LeetCode 21: Merge Two Sorted Lists — Python Solution

Solve LeetCode 21: Merge Two Sorted Lists in Python with a dummy-tail merge 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

Attach the smaller current node to a dummy-backed output tail, advance that list, then attach the unexhausted suffix.

Algorithm

1. Attach the smaller current node to a dummy-backed output tail, advance that list, then attach the unexhausted suffix.
2. Maintain this invariant: The output through tail is sorted and contains exactly the consumed input 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 mergeTwoLists(self, list1, list2):
        dummy = tail = ListNode()
        while list1 and list2:
            if list1.val <= list2.val:
                tail.next, list1 = list1, list1.next
            else:
                tail.next, list2 = list2, list2.next
            tail = tail.next
        tail.next = list1 or list2
        return dummy.next

Why this is correct

The proof follows the maintained state: The output through tail is sorted and contains exactly the consumed input 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(m+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

Either list may be empty; nodes can be reused rather than copied.

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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