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Problem · Array

Maximum Weighted Sum After Left Rotations

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Problem statement

You are given a non-empty integer array nums of length n.

For an array a, define its weighted sum as a[0] * 1 + a[1] * 2 + ... + a[n - 1] * n.

Consider the original array and every array obtained by left-rotating nums. Return the maximum weighted sum among all n rotations.

Function

maximumWeightedLeftRotation(nums: int[]) → long

Examples

Example 1

nums = [3,2,1]return = 13

The rotations have weighted sums 10 for [3,2,1], 13 for [2,1,3], and 13 for [1,3,2]. The maximum is 13.

Example 2

nums = [8,3,1,2]return = 43

The left rotation [3,1,2,8] has weighted sum 3 + 2 + 6 + 32 = 43, which is the maximum.

Example 3

nums = [-5]return = -5

A length-one array has only its original rotation.

Constraints

  • 1 <= nums.length <= 200000
  • -2147483648 <= nums[i] <= 2147483647
  • Every rotation's weighted sum fits in a signed 64-bit integer.

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public long maximumWeightedLeftRotation(int[] nums) {
    // write your code here
}
nums[3,2,1]
expected13
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