LeetCode 189: Rotate Array — Python Solution

Solve LeetCode 189: Rotate Array in Python with a three reversals 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

Normalize k, reverse the whole array, then reverse the two rotated segments. Reversal moves both groups into their final cyclic order.

Algorithm

1. Normalize k, reverse the whole array, then reverse the two rotated segments. Reversal moves both groups into their final cyclic order.
2. Maintain this invariant: After the three reversals, each original index maps to (index + k) modulo n.
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 rotate(self, nums, k):
        if not nums:
            return
        k %= len(nums)
        nums.reverse()
        nums[:k] = reversed(nums[:k])
        nums[k:] = reversed(nums[k:])

Why this is correct

The proof follows the maintained state: After the three reversals, each original index maps to (index + k) modulo n. 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

Reduce k modulo the length; an empty array and k equal to zero need no work.

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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