Catalog

1. Problem description

2. Problem solving analysis

 3. Code implementation

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1. Problem description

Given a length of  n  Array of integers for  nums .

hypothesis  arrk  It's an array  nums  Clockwise rotation  k  Array after position , We define  nums  Of   Rotation function   F  by ：

• F(k) = 0 * arrk[0] + 1 * arrk[1] + ... + (n - 1) * arrk[n - 1]

return  F(0), F(1), ..., F(n-1) Maximum of  .

The generated test cases make the answers meet the requirements  32 position   Integers .

Example 1:

 Input : nums = [4,3,2,6]
 Output : 26
 explain :
F(0) = (0 * 4) + (1 * 3) + (2 * 2) + (3 * 6) = 0 + 3 + 4 + 18 = 25
F(1) = (0 * 6) + (1 * 4) + (2 * 3) + (3 * 2) = 0 + 4 + 6 + 6 = 16
F(2) = (0 * 2) + (1 * 6) + (2 * 4) + (3 * 3) = 0 + 6 + 8 + 9 = 23
F(3) = (0 * 3) + (1 * 2) + (2 * 6) + (3 * 4) = 0 + 2 + 12 + 12 = 26
 therefore  F(0), F(1), F(2), F(3)  The maximum value in is  F(3) = 26 .

Example 2:

 Input : nums = [100]
 Output : 0

Tips :

• n == nums.length
• 1 <= n <= 10^5
• -100 <= nums[i] <= 100

2. Problem solving analysis

        Of course, you can get the answer . however , Should not be satisfied with this .

        however , Considering the characteristics of rotation , We can get the following recurrence relation ：

 

More generally, 

 

 3. Code implementation

from typing import List

class Solution:
    def maxRotateFunction(self, nums: List[int]) -> int:
        
        if len(nums)==1:
            return 0
        
        # Calculate F(0) and sum of nums
        nums_sum = 0
        F  = 0
        N  = len(nums)
        for k in range(N):
            nums_sum += nums[k]
            F  += k*nums[k]
            
        maxvalue = F
        for k in range(1,N):
            print(k,F)
            F = nums_sum + F - N * nums[(N-k)%N]
            maxvalue = F if F> maxvalue else maxvalue
        
        return maxvalue
    
if __name__ == "__main__":
    
    sln = Solution()    
    nums = [4,3,2,6]
    print(sln.maxRotateFunction(nums))

         Execution time ：264 ms, In all  Python3  Defeated in submission 89.73% Users of

         Memory consumption ：22 MB, In all  Python3  Defeated in submission 61.98% Users of

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