## Introduction to the Rotate Array Problem

In this tutorial, we will explore the “Rotate Array” interview question, a common problem often asked in technical coding interviews. The problem involves rotating the elements of an array to the right by a specified number of positions. This operation can be achieved through various approaches, and we will discuss both the brute-force and optimized solutions in C++. We’ll cover the problem statement, the two main strategies to solve it, and provide step-by-step explanations of the code implementations.

## Problem Statement

Given an array of integers and a positive integer `k`

, rotate the array to the right by `k`

steps. For example, if the array is `[1, 2, 3, 4, 5, 6, 7]`

and `k`

is `3`

, then the array should be rotated to `[5, 6, 7, 1, 2, 3, 4]`

.

## Brute-Force Solution

The brute-force solution to this problem involves performing the rotation step by step, moving each element to its new position. While not the most efficient approach, it helps us understand the problem and its requirements better.

```
#include <iostream>
#include <vector>
void rotate(std::vector<int>& nums, int k) {
int n = nums.size();
k %= n; // Handle cases where k is larger than the array size
for (int i = 0; i < k; ++i) {
int last = nums[n - 1];
for (int j = n - 1; j > 0; --j) {
nums[j] = nums[j - 1];
}
nums[0] = last;
}
}
int main() {
std::vector<int> nums = {1, 2, 3, 4, 5, 6, 7};
int k = 3;
rotate(nums, k);
for (int num : nums) {
std::cout << num << " ";
}
return 0;
}
```

In this solution, we iterate through the array `k`

times, and for each iteration, we shift all elements one position to the right. The last element’s value is stored in a temporary variable and placed at the beginning of the array. This process simulates the rotation.

## Optimized Solution using Reverse Technique

The brute-force solution has a time complexity of O(n * k), where `n`

is the number of elements in the array and `k`

is the number of rotations. This approach is not efficient when the array is large or the number of rotations is significant. We can use a more optimized approach that leverages the reverse technique.

### Idea behind the Optimized Solution

The idea is to reverse the entire array, then reverse the first `k`

elements, and finally reverse the remaining elements. This operation effectively rotates the array to the right by `k`

steps.

Let’s go through the steps of this solution:

- Reverse the entire array.
- Reverse the first
`k`

elements. - Reverse the remaining
`n - k`

elements.

The combined effect of these three steps is a rotation of the array by `k`

steps.

### Implementation of the Optimized Solution

```
#include <iostream>
#include <vector>
void reverse(std::vector<int>& nums, int start, int end) {
while (start < end) {
std::swap(nums[start], nums[end]);
++start;
--end;
}
}
void rotate(std::vector<int>& nums, int k) {
int n = nums.size();
k %= n;
// Step 1: Reverse the entire array
reverse(nums, 0, n - 1);
// Step 2: Reverse the first k elements
reverse(nums, 0, k - 1);
// Step 3: Reverse the remaining n - k elements
reverse(nums, k, n - 1);
}
int main() {
std::vector<int> nums = {1, 2, 3, 4, 5, 6, 7};
int k = 3;
rotate(nums, k);
for (int num : nums) {
std::cout << num << " ";
}
return 0;
}
```

This solution has a time complexity of O(n), where `n`

is the number of elements in the array. The reversing operations are efficient and ensure that the rotation is achieved in a more optimal manner.

## Conclusion

In this tutorial, we explored the “Rotate Array” interview question and discussed two solutions to the problem: the brute-force solution and the optimized solution using the reverse technique. The brute-force solution involves shifting elements repeatedly, resulting in a time complexity of O(n * k). On the other hand, the optimized solution leverages the reverse technique to achieve a rotation in O(n) time.

When faced with similar interview questions, it’s important to understand the problem requirements and constraints, and to come up with efficient solutions that showcase your coding skills. The optimized solution demonstrated in this tutorial can help you efficiently tackle the “Rotate Array” problem and similar rotation-related challenges.