LeetCode 86: Partition List — Python Solution

Solve LeetCode 86: Partition List in Python with a stable dual lists 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

Append nodes to separate less-than and greater-or-equal chains, then connect the chains and terminate the second tail.

Algorithm

1. Append nodes to separate less-than and greater-or-equal chains, then connect the chains and terminate the second tail.
2. Maintain this invariant: Each chain preserves the original relative order of its processed nodes.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

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

class Solution:
    def partition(self, head, x):
        low_dummy = low = ListNode()
        high_dummy = high = ListNode()
        while head:
            following = head.next
            if head.val < x:
                low.next = head; low = low.next
            else:
                high.next = head; high = high.next
            head = following
        high.next = None
        low.next = high_dummy.next
        return low_dummy.next

Why this is correct

The proof follows the maintained state: Each chain preserves the original relative order of its processed nodes. 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) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

One partition may remain empty; terminate the reused tail to avoid a cycle.

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.

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