Right rotating an array involves shifting the elements of the array to the right by a specified number of places. In this article, we'll discuss two efficient methods to achieve this rotation.

### Solution 1: Brute Force Approach (using a Temp Array)

This method uses an auxiliary array to store the last D elements and then shifts the rest of the elements to the right.

**Implementation**:

```
// Solution-1: Using a Temp Array
// Time Complexity: O(n)
// Space Complexity: O(k)
// since k array elements need to be stored in temp array
void rightRotate1(int arr[], int n, int k)
{
// Adjust k to be within the valid range (0 to n-1)
k = k % n;
// Handle edge case: empty array
if (n == 0)
{
return;
}
int temp[k];
// Storing k elements in temp array from the right
for (int i = n - k; i < n; i++)
{
temp[i - n + k] = arr[i];
}
// Shifting the rest of elements to the right
for (int i = n - k - 1; i >= 0; i--)
{
arr[i + k] = arr[i];
}
// Putting k elements back to main array
for (int i = 0; i < k; i++)
{
arr[i] = temp[i];
}
}
```

**Logic**:

**Adjust k**: Ensure`k`

is within the valid range by taking`k % n`

.**Store in Temp**: Store the last`k`

elements in a temporary array.**Shift Elements**: Shift the remaining elements of the array to the right by`k`

positions.**Copy Back**: Copy the elements from the temporary array back to the start of the main array.

**Time Complexity**: O(n)

**Explanation**: Each element is moved once.

**Space Complexity**: O(k)

**Explanation**: An additional array of size`k`

is used.

**Example**:

**Input**:`arr = [1, 2, 3, 4, 5, 6, 7]`

,`k = 3`

**Output**:`arr = [5, 6, 7, 1, 2, 3, 4]`

**Explanation**: The last 3 elements`[5, 6, 7]`

are stored in a temp array, the rest are shifted right and then the temp array is copied back to the start.

### Solution 2: Optimal Approach (using Reversal Algorithm)

This method uses a three-step reversal process to achieve the rotation without needing **extra space**.

**Implementation**:

```
// Solution-2: Using Reversal Algorithm
// Time Complexity: O(n)
// Space Complexity: O(1)
// Function to Reverse Array
void reverseArray(int arr[], int start, int end)
{
while (start < end)
{
int temp = arr[start];
arr[start] = arr[end];
arr[end] = temp;
start++;
end--;
}
}
// Function to Rotate k elements to the right
void rightRotate2(int arr[], int n, int k)
{
// Adjust k to be within the valid range (0 to n-1)
k = k % n;
// Handle edge case: empty array
if (n == 0)
{
return;
}
// Reverse first n-k elements
reverseArray(arr, 0, n - 1 - k);
// Reverse last k elements
reverseArray(arr, n - k, n - 1);
// Reverse whole array
reverseArray(arr, 0, n - 1);
}
```

**Logic**:

**Adjust k**: Ensure`k`

is within the valid range by taking`k % n`

.**Reverse First Part**: Reverse the first`n - k`

elements.**Reverse Second Part**: Reverse the remaining`k`

elements.**Reverse Entire Array**: Reverse the entire array to achieve the final rotated array.

**Time Complexity**: O(n)

**Explanation**: The array is reversed three times, each taking O(n) time.

**Space Complexity**: O(1)

**Explanation**: The algorithm operates in place, using only a constant amount of extra space.

**Example**:

**Input**:`arr = [1, 2, 3, 4, 5, 6, 7]`

,`k = 3`

**Output**:`arr = [5, 6, 7, 1, 2, 3, 4]`

**Explanation**:Reverse the first 4 elements:

`[4, 3, 2, 1, 5, 6, 7]`

Reverse the last 3 elements:

`[4, 3, 2, 1, 7, 6, 5]`

Reverse the entire array:

`[5, 6, 7, 1, 2, 3, 4]`

### Comparison

**Temp Array Method**:**Pros**: Simple and easy to understand.**Cons**: Uses additional space for the temporary array, which may not be efficient for large values of`k`

.

**Reversal Algorithm**:**Pros**: Efficient with O(n) time complexity and O(1) space complexity.**Cons**: Slightly more complex to implement but highly efficient for large arrays.

### Edge Cases

**Empty Array**: Returns immediately as there are no elements to rotate.**k >= n**: Correctly handles cases where`k`

is greater than or equal to the array length by using`k % n`

.**Single Element Array**: Returns the same array as it only contains one element.

### Additional Notes

**Efficiency**: The reversal algorithm is more space-efficient, making it preferable for large arrays.**Practicality**: Both methods handle rotations efficiently but the choice depends on space constraints.

### Conclusion

Right rotating an array by `k`

positions can be efficiently achieved using either a temporary array or an in-place reversal algorithm. The optimal choice depends on the specific constraints and requirements of the problem.