loop at wrong index
• Wrong comparison operator

5. Given a sorted array nums = [0,0,1,1,1,2,2,3,3,4], what will be the length of the array after removing duplicates using the two-pointer method, and what will the first part of the array look like?

hard

A. Length: 4, Array start: [0, 1, 2, 3]

B. Length: 6, Array start: [0, 1, 1, 2, 3, 4]

C. Length: 5, Array start: [0, 1, 2, 3, 4]

D. Length: 5, Array start: [0, 0, 1, 2, 3]

Solution

1. Step 1: Apply two-pointer method on nums

   Traverse array, move unique elements forward: 0,1,2,3,4.

2. Step 2: Count unique elements and array start

   There are 5 unique elements, so length is 5, and array start is [0,1,2,3,4].

3. Final Answer:

   Length: 5, Array start: [0, 1, 2, 3, 4] -> Option C

4. Quick Check:

   Unique count = 5, array front = [0,1,2,3,4] [OK]

Hint: Count unique elements, array front holds them [OK]

Common Mistakes:

• Counting duplicates as unique
• Not updating array in place
• Miscounting length after removal