rotate-function.js

// Given an array of integers A and let n to be its length.
//
//
//
// Assume Bk to be an array obtained by rotating the array A k positions clock-wise, we define a "rotation function" F on A as follow:
//
//
//
// F(k) = 0 * Bk[0] + 1 * Bk[1] + ... + (n-1) * Bk[n-1].
//
// Calculate the maximum value of F(0), F(1), ..., F(n-1). 
//
//
// Note:
// n is guaranteed to be less than 105.
//
//
// Example:
//
// A = [4, 3, 2, 6]
//
// 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.


/**
 * @param {number[]} A
 * @return {number}
 */
var maxRotateFunction = function(A) {
    if(A.length===0) return 0;

    var res = [],
       n = A.length,
       sum=0,
       f=0;
      
    for(var i=0;i<n;i++){
          sum += A[i];
          f += i*A[i];
    }
    
    res[0] = f;
    for (var j = 1; j < n; j++) {
        res[j] = res[j-1] + sum - n*A[n-j];
    }
    return Math.max(...res);
};