How do you solve Rotate Function on LeetCode?

Rotate Function (LeetCode #396) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the relationship between F(k) and F(k-1) is crucial for optimizing the solution.

What is the time complexity of Rotate Function?

The optimal solution for Rotate Function runs in O(n) time and uses O(1) space. The time complexity is O(n) because we compute F(0) in O(n) and then derive each subsequent F(k) in constant time.

What is the brute force solution for Rotate Function?

The brute force approach for Rotate Function is Brute Force, with O(n²) time complexity and O(1) space complexity. We can calculate the rotation function F(k) for each possible rotation k from 0 to n-1. This involves creating a new rotated array for each k and calculating the sum based on the defined formula. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Rotate Function?

Rotate Function uses the following concepts: Array, Math, Dynamic Programming. The recommended patterns to study are: Math, Array.

What are the interview tips for Rotate Function?

Always start with a brute force solution to clarify your understanding of the problem. Look for patterns or relationships in the problem that can simplify calculations. Practice explaining your thought process out loud, as communication is key in interviews.

What are common mistakes when solving Rotate Function?

Not recognizing that F(k) can be derived from F(k-1), leading to unnecessary recalculations. Failing to handle edge cases, such as when the array has only one element.

#396

Rotate Function

Medium

ArrayMathDynamic ProgrammingMathArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

Instead of recalculating F(k) from scratch for each rotation, we can derive F(k) from F(k-1) using a mathematical relationship, which allows us to compute all F(k) in O(n) time.

⚙️

Algorithm

4 steps

1Step 1: Calculate F(0) using the initial formula.
2Step 2: Use the relationship F(k) = F(k-1) + sum(nums) - n * nums[n-k] to compute F(k) from F(k-1).
3Step 3: Keep track of the maximum value while calculating F(k) for k from 1 to n-1.
4Step 4: Return the maximum value.

solution.py14 lines

1# Full working Python code
2
3def rotate_function_optimal(nums):
4    n = len(nums)
5    total_sum = sum(nums)
6    F = sum(i * nums[i] for i in range(n))
7    max_value = F
8    for k in range(1, n):
9        F = F + total_sum - n * nums[n - k]
10        max_value = max(max_value, F)
11    return max_value
12
13# Example usage
14print(rotate_function_optimal([4, 3, 2, 6]))

ℹ

Complexity note: The time complexity is O(n) because we compute F(0) in O(n) and then derive each subsequent F(k) in constant time.

1Understanding the relationship between F(k) and F(k-1) is crucial for optimizing the solution.
2The brute force method is often a good starting point to understand the problem before optimizing.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.