What is the brute force approach and complexity for Remove Duplicates from Sorted Array II?

Keep an element if the map says fewer than 2 copies are kept; copy back with time complexity O(N log N) and space complexity O(N).

What is the optimal approach and complexity for Remove Duplicates from Sorted Array II?

Keep nums[read] if write < 2 or nums[read] != nums[write − 2] with optimal time complexity O(N) and space complexity O(1).

Remove Duplicates from Sorted Array II

Q: How do you identify the pattern for Remove Duplicates from Sorted Array II?

Look for key signals in the prompt: "sorted in non-decreasing order" indicates Copies sit together, in the input and in the answer → the last few written elements tell us the count.; "in place, keep the order, return k" indicates Read / write: build the answer as the prefix `nums[0 … write−1]`.; "at most twice" indicates Look 2 slots back into the written part: keep if `nums[read] != nums[write − 2]`..

Medium·LeetCode #80 Pro OnlyMedium

LeetCode

Problem Statement

You are given an integer array nums sorted in non-decreasing order.

Remove extra copies in place so that every value appears at most twice. The elements you keep must stay in their original order. Return k, the number of elements kept.

After your function runs, the first k slots of nums must hold the kept elements in order. Whatever is after slot k − 1 is ignored. Use only O(1) extra memory.

Input

An integer array nums, sorted in non-decreasing order.

Output

An integer k. The judge also checks that nums[0 … k−1] is the kept elements, in order.

Example 1

Input: nums = [1, 1, 1, 2, 2, 3]

Output: 5, nums = [1, 1, 2, 2, 3, _]

1 appears three times, so one copy is dropped. 2 appears twice and 3 once — both are fine.

Example 2

Input: nums = [0, 0, 1, 1, 1, 1, 2, 3, 3]

Output: 7, nums = [0, 0, 1, 1, 2, 3, 3, _, _]

1 appears four times, so two copies are dropped. Every other value already appears at most twice.

Constraints

• 1 ≤ nums.length ≤ 3 · 10^4
• −10^4 ≤ nums[i] ≤ 10^4
• nums is sorted in non-decreasing order

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“sorted in non-decreasing order”

→ Copies sit together, in the input and in the answer → the last few written elements tell us the count.

“in place, keep the order, return k”

→ Read / write: build the answer as the prefix `nums[0 … write−1]`.

“at most twice”

→ Look 2 slots back into the written part: keep if `nums[read] != nums[write − 2]`.

Approach Complexity Ladder

Brute Force — count copies with a mapO(N log N)O(N)

Keep an element if the map says fewer than 2 copies are kept; copy back

Better — read / write with a run counterO(N)O(1)

Count the length of the current run of equal values; keep the first 2 of each run

Optimal — read / write, compare with nums[write − 2]O(N)O(1)

Keep nums[read] if write < 2 or nums[read] != nums[write − 2]

Brute Force Intuition

Walk nums. Keep a map keptCount[value] of how many copies we have kept. If it is below 2, append the element to a new array and increase the count. Copy the new array back into nums.

Recognition rule for this sub-pattern:

One pointer reads every element, the other marks where the next "kept" element should be written.

Remember this · Two Pointers

Trigger

Sorted array, pairs/triplets with a target, comparing from both ends, compacting an array in place.

Think

If I compare the elements at two positions, can I safely discard one side?

Key question

Which pointer moves, and why can the skipped elements never be the answer?

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