LeetCode 128: Longest Consecutive Sequence — Python Solution

Solve LeetCode 128: Longest Consecutive Sequence in Python with a set sequence starts approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Insert all values into a set and count forward only from values whose predecessor is absent.

Algorithm

1. Insert all values into a set and count forward only from values whose predecessor is absent.
2. Maintain this invariant: Every consecutive run is counted exactly once from its unique smallest value.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def longestConsecutive(self, nums):
        values, best = set(nums), 0
        for value in values:
            if value - 1 not in values:
                end = value
                while end in values: end += 1
                best = max(best, end - value)
        return best

Why this is correct

The proof follows the maintained state: Every consecutive run is counted exactly once from its unique smallest value. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) expected time and O(n) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Duplicates disappear in the set; negative and unsorted values behave normally.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

Browse the searchable 100 LeetCode Python Solutions hub. Previous: 219. Contains Duplicate II · Next: 228. Summary Ranges