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LeetCode 396: Rotate Function Solution

Master LeetCode problem 396 (Rotate Function), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

396. Rotate Function

Medium
ArrayMathDynamic Programming

Problem Explanation

Explanation

To find the maximum rotation function value, we can use the observation that the next rotation function value F(i+1) can be derived from the current rotation function value F(i) by subtracting the sum of the array elements and adding n times the last element of the array. Based on this observation, we can calculate the maximum rotation function value by iterating through each rotation and updating the maximum value.

Algorithm:

  1. Calculate the initial rotation function value F(0).
  2. Initialize variables to keep track of the current rotation function value and the maximum rotation function value.
  3. Iterate through each rotation from 1 to n-1:
    • Calculate the current rotation function value F(i) based on F(i-1).
    • Update the maximum rotation function value if F(i) is greater.
  4. Return the maximum rotation function value.

Time Complexity: O(n) where n is the number of elements in the input array. Space Complexity: O(1) as we are using a constant amount of extra space.

Solution Code

class Solution {
    public int maxRotateFunction(int[] nums) {
        int n = nums.length;
        int sum = 0;
        int rotation = 0;
        
        for (int i = 0; i < n; i++) {
            sum += nums[i];
            rotation += i * nums[i];
        }
        
        int maxRotation = rotation;
        
        for (int i = 1; i < n; i++) {
            rotation = rotation - sum + n * nums[i - 1];
            maxRotation = Math.max(maxRotation, rotation);
        }
        
        return maxRotation;
    }
}

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