Rotate Array

Rotating an array by k steps splits it into two blocks that swap their relative positions: the prefix of length n - k and the suffix of length k. Reversing each section individually orients their contents backwards, and reversing the entire array flips them back into their correct relative order in place.

Full solution

Three-step block reversal: reverse the whole array, then each of the two blocks, all in place. It is O(n) time like the buffer copy but O(1) space, which is exactly the follow-up an interviewer asks after the obvious (i + k) % n version.

def rotate(nums: list[int], k: int) -> None:
    n = len(nums)
    k %= n  # k >= n wraps around; k % n == 0 leaves the array untouched

    def reverse(lo: int, hi: int) -> None:
        while lo < hi:
            nums[lo], nums[hi] = nums[hi], nums[lo]
            lo += 1
            hi -= 1

    reverse(0, n - 1)  # whole array: the last k now sit first, but backwards
    reverse(0, k - 1)  # fix the order of the moved block
    reverse(k, n - 1)  # fix the order of the rest

function rotate(nums, k) {
  const n = nums.length;
  k %= n; // k >= n wraps around; k % n === 0 leaves the array untouched
  const reverse = (lo, hi) => {
    while (lo < hi) {
      [nums[lo], nums[hi]] = [nums[hi], nums[lo]];
      lo++;
      hi--;
    }
  };
  reverse(0, n - 1); // whole array: the last k now sit first, but backwards
  reverse(0, k - 1); // fix the order of the moved block
  reverse(k, n - 1); // fix the order of the rest
}

The theory behind it

Arrays — the ground this problem stands on. All Arrays problems

What Arrays is

An array is a row of fixed boxes laid side by side in computer memory, like numbered lockers in a hallway. Because each box occupies identical space and sits directly next to its neighbors, jumping to locker zero or locker ten thousand takes the exact same tiny fraction of time. Every box holds an item of the same type, addressed by an offset number called an index.

When to reach for it

Reach for an array when items arrive in a known sequence and need immediate retrieval by position number. Problems asking for running totals, prefix accumulations, cyclic rotations, or in-place rearrangements signal array mechanics. Whenever constraints require constant-time random lookups or contiguous cache scans across fixed collections, a flat sequence is the default container.

How the pattern works

Visualize a tape with zero-indexed slots stretching from start to end. Keep track of write and read cursors when modifying contents without allocating helper buffers. For running computations, maintain an invariant such as having processed all elements left of the current index while pending elements wait to the right. When modifying entries in place, consider scanning backwards from the end so unread data is not overwritten.