LeetCode - 396. Rotate Function

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本文探讨了在给定整数列表A的情况下，通过不同旋转次数来计算旋转函数的最大值。介绍了三种方法：暴力法、数学技巧法和优化后的数学技巧法。其中，优化后的数学技巧法避免了重复计算，显著提高了效率。

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396. Rotate Function

Brute Force TLE

class Solution(object):
    def maxRotateFunction(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        res = self.cal(A)
        for i in range(len(A)-1):
            A = self.rotate(A)
            res = max(res, self.cal(A))
        return res
    def cal(self, A):
        sum = 0
        for i in range(len(A)):
            sum += i*A[i]
        return sum
    def rotate(self, A):
        pre = A[0]
        for i in range(1, len(A)):
            temp = A[i]
            A[i] = pre
            pre = temp
        A[0] = pre
        return A

class Solution(object):
    def maxRotateFunction(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        res = float('-inf')
        n = len(A)
        if n==0: return 0
        for i in range(n):
            sum = 0
            for j in range(n):
                sum += j*A[(i+j)%n]
            res = max(res, sum)
        return res

Math trick

class Solution(object):
    def maxRotateFunction(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        size = len(A)
        sums = sum(A)
        summ = sum( x*n for x, n in enumerate(A))
        ans = summ
        for i in range(0, len(A)-1):
            summ -= sums - size*A[i]
            ans = max(ans, summ)
        return ans