128. Longest Consecutive Sequence

MediumLeetCode

Given an unsorted array of integers nums, return the length of the longest consecutive elements sequence.

You must write an algorithm that runs in O(n) time.

Example 1

Input: nums = [100,4,200,1,3,2] Output: 4 Explanation: The longest consecutive elements sequence is [1, 2, 3, 4]. Therefore its length is 4.

Example 2

Input: nums = [0,3,7,2,5,8,4,6,0,1] Output: 9

Example 3

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

Constraints

• 0 <= nums.length <= 10^5
• -10^9 <= nums[i] <= 10^9

How to solve the problem

• Sorting

class Solution:
    def longestConsecutive(self, nums: List[int]) -> int:
        if not nums:
            return 0
        nums = sorted(set(nums))
        current_len = 1
        max_len = 1
        for i in range(1, len(nums)):
            if nums[i] == nums[i-1] + 1:
                current_len += 1
                max_len = max(current_len, max_len)
            else: 
                current_len = 1
        return max_len

• Hashing

class Solution:
    def longestConsecutive(self, nums: List[int]) -> int:
        nums = set(nums)
        length = 0
        max_length = 0
        for num in nums:
            if num - 1 not in nums:
                length = 1
                while num + length in nums:
                    length += 1
                max_length = max(length, max_length)
        return max_length

Complexity

• Sorting: Time complexity: O(n log n), Space complexity: O(1)
• Hashing: Time complexity: O(n), Space complexity: O(n)
  • Each element is visited at most twice (once in the outer loop, once in the inner while loop)