396-RotateFunction.go

package main

// 396. Rotate Function
// You are given an integer array nums of length n.
// Assume arrk to be an array obtained by rotating nums by k positions clock-wise. 
// We define the rotation function F on nums as follow:
//     F(k) = 0 * arrk[0] + 1 * arrk[1] + ... + (n - 1) * arrk[n - 1].
//     Return the maximum value of F(0), F(1), ..., F(n-1).

// The test cases are generated so that the answer fits in a 32-bit integer.

// Example 1:
// Input: nums = [4,3,2,6]
// Output: 26
// Explanation:
// 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
// So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.

// Example 2:
// Input: nums = [100]
// Output: 0
 
// Constraints:
//     n == nums.length
//     1 <= n <= 10^5
//     -100 <= nums[i] <= 100

import "fmt"

func maxRotateFunction(nums []int) int {
    n, sum, res := len(nums), 0, 0
    for i, num := range nums {
        sum += num
        res += i*num
    }
    last := res
    for k := 1; k <= n; k++ {
        cur := last + sum - n * nums[n-k]
        if cur > res {
            res = cur
        }
        last = cur
    }
    return res
}

func main() {
    // Example 1:
    // Input: nums = [4,3,2,6]
    // Output: 26
    // Explanation:
    // 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
    // So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.
    fmt.Println(maxRotateFunction([]int{4,3,2,6})) // 26
    // Example 2:
    // Input: nums = [100]
    // Output: 0
    fmt.Println(maxRotateFunction([]int{100})) // 0
}