LeetCode 61: Rotate List — Python Solution

Solve LeetCode 61: Rotate List in Python with a cycle then cut 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

Measure the length, connect tail to head to form a cycle, then cut after length minus k modulo length steps.

Algorithm

1. Measure the length, connect tail to head to form a cycle, then cut after length minus k modulo length steps.
2. Maintain this invariant: The temporary cycle preserves order, and the cut selects the node whose predecessor becomes the new tail.
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 rotateRight(self, head, k):
        if not head or not head.next or k == 0:
            return head
        length, tail = 1, head
        while tail.next:
            tail = tail.next
            length += 1
        k %= length
        if k == 0:
            return head
        tail.next = head
        new_tail = head
        for _ in range(length - k - 1):
            new_tail = new_tail.next
        new_head = new_tail.next
        new_tail.next = None
        return new_head

Why this is correct

The proof follows the maintained state: The temporary cycle preserves order, and the cut selects the node whose predecessor becomes the new tail. 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

Normalize k; empty and one-node lists need no rotation.

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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