Problem Statement
Array Rotator
Given an array, rotate the array to the right by k steps, where k is non-negative.
In other words, shift each element k positions to the right, with elements that would go beyond the end of the array wrapping around to the beginning.
Examples
Example 1:
Input: nums = [1,2,3,4,5,6,7], k = 3
Output: [5,6,7,1,2,3,4]
Explanation: rotate 1 step to the right: [7,1,2,3,4,5,6]
rotate 2 steps to the right: [6,7,1,2,3,4,5]
rotate 3 steps to the right: [5,6,7,1,2,3,4]
Example 2:
Input: nums = [-1,-100,3,99], k = 2
Output: [3,99,-1,-100]
Explanation: rotate 1 step to the right: [99,-1,-100,3]
rotate 2 steps to the right: [3,99,-1,-100]
Constraints
- 1 <= nums.length <= 10^5
- -2^31 <= nums[i] <= 2^31 - 1
- 0 <= k <= 10^5
Problem Breakdown
To solve this problem, we need to:
- The problem can be solved in multiple ways, including using extra space, cyclic replacements, or array reversals
- When k is larger than the array length, only k % n rotations are needed, where n is the array length
- The problem can be solved in-place with O(1) extra space using array reversal techniques
- Reversing the entire array, then reversing the first k elements, and finally reversing the remaining elements gives the correct result
- The problem is equivalent to splitting the array at the n-k position and swapping the two parts
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Array Rotator
Given an array, rotate the array to the right by k steps, where k is non-negative.
In other words, shift each element k positions to the right, with elements that would go beyond the end of the array wrapping around to the beginning.
Examples
Example 1:
rotate 1 step to the right: [7,1,2,3,4,5,6] rotate 2 steps to the right: [6,7,1,2,3,4,5] rotate 3 steps to the right: [5,6,7,1,2,3,4]
Example 2:
rotate 1 step to the right: [99,-1,-100,3] rotate 2 steps to the right: [3,99,-1,-100]
Problem Breakdown
Constraints:
- 1 <= nums.length <= 10^5
- -2^31 <= nums[i] <= 2^31 - 1
- 0 <= k <= 10^5
Key Insights:
The problem can be solved in multiple ways, including using extra space, cyclic replacements, or array reversals
When k is larger than the array length, only k % n rotations are needed, where n is the array length
The problem can be solved in-place with O(1) extra space using array reversal techniques
Reversing the entire array, then reversing the first k elements, and finally reversing the remaining elements gives the correct result
The problem is equivalent to splitting the array at the n-k position and swapping the two parts
Real-World Application
This problem has several practical applications:
Data Processing
Rotating data in circular buffers or queues in operating systems and data processing applications.
Image Processing
Rotating pixels in image processing algorithms for transformations and animations.
Scheduling Algorithms
Implementing round-robin scheduling algorithms where tasks are rotated in a circular manner.
Cryptography
Implementing certain encryption algorithms that involve rotating or shifting data.
Data Visualization
Rotating data points in visualization tools to present different perspectives of the same dataset.