128. Longest Consecutive Sequence

Problem

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.

https://leetcode.com/problems/longest-consecutive-sequence/

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

Constraints:

0 <= nums.length <= 10⁵
-10⁹ <= nums[i] <= 10⁹

Test Cases

    python
    
  
class Solution:
    def longestConsecutive(self, nums: List[int]) -> int:

solution_test.py下载完整源码

    py
    
  
import pytest

from solution import Solution


@pytest.mark.parametrize('nums, expected', [
    ([100,4,200,1,3,2], 4),
    ([0,3,7,2,5,8,4,6,0,1], 9),
])
def test_longest_consecutive(nums, expected):
    sol = Solution()
    assert sol.longestConsecutive(nums) == expected

Thoughts

开始以为是那个经典的动态规划 LCS (Longest Common Subsequence) 问题，仔细看发现不是。

限制 O(n) 是最大的难度。

初步考虑用散列排序。虽然 O(10⁹) + O(n) 依然算 O(n)，但实际的速度就过于慢了，内存占用也大。

需要借助哈希表，假设哈希表的查找是 O(1) 时间。

难点：

如何借助哈希表，判定 consecutive sequence 及其长度。

哈希表的 key 也是无序的。所以对 consecutive sequence 的第一个数和非第一个数要区别对待。

判定是不是第一个数，看其减一是否也在哈希表中。不是第一个数就不用管了。

如果是第一个数，不断加一，直到加出来的数不在哈希表中。

时间复杂度是 O(n)。因为每个序列的第一个数，向后检查的数字个数约等于这个序列的长度，累加起来约等于总数量。

Code

solution.py下载完整源码

    py
    
  
from typing import List


class Solution:
    def longestConsecutive(self, nums: List[int]) -> int:
        num_set = set(nums)
        lcs = 0
        for v in num_set:
            # Check if v is the min number of a sequence.
            # If not, ignore it.
            if v - 1 in num_set:
                continue

            # Found the min number of a sequence, iterate this sequence to get its length.
            length = 1
            v += 1
            while v in num_set:
                v += 1
                length += 1

            lcs = max(lcs, length)

        return lcs

#Problem

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Problem

Test Cases

Thoughts

Code