Rotate Array - Video Solutions

Problem Overview: You’re given an integer array nums and an integer k. The task is to rotate the array to the right by k steps, meaning each element shifts right and wraps around to the beginning. For example, rotating [1,2,3,4,5,6,7] by 3 results in [5,6,7,1,2,3,4].

This problem tests your understanding of array manipulation and how to perform cyclic shifts efficiently. A key detail: when k is larger than the array length, only k % n rotations matter.

Approach 1: Using Additional Array (O(n) time, O(n) space)

Create a new array of the same size and place each element directly in its rotated position. First compute k = k % n so unnecessary rotations are avoided. Then iterate through the array and place each element at index (i + k) % n in the new array. After the pass finishes, copy the result back to the original array.

This approach works because the modulo operation naturally handles the wrap‑around from the end of the array back to the front. It’s easy to implement and very readable. The tradeoff is extra memory usage since an additional array of size n is required.

Approach 2: In-Place Reversal (O(n) time, O(1) space)

The optimal solution avoids extra memory by reversing sections of the array in place. The key insight: a right rotation can be expressed as three reversals. First reverse the entire array. Then reverse the first k elements. Finally reverse the remaining n - k elements.

Example: [1,2,3,4,5,6,7] with k = 3. Reverse all → [7,6,5,4,3,2,1]. Reverse first 3 → [5,6,7,4,3,2,1]. Reverse the rest → [5,6,7,1,2,3,4]. Each reversal uses two pointers moving from both ends toward the center, a common pattern in two pointers problems.

This method performs a constant number of passes over the array, giving O(n) time complexity and O(1) extra space. The math behind the rotation and modulo operation ties directly to concepts in math and cyclic indexing.

Recommended for interviews: Interviewers typically expect the in-place reversal approach. The additional array solution shows you understand the rotation mapping, but the reversal method demonstrates deeper algorithmic thinking and space optimization. Both run in linear time, but achieving O(1) space is the key differentiator.